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Annual Review of Fluid Mechanics is a peer-reviewed scientific journal covering research on fluid mechanics. It is published once a year by Annual Reviews and the editors are Parviz Moin and Howard Stone. As of 2023, Annual Review of Fluid Mechanics is being published as open access, under the Subscribe to Open model.
As of 2024, Journal Citation Reports gives the journal a 2023 impact factor of 25.4, ranking it first out of 40 journals in "Physics, Fluids and Plasmas" and first out of 170 journals in the category "Mechanics".
== History ==
The Annual Review of Fluid Mechanics was first published in 1969 by the nonprofit publisher Annual Reviews. Its inaugural editor was William R. Sears. Taking after the Annual Review of Biochemistry, each volume typically begins with a prefatory chapter in which a notable scientist in the field reflects on their career and accomplishments. As of 2020, it was published both in print and electronically. Some of its articles are available online in advance of the volume's publication date.
== Scope and indexing ==
Annual Review of Fluid Mechanics defines its scope as covering significant developments in the field of fluid mechanics, including its history and foundations, non-newtonian fluids, rheology, incompressible and compressible flow, plasma flow, flow stability, multiphase flow, heat mixture and transport, control of fluid flow, combustion, turbulence, shock waves, and explosions. It is abstracted and indexed in Scopus, Science Citation Index Expanded, PASCAL, Inspec, GEOBASE, and Academic Search, among others.
== Editorial processes ==
The Annual Review of Fluid Mechanics is helmed by the editor or the co-editors. The editor is assisted by the editorial committee, which includes associate editors, regular members, and occasionally guest editors. Guest members participate at the invitation of the editor, and serve terms of one year. All other members of the editorial committee are appointed by the Annual Reviews board of directors and serve five-year terms. The editorial committee determines which topics should be included in each volume and solicits reviews from qualified authors. Unsolicited manuscripts are not accepted. Peer review of accepted manuscripts is undertaken by the editorial committee.
=== Editors of volumes ===
Dates indicate publication years in which someone was credited as a lead editor or co-editor of a journal volume. The planning process for a volume begins well before the volume appears, so appointment to the position of lead editor generally occurred prior to the first year shown here. An editor who has retired or died may be credited as a lead editor of a volume that they helped to plan, even if it is published after their retirement or death.
William R. Sears (1969)
Milton Van Dyke, Walter G. Vincenti, and John V. Wehausen (1970–1976)
Van Dyke, Wehausen, and John L. Lumley (1977–1986)
Van Dyke, Lumley, and Helen L. Reed (1987–2000)
Lumley, Reed, and Stephen H. Davis (2001)
Lumley, Davis, and Parviz Moin (2002)
Davis and Moin (2003–2021)
Moin and Howard A. Stone (2021-2025)
Stone and Jonathan B. Freund (2025-)
=== Current editorial committee ===
As of 2025, the editorial committee consists of the co-editors and the following members:
As of 2022, the editorial committe's members were:
== See also ==
List of fluid mechanics journals
== References == | Wikipedia/Annual_Review_of_Fluid_Mechanics |
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation.
The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy–Weisbach friction factor, friction factor, resistance coefficient, or flow coefficient.
== Historical background ==
The Darcy-Weisbach equation, combined with the Moody chart for calculating head losses in pipes, is traditionally attributed to Henry Darcy, Julius Weisbach, and Lewis Ferry Moody. However, the development of these formulas and charts also involved other scientists and engineers over its historical development. Generally, the Bernoulli's equation would provide the head losses but in terms of quantities not known a priori, such as pressure. Therefore, empirical relationships were sought to correlate the head loss with quantities like pipe diameter and fluid velocity.
Julius Weisbach was certainly not the first to introduce a formula correlating the length and diameter of a pipe to the square of the fluid velocity. Antoine Chézy (1718-1798), in fact, had published a formula in 1770 that, although referring to open channels (i.e., not under pressure), was formally identical to the one Weisbach would later introduce, provided it was reformulated in terms of the hydraulic radius. However, Chézy's formula was lost until 1800, when Gaspard de Prony (a former student of his) published an account describing his results. It is likely that Weisbach was aware of Chézy's formula through Prony's publications.
Weisbach's formula was proposed in 1845 in the form we still use today:
Δ
H
=
f
⋅
L
V
2
2
g
D
{\displaystyle \Delta H=f\cdot {LV^{2} \over {2gD}}}
where:
Δ
H
{\displaystyle \Delta H}
: head loss.
L
{\displaystyle L}
: length of the pipe.
D
{\displaystyle D}
: diameter of the pipe.
V
{\displaystyle V}
: velocity of the fluid.
g
{\displaystyle g}
: acceleration due to gravity.
However, the friction factor f was expressed by Weisbach through the following empirical formula:
f
=
α
+
β
V
{\displaystyle f=\alpha +{\beta \over {\sqrt {V}}}}
with
α
{\displaystyle \alpha }
and
β
{\displaystyle \beta }
depending on the diameter and the type of pipe wall.
Weisbach's work was published in the United States of America in 1848 and soon became well known there. In contrast, it did not initially gain much traction in France, where Prony equation, which had a polynomial form in terms of velocity (often approximated by the square of the velocity), continued to be used. Beyond the historical developments, Weisbach's formula had the objective merit of adhering to dimensional analysis, resulting in a dimensionless friction factor f. The complexity of f, dependent on the mechanics of the boundary layer and the flow regime (laminar, transitional, or turbulent), tended to obscure its dependence on the quantities in Weisbach's formula, leading many researchers to derive irrational and dimensionally inconsistent empirical formulas. It was understood not long after Weisbach's work that the friction factor f depended on the flow regime and was independent of the Reynolds number (and thus the velocity) only in the case of rough pipes in a fully turbulent flow regime (Prandtl-von Kármán equation).
== Pressure-loss equation ==
In a cylindrical pipe of uniform diameter D, flowing full, the pressure loss due to viscous effects Δp is proportional to length L and can be characterized by the Darcy–Weisbach equation:
Δ
p
L
=
f
D
⋅
ρ
2
⋅
⟨
v
⟩
2
D
H
,
{\displaystyle {\frac {\Delta p}{L}}=f_{\mathrm {D} }\cdot {\frac {\rho }{2}}\cdot {\frac {{\langle v\rangle }^{2}}{D_{H}}},}
where the pressure loss per unit length Δp/L (SI units: Pa/m) is a function of:
ρ
{\displaystyle \rho }
, the density of the fluid (kg/m3);
D
H
{\displaystyle D_{H}}
, the hydraulic diameter of the pipe (for a pipe of circular section, this equals D; otherwise DH = 4A/P for a pipe of cross-sectional area A and perimeter P) (m);
⟨
v
⟩
{\displaystyle \langle v\rangle }
, the mean flow velocity, experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted area (m/s);
f
D
{\displaystyle f_{\mathrm {D} }}
, the Darcy friction factor (also called flow coefficient λ).
For laminar flow in a circular pipe of diameter
D
c
{\displaystyle D_{c}}
, the friction factor is inversely proportional to the Reynolds number alone (fD = 64/Re) which itself can be expressed in terms of easily measured or published physical quantities (see section below). Making this substitution the Darcy–Weisbach equation is rewritten as
Δ
p
L
=
128
π
⋅
μ
Q
D
c
4
,
{\displaystyle {\frac {\Delta p}{L}}={\frac {128}{\pi }}\cdot {\frac {\mu Q}{D_{c}^{4}}},}
where
μ is the dynamic viscosity of the fluid (Pa·s = N·s/m2 = kg/(m·s));
Q is the volumetric flow rate, used here to measure flow instead of mean velocity according to Q = π/4Dc2<v> (m3/s).
Note that this laminar form of Darcy–Weisbach is equivalent to the Hagen–Poiseuille equation, which is analytically derived from the Navier–Stokes equations.
== Head-loss formula ==
The head loss Δh (or hf) expresses the pressure loss due to friction in terms of the equivalent height of a column of the working fluid, so the pressure drop is
Δ
p
=
ρ
g
Δ
h
,
{\displaystyle \Delta p=\rho g\,\Delta h,}
where:
Δh = The head loss due to pipe friction over the given length of pipe (SI units: m);
g = The local acceleration due to gravity (m/s2).
It is useful to present head loss per length of pipe (dimensionless):
S
=
Δ
h
L
=
1
ρ
g
⋅
Δ
p
L
,
{\displaystyle S={\frac {\Delta h}{L}}={\frac {1}{\rho g}}\cdot {\frac {\Delta p}{L}},}
where L is the pipe length (m).
Therefore, the Darcy–Weisbach equation can also be written in terms of head loss:
S
=
f
D
⋅
1
2
g
⋅
⟨
v
⟩
2
D
.
{\displaystyle S=f_{\text{D}}\cdot {\frac {1}{2g}}\cdot {\frac {{\langle v\rangle }^{2}}{D}}.}
=== In terms of volumetric flow ===
The relationship between mean flow velocity <v> and volumetric flow rate Q is
Q
=
A
⋅
⟨
v
⟩
,
{\displaystyle Q=A\cdot \langle v\rangle ,}
where:
Q = The volumetric flow (m3/s),
A = The cross-sectional wetted area (m2).
In a full-flowing, circular pipe of diameter
D
c
{\displaystyle D_{c}}
,
Q
=
π
4
D
c
2
⟨
v
⟩
.
{\displaystyle Q={\frac {\pi }{4}}D_{c}^{2}\langle v\rangle .}
Then the Darcy–Weisbach equation in terms of Q is
S
=
f
D
⋅
8
π
2
g
⋅
Q
2
D
c
5
.
{\displaystyle S=f_{\text{D}}\cdot {\frac {8}{\pi ^{2}g}}\cdot {\frac {Q^{2}}{D_{c}^{5}}}.}
== Shear-stress form ==
The mean wall shear stress τ in a pipe or open channel is expressed in terms of the Darcy–Weisbach friction factor as
τ
=
1
8
f
D
ρ
⟨
v
⟩
2
.
{\displaystyle \tau ={\frac {1}{8}}f_{\text{D}}\rho {\langle v\rangle }^{2}.}
The wall shear stress has the SI unit of pascals (Pa).
== Darcy friction factor ==
The friction factor fD is not a constant: it depends on such things as the characteristics of the pipe (diameter D and roughness height ε), the characteristics of the fluid (its kinematic viscosity ν [nu]), and the velocity of the fluid flow ⟨v⟩. It has been measured to high accuracy within certain flow regimes and may be evaluated by the use of various empirical relations, or it may be read from published charts. These charts are often referred to as Moody diagrams, after L. F. Moody, and hence the factor itself is sometimes erroneously called the Moody friction factor. It is also sometimes called the Blasius friction factor, after the approximate formula he proposed.
Figure 1 shows the value of fD as measured by experimenters for many different fluids, over a wide range of Reynolds numbers, and for pipes of various roughness heights. There are three broad regimes of fluid flow encountered in these data: laminar, critical, and turbulent.
=== Laminar regime ===
For laminar (smooth) flows, it is a consequence of Poiseuille's law (which stems from an exact classical solution for the fluid flow) that
f
D
=
64
R
e
,
{\displaystyle f_{\mathrm {D} }={\frac {64}{\mathrm {Re} }},}
where Re is the Reynolds number
R
e
=
ρ
μ
⟨
v
⟩
D
=
⟨
v
⟩
D
ν
,
{\displaystyle \mathrm {Re} ={\frac {\rho }{\mu }}\langle v\rangle D={\frac {\langle v\rangle D}{\nu }},}
and where μ is the viscosity of the fluid and
ν
=
μ
ρ
{\displaystyle \nu ={\frac {\mu }{\rho }}}
is known as the kinematic viscosity. In this expression for Reynolds number, the characteristic length D is taken to be the hydraulic diameter of the pipe, which, for a cylindrical pipe flowing full, equals the inside diameter. In Figures 1 and 2 of friction factor versus Reynolds number, the regime Re < 2000 demonstrates laminar flow; the friction factor is well represented by the above equation.
In effect, the friction loss in the laminar regime is more accurately characterized as being proportional to flow velocity, rather than proportional to the square of that velocity: one could regard the Darcy–Weisbach equation as not truly applicable in the laminar flow regime.
In laminar flow, friction loss arises from the transfer of momentum from the fluid in the center of the flow to the pipe wall via the viscosity of the fluid; no vortices are present in the flow. Note that the friction loss is insensitive to the pipe roughness height ε: the flow velocity in the neighborhood of the pipe wall is zero.
=== Critical regime ===
For Reynolds numbers in the range 2000 < Re < 4000, the flow is unsteady (varies grossly with time) and varies from one section of the pipe to another (is not "fully developed"). The flow involves the incipient formation of vortices; it is not well understood.
=== Turbulent regime ===
For Reynolds number greater than 4000, the flow is turbulent; the resistance to flow follows the Darcy–Weisbach equation: it is proportional to the square of the mean flow velocity. Over a domain of many orders of magnitude of Re (4000 < Re < 108), the friction factor varies less than one order of magnitude (0.006 < fD < 0.06). Within the turbulent flow regime, the nature of the flow can be further divided into a regime where the pipe wall is effectively smooth, and one where its roughness height is salient.
==== Smooth-pipe regime ====
When the pipe surface is smooth (the "smooth pipe" curve in Figure 2), the friction factor's variation with Re can be modeled by the Kármán–Prandtl resistance equation for turbulent flow in smooth pipes with the parameters suitably adjusted
1
f
D
=
1.930
log
(
R
e
f
D
)
−
0.537.
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=1.930\log \left(\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}\right)-0.537.}
The numbers 1.930 and 0.537 are phenomenological; these specific values provide a fairly good fit to the data. The product Re√fD (called the "friction Reynolds number") can be considered, like the Reynolds number, to be a (dimensionless) parameter of the flow: at fixed values of Re√fD, the friction factor is also fixed.
In the Kármán–Prandtl resistance equation, fD can be expressed in closed form as an analytic function of Re through the use of the Lambert W function:
1
f
D
=
1.930
ln
(
10
)
W
(
10
−
0.537
1.930
ln
(
10
)
1.930
R
e
)
=
0.838
W
(
0.629
R
e
)
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}={\frac {1.930}{\ln(10)}}W\left(10^{\frac {-0.537}{1.930}}{\frac {\ln(10)}{1.930}}\mathrm {Re} \right)=0.838\ W(0.629\ \mathrm {Re} )}
In this flow regime, many small vortices are responsible for the transfer of momentum between the bulk of the fluid to the pipe wall. As the friction Reynolds number Re√fD increases, the profile of the fluid velocity approaches the wall asymptotically, thereby transferring more momentum to the pipe wall, as modeled in Blasius boundary layer theory.
==== Rough-pipe regime ====
When the pipe surface's roughness height ε is significant (typically at high Reynolds number), the friction factor departs from the smooth pipe curve, ultimately approaching an asymptotic value ("rough pipe" regime). In this regime, the resistance to flow varies according to the square of the mean flow velocity and is insensitive to Reynolds number. Here, it is useful to employ yet another dimensionless parameter of the flow, the roughness Reynolds number
R
∗
=
1
8
(
R
e
f
D
)
ε
D
{\displaystyle R_{*}={\frac {1}{\sqrt {8}}}\left(\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}\,\right){\frac {\varepsilon }{D}}}
where the roughness height ε is scaled to the pipe diameter D.
It is illustrative to plot the roughness function B:
B
(
R
∗
)
=
1
1.930
f
D
+
log
(
1.90
8
⋅
ε
D
)
{\displaystyle B(R_{*})={\frac {1}{1.930{\sqrt {f_{\mathrm {D} }}}}}+\log \left({\frac {1.90}{\sqrt {8}}}\cdot {\frac {\varepsilon }{D}}\right)}
Figure 3 shows B versus R∗ for the rough pipe data of Nikuradse, Shockling, and Langelandsvik.
In this view, the data at different roughness ratio ε/D fall together when plotted against R∗, demonstrating scaling in the variable R∗. The following features are present:
When ε = 0, then R∗ is identically zero: flow is always in the smooth pipe regime. The data for these points lie to the left extreme of the abscissa and are not within the frame of the graph.
When R∗ < 5, the data lie on the line B(R∗) = R∗; flow is in the smooth pipe regime.
When R∗ > 100, the data asymptotically approach a horizontal line; they are independent of Re, fD, and ε/D.
The intermediate range of 5 < R∗ < 100 constitutes a transition from one behavior to the other. The data depart from the line B(R∗) = R∗ very slowly, reach a maximum near R∗ = 10, then fall to a constant value.
Afzal's fit to these data in the transition from smooth pipe flow to rough pipe flow employs an exponential expression in R∗ that ensures proper behavior for 1 < R∗ < 50 (the transition from the smooth pipe regime to the rough pipe regime):
1
f
D
=
−
2
log
(
2.51
R
e
f
D
(
1
+
0.305
R
∗
exp
−
11
R
∗
)
)
,
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=-2\log \left({\frac {2.51}{\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}}}\left(1+0.305R_{*}\exp {\frac {-11}{R_{*}}}\right)\right),}
and
1
f
D
=
−
1.930
log
(
1.90
R
e
f
D
(
1
+
0.34
R
∗
exp
−
11
R
∗
)
)
,
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=-1.930\log \left({\frac {1.90}{\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}}}\left(1+0.34R_{*}\exp {\frac {-11}{R_{*}}}\right)\right),}
This function shares the same values for its term in common with the Kármán–Prandtl resistance equation, plus one parameter 0.305 or 0.34 to fit the asymptotic behavior for R∗ → ∞ along with one further parameter, 11, to govern the transition from smooth to rough flow. It is exhibited in Figure 3.
The friction factor for another analogous roughness becomes
:
1
f
D
=
−
2.0
log
10
(
2.51
R
e
f
D
{
1
+
0.305
R
∗
(
1
−
exp
−
R
∗
26
)
}
)
,
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=-2.0\,\log _{10}\left({\frac {2.51}{\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}}}\left\{1+0.305R_{*}\;\left(1-\exp {\frac {-R_{*}}{26}}\right)\right\}\right),}
and
:
1
f
D
=
−
1.93
log
10
(
1.91
R
e
f
D
{
1
+
0.34
R
∗
(
1
−
exp
−
R
∗
26
)
}
)
,
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=-1.93\,\log _{10}\left({\frac {1.91}{\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}}}\left\{1+0.34R_{*}\;\left(1-\exp {\frac {-R_{*}}{26}}\right)\right\}\right),}
This function shares the same values for its term in common with the Kármán–Prandtl resistance equation, plus one parameter 0.305 or 0.34 to fit the asymptotic behavior for R∗ → ∞ along with one further parameter, 26, to govern the transition from smooth to rough flow.
The Colebrook–White relation fits the friction factor with a function of the form
1
f
D
=
−
2.00
log
(
2.51
R
e
f
D
(
1
+
R
∗
3.3
)
)
.
{\displaystyle {\frac {1}{\sqrt {f_{\mathrm {D} }}}}=-2.00\log \left({\frac {2.51}{\mathrm {Re} {\sqrt {f_{\mathrm {D} }}}}}\left(1+{\frac {R_{*}}{3.3}}\right)\right).}
This relation has the correct behavior at extreme values of R∗, as shown by the labeled curve in Figure 3: when R∗ is small, it is consistent with smooth pipe flow, when large, it is consistent with rough pipe flow. However its performance in the transitional domain overestimates the friction factor by a substantial margin. Colebrook acknowledges the discrepancy with Nikuradze's data but argues that his relation is consistent with the measurements on commercial pipes. Indeed, such pipes are very different from those carefully prepared by Nikuradse: their surfaces are characterized by many different roughness heights and random spatial distribution of roughness points, while those of Nikuradse have surfaces with uniform roughness height, with the points extremely closely packed.
=== Calculating the friction factor from its parametrization ===
For turbulent flow, methods for finding the friction factor fD include using a diagram, such as the Moody chart, or solving equations such as the Colebrook–White equation (upon which the Moody chart is based), or the Swamee–Jain equation. While the Colebrook–White relation is, in the general case, an iterative method, the Swamee–Jain equation allows fD to be found directly for full flow in a circular pipe.
==== Direct calculation when friction loss S is known ====
In typical engineering applications, there will be a set of given or known quantities. The acceleration of gravity g and the kinematic viscosity of the fluid ν are known, as are the diameter of the pipe D and its roughness height ε. If as well the head loss per unit length S is a known quantity, then the friction factor fD can be calculated directly from the chosen fitting function. Solving the Darcy–Weisbach equation for √fD,
f
D
=
2
g
S
D
⟨
v
⟩
{\displaystyle {\sqrt {f_{\mathrm {D} }}}={\frac {\sqrt {2gSD}}{\langle v\rangle }}}
we can now express Re√fD:
R
e
f
D
=
1
ν
2
g
S
D
3
{\displaystyle \mathrm {Re} {\sqrt {f_{\mathrm {D} }}}={\frac {1}{\nu }}{\sqrt {2g}}{\sqrt {S}}{\sqrt {D^{3}}}}
Expressing the roughness Reynolds number R∗,
R
∗
=
ε
D
⋅
R
e
f
D
⋅
1
8
=
1
2
g
ν
ε
S
D
{\displaystyle {\begin{aligned}R_{*}&={\frac {\varepsilon }{D}}\cdot \mathrm {Re} {\sqrt {f_{\mathrm {D} }}}\cdot {\frac {1}{\sqrt {8}}}\\&={\frac {1}{2}}{\frac {\sqrt {g}}{\nu }}\varepsilon {\sqrt {S}}{\sqrt {D}}\end{aligned}}}
we have the two parameters needed to substitute into the Colebrook–White relation, or any other function, for the friction factor fD, the flow velocity ⟨v⟩, and the volumetric flow rate Q.
=== Confusion with the Fanning friction factor ===
The Darcy–Weisbach friction factor fD is 4 times larger than the Fanning friction factor f, so attention must be paid to note which one of these is meant in any "friction factor" chart or equation being used. Of the two, the Darcy–Weisbach factor fD is more commonly used by civil and mechanical engineers, and the Fanning factor f by chemical engineers, but care should be taken to identify the correct factor regardless of the source of the chart or formula.
Note that
Δ
p
=
f
D
⋅
L
D
⋅
ρ
⟨
v
⟩
2
2
=
f
⋅
L
D
⋅
2
ρ
⟨
v
⟩
2
{\displaystyle \Delta p=f_{\mathrm {D} }\cdot {\frac {L}{D}}\cdot {\frac {\rho {\langle v\rangle }^{2}}{2}}=f\cdot {\frac {L}{D}}\cdot {2\rho {\langle v\rangle }^{2}}}
Most charts or tables indicate the type of friction factor, or at least provide the formula for the friction factor with laminar flow. If the formula for laminar flow is f = 16/Re, it is the Fanning factor f, and if the formula for laminar flow is fD = 64/Re, it is the Darcy–Weisbach factor fD.
Which friction factor is plotted in a Moody diagram may be determined by inspection if the publisher did not include the formula described above:
Observe the value of the friction factor for laminar flow at a Reynolds number of 1000.
If the value of the friction factor is 0.064, then the Darcy friction factor is plotted in the Moody diagram. Note that the nonzero digits in 0.064 are the numerator in the formula for the laminar Darcy friction factor: fD = 64/Re.
If the value of the friction factor is 0.016, then the Fanning friction factor is plotted in the Moody diagram. Note that the nonzero digits in 0.016 are the numerator in the formula for the laminar Fanning friction factor: f = 16/Re.
The procedure above is similar for any available Reynolds number that is an integer power of ten. It is not necessary to remember the value 1000 for this procedure—only that an integer power of ten is of interest for this purpose.
== History ==
Historically this equation arose as a variant on the Prony equation; this variant was developed by Henry Darcy of France, and further refined into the form used today by Julius Weisbach of Saxony in 1845. Initially, data on the variation of fD with velocity was lacking, so the Darcy–Weisbach equation was outperformed at first by the empirical Prony equation in many cases. In later years it was eschewed in many special-case situations in favor of a variety of empirical equations valid only for certain flow regimes, notably the Hazen–Williams equation or the Manning equation, most of which were significantly easier to use in calculations. However, since the advent of the calculator, ease of calculation is no longer a major issue, and so the Darcy–Weisbach equation's generality has made it the preferred one.
== Derivation by dimensional analysis ==
Away from the ends of the pipe, the characteristics of the flow are independent of the position along the pipe. The key quantities are then the pressure drop along the pipe per unit length, Δp/L, and the volumetric flow rate. The flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid).
Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q. We also know that pressure must be proportional to the length of the pipe between the two points L as the pressure drop per unit length is a constant. To turn the relationship into a proportionality coefficient of dimensionless quantity, we can divide by the hydraulic diameter of the pipe, D, which is also constant along the pipe. Therefore,
Δ
p
∝
L
D
q
=
L
D
⋅
ρ
2
⋅
⟨
v
⟩
2
{\displaystyle \Delta p\propto {\frac {L}{D}}q={\frac {L}{D}}\cdot {\frac {\rho }{2}}\cdot {\langle v\rangle }^{2}}
The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π, the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter).
Note that the dynamic pressure is not the kinetic energy of the fluid per unit volume, for the following reasons. Even in the case of laminar flow, where all the flow lines are parallel to the length of the pipe, the velocity of the fluid on the inner surface of the pipe is zero due to viscosity, and the velocity in the center of the pipe must therefore be larger than the average velocity obtained by dividing the volumetric flow rate by the wet area. The average kinetic energy then involves the root mean-square velocity, which always exceeds the mean velocity. In the case of turbulent flow, the fluid acquires random velocity components in all directions, including perpendicular to the length of the pipe, and thus turbulence contributes to the kinetic energy per unit volume but not to the average lengthwise velocity of the fluid.
== Practical application ==
In a hydraulic engineering application, it is typical for the volumetric flow Q within a pipe (that is, its productivity) and the head loss per unit length S (the concomitant power consumption) to be the critical important factors. The practical consequence is that, for a fixed volumetric flow rate Q, head loss S decreases with the inverse fifth power of the pipe diameter, D. Doubling the diameter of a pipe of a given schedule (say, ANSI schedule 40) roughly doubles the amount of material required per unit length and thus its installed cost. Meanwhile, the head loss is decreased by a factor of 32 (about a 97% reduction). Thus the energy consumed in moving a given volumetric flow of the fluid is cut down dramatically for a modest increase in capital cost.
== Advantages ==
The Darcy-Weisbach's accuracy and universal applicability makes it the ideal formula for flow in pipes. The advantages of the equation are as follows:
It is based on fundamentals.
It is dimensionally consistent.
It is useful for any fluid, including oil, gas, brine, and sludges.
It can be derived analytically in the laminar flow region.
It is useful in the transition region between laminar flow and fully developed turbulent flow.
The friction factor variation is well documented.
== See also ==
Bernoulli's principle
Darcy friction factor formulae
Euler number
Friction loss
Hazen–Williams equation
Hagen–Poiseuille equation
Water pipe
== Notes ==
== References ==
18. Afzal, Noor (2013) "Roughness effects of commercial steel pipe in turbulent flow:
Universal scaling". Canadian Journal of Civil Engineering 40, 188-193.
== Further reading ==
De Nevers (1970). Fluid Mechanics. Addison–Wesley. ISBN 0-201-01497-1.
Shah, R. K.; London, A. L. (1978). "Laminar Flow Forced Convection in Ducts". Supplement 1 to Advances in Heat Transfer. New York: Academic.
Rohsenhow, W. M.; Hartnett, J. P.; Ganić, E. N. (1985). Handbook of Heat Transfer Fundamentals (2nd ed.). McGraw–Hill Book Company. ISBN 0-07-053554-X.
Glenn O. Brown (2002). "The History of the Darcy-Weisbach Equation for Pipe Flow Resistance". researchgate.net.
== External links ==
The History of the Darcy–Weisbach Equation Archived 2011-07-20 at the Wayback Machine
Darcy–Weisbach equation calculator
Pipe pressure drop calculator Archived 2019-07-13 at the Wayback Machine for single phase flows.
Pipe pressure drop calculator for two phase flows. Archived 2019-07-13 at the Wayback Machine
Open source pipe pressure drop calculator.
Web application with pressure drop calculations for pipes and ducts
ThermoTurb – A web application for thermal and turbulent flow analysis | Wikipedia/Darcy–Weisbach_equation |
In applied mathematics, the Kelvin functions berν(x) and beiν(x) are the real and imaginary parts, respectively, of
J
ν
(
x
e
3
π
i
4
)
,
{\displaystyle J_{\nu }\left(xe^{\frac {3\pi i}{4}}\right),\,}
where x is real, and Jν(z), is the νth order Bessel function of the first kind. Similarly, the functions kerν(x) and keiν(x) are the real and imaginary parts, respectively, of
K
ν
(
x
e
π
i
4
)
,
{\displaystyle K_{\nu }\left(xe^{\frac {\pi i}{4}}\right),\,}
where Kν(z) is the νth order modified Bessel function of the second kind.
These functions are named after William Thomson, 1st Baron Kelvin.
While the Kelvin functions are defined as the real and imaginary parts of Bessel functions with x taken to be real, the functions can be analytically continued for complex arguments xeiφ, 0 ≤ φ < 2π. With the exception of bern(x) and bein(x) for integral n, the Kelvin functions have a branch point at x = 0.
Below, Γ(z) is the gamma function and ψ(z) is the digamma function.
== ber(x) ==
For integers n, bern(x) has the series expansion
b
e
r
n
(
x
)
=
(
x
2
)
n
∑
k
≥
0
cos
[
(
3
n
4
+
k
2
)
π
]
k
!
Γ
(
n
+
k
+
1
)
(
x
2
4
)
k
,
{\displaystyle \mathrm {ber} _{n}(x)=\left({\frac {x}{2}}\right)^{n}\sum _{k\geq 0}{\frac {\cos \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]}{k!\Gamma (n+k+1)}}\left({\frac {x^{2}}{4}}\right)^{k},}
where Γ(z) is the gamma function. The special case ber0(x), commonly denoted as just ber(x), has the series expansion
b
e
r
(
x
)
=
1
+
∑
k
≥
1
(
−
1
)
k
[
(
2
k
)
!
]
2
(
x
2
)
4
k
{\displaystyle \mathrm {ber} (x)=1+\sum _{k\geq 1}{\frac {(-1)^{k}}{[(2k)!]^{2}}}\left({\frac {x}{2}}\right)^{4k}}
and asymptotic series
b
e
r
(
x
)
∼
e
x
2
2
π
x
(
f
1
(
x
)
cos
α
+
g
1
(
x
)
sin
α
)
−
k
e
i
(
x
)
π
{\displaystyle \mathrm {ber} (x)\sim {\frac {e^{\frac {x}{\sqrt {2}}}}{\sqrt {2\pi x}}}\left(f_{1}(x)\cos \alpha +g_{1}(x)\sin \alpha \right)-{\frac {\mathrm {kei} (x)}{\pi }}}
,
where
α
=
x
2
−
π
8
,
{\displaystyle \alpha ={\frac {x}{\sqrt {2}}}-{\frac {\pi }{8}},}
f
1
(
x
)
=
1
+
∑
k
≥
1
cos
(
k
π
/
4
)
k
!
(
8
x
)
k
∏
l
=
1
k
(
2
l
−
1
)
2
{\displaystyle f_{1}(x)=1+\sum _{k\geq 1}{\frac {\cos(k\pi /4)}{k!(8x)^{k}}}\prod _{l=1}^{k}(2l-1)^{2}}
g
1
(
x
)
=
∑
k
≥
1
sin
(
k
π
/
4
)
k
!
(
8
x
)
k
∏
l
=
1
k
(
2
l
−
1
)
2
.
{\displaystyle g_{1}(x)=\sum _{k\geq 1}{\frac {\sin(k\pi /4)}{k!(8x)^{k}}}\prod _{l=1}^{k}(2l-1)^{2}.}
== bei(x) ==
For integers n, bein(x) has the series expansion
b
e
i
n
(
x
)
=
(
x
2
)
n
∑
k
≥
0
sin
[
(
3
n
4
+
k
2
)
π
]
k
!
Γ
(
n
+
k
+
1
)
(
x
2
4
)
k
.
{\displaystyle \mathrm {bei} _{n}(x)=\left({\frac {x}{2}}\right)^{n}\sum _{k\geq 0}{\frac {\sin \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]}{k!\Gamma (n+k+1)}}\left({\frac {x^{2}}{4}}\right)^{k}.}
The special case bei0(x), commonly denoted as just bei(x), has the series expansion
b
e
i
(
x
)
=
∑
k
≥
0
(
−
1
)
k
[
(
2
k
+
1
)
!
]
2
(
x
2
)
4
k
+
2
{\displaystyle \mathrm {bei} (x)=\sum _{k\geq 0}{\frac {(-1)^{k}}{[(2k+1)!]^{2}}}\left({\frac {x}{2}}\right)^{4k+2}}
and asymptotic series
b
e
i
(
x
)
∼
e
x
2
2
π
x
[
f
1
(
x
)
sin
α
−
g
1
(
x
)
cos
α
]
−
k
e
r
(
x
)
π
,
{\displaystyle \mathrm {bei} (x)\sim {\frac {e^{\frac {x}{\sqrt {2}}}}{\sqrt {2\pi x}}}[f_{1}(x)\sin \alpha -g_{1}(x)\cos \alpha ]-{\frac {\mathrm {ker} (x)}{\pi }},}
where α,
f
1
(
x
)
{\displaystyle f_{1}(x)}
, and
g
1
(
x
)
{\displaystyle g_{1}(x)}
are defined as for ber(x).
== ker(x) ==
For integers n, kern(x) has the (complicated) series expansion
k
e
r
n
(
x
)
=
−
ln
(
x
2
)
b
e
r
n
(
x
)
+
π
4
b
e
i
n
(
x
)
+
1
2
(
x
2
)
−
n
∑
k
=
0
n
−
1
cos
[
(
3
n
4
+
k
2
)
π
]
(
n
−
k
−
1
)
!
k
!
(
x
2
4
)
k
+
1
2
(
x
2
)
n
∑
k
≥
0
cos
[
(
3
n
4
+
k
2
)
π
]
ψ
(
k
+
1
)
+
ψ
(
n
+
k
+
1
)
k
!
(
n
+
k
)
!
(
x
2
4
)
k
.
{\displaystyle {\begin{aligned}&\mathrm {ker} _{n}(x)=-\ln \left({\frac {x}{2}}\right)\mathrm {ber} _{n}(x)+{\frac {\pi }{4}}\mathrm {bei} _{n}(x)\\&+{\frac {1}{2}}\left({\frac {x}{2}}\right)^{-n}\sum _{k=0}^{n-1}\cos \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]{\frac {(n-k-1)!}{k!}}\left({\frac {x^{2}}{4}}\right)^{k}\\&+{\frac {1}{2}}\left({\frac {x}{2}}\right)^{n}\sum _{k\geq 0}\cos \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]{\frac {\psi (k+1)+\psi (n+k+1)}{k!(n+k)!}}\left({\frac {x^{2}}{4}}\right)^{k}.\end{aligned}}}
The special case ker0(x), commonly denoted as just ker(x), has the series expansion
k
e
r
(
x
)
=
−
ln
(
x
2
)
b
e
r
(
x
)
+
π
4
b
e
i
(
x
)
+
∑
k
≥
0
(
−
1
)
k
ψ
(
2
k
+
1
)
[
(
2
k
)
!
]
2
(
x
2
4
)
2
k
{\displaystyle \mathrm {ker} (x)=-\ln \left({\frac {x}{2}}\right)\mathrm {ber} (x)+{\frac {\pi }{4}}\mathrm {bei} (x)+\sum _{k\geq 0}(-1)^{k}{\frac {\psi (2k+1)}{[(2k)!]^{2}}}\left({\frac {x^{2}}{4}}\right)^{2k}}
and the asymptotic series
k
e
r
(
x
)
∼
π
2
x
e
−
x
2
[
f
2
(
x
)
cos
β
+
g
2
(
x
)
sin
β
]
,
{\displaystyle \mathrm {ker} (x)\sim {\sqrt {\frac {\pi }{2x}}}e^{-{\frac {x}{\sqrt {2}}}}[f_{2}(x)\cos \beta +g_{2}(x)\sin \beta ],}
where
β
=
x
2
+
π
8
,
{\displaystyle \beta ={\frac {x}{\sqrt {2}}}+{\frac {\pi }{8}},}
f
2
(
x
)
=
1
+
∑
k
≥
1
(
−
1
)
k
cos
(
k
π
/
4
)
k
!
(
8
x
)
k
∏
l
=
1
k
(
2
l
−
1
)
2
{\displaystyle f_{2}(x)=1+\sum _{k\geq 1}(-1)^{k}{\frac {\cos(k\pi /4)}{k!(8x)^{k}}}\prod _{l=1}^{k}(2l-1)^{2}}
g
2
(
x
)
=
∑
k
≥
1
(
−
1
)
k
sin
(
k
π
/
4
)
k
!
(
8
x
)
k
∏
l
=
1
k
(
2
l
−
1
)
2
.
{\displaystyle g_{2}(x)=\sum _{k\geq 1}(-1)^{k}{\frac {\sin(k\pi /4)}{k!(8x)^{k}}}\prod _{l=1}^{k}(2l-1)^{2}.}
== kei(x) ==
For integer n, kein(x) has the series expansion
k
e
i
n
(
x
)
=
−
ln
(
x
2
)
b
e
i
n
(
x
)
−
π
4
b
e
r
n
(
x
)
−
1
2
(
x
2
)
−
n
∑
k
=
0
n
−
1
sin
[
(
3
n
4
+
k
2
)
π
]
(
n
−
k
−
1
)
!
k
!
(
x
2
4
)
k
+
1
2
(
x
2
)
n
∑
k
≥
0
sin
[
(
3
n
4
+
k
2
)
π
]
ψ
(
k
+
1
)
+
ψ
(
n
+
k
+
1
)
k
!
(
n
+
k
)
!
(
x
2
4
)
k
.
{\displaystyle {\begin{aligned}&\mathrm {kei} _{n}(x)=-\ln \left({\frac {x}{2}}\right)\mathrm {bei} _{n}(x)-{\frac {\pi }{4}}\mathrm {ber} _{n}(x)\\&-{\frac {1}{2}}\left({\frac {x}{2}}\right)^{-n}\sum _{k=0}^{n-1}\sin \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]{\frac {(n-k-1)!}{k!}}\left({\frac {x^{2}}{4}}\right)^{k}\\&+{\frac {1}{2}}\left({\frac {x}{2}}\right)^{n}\sum _{k\geq 0}\sin \left[\left({\frac {3n}{4}}+{\frac {k}{2}}\right)\pi \right]{\frac {\psi (k+1)+\psi (n+k+1)}{k!(n+k)!}}\left({\frac {x^{2}}{4}}\right)^{k}.\end{aligned}}}
The special case kei0(x), commonly denoted as just kei(x), has the series expansion
k
e
i
(
x
)
=
−
ln
(
x
2
)
b
e
i
(
x
)
−
π
4
b
e
r
(
x
)
+
∑
k
≥
0
(
−
1
)
k
ψ
(
2
k
+
2
)
[
(
2
k
+
1
)
!
]
2
(
x
2
4
)
2
k
+
1
{\displaystyle \mathrm {kei} (x)=-\ln \left({\frac {x}{2}}\right)\mathrm {bei} (x)-{\frac {\pi }{4}}\mathrm {ber} (x)+\sum _{k\geq 0}(-1)^{k}{\frac {\psi (2k+2)}{[(2k+1)!]^{2}}}\left({\frac {x^{2}}{4}}\right)^{2k+1}}
and the asymptotic series
k
e
i
(
x
)
∼
−
π
2
x
e
−
x
2
[
f
2
(
x
)
sin
β
+
g
2
(
x
)
cos
β
]
,
{\displaystyle \mathrm {kei} (x)\sim -{\sqrt {\frac {\pi }{2x}}}e^{-{\frac {x}{\sqrt {2}}}}[f_{2}(x)\sin \beta +g_{2}(x)\cos \beta ],}
where β, f2(x), and g2(x) are defined as for ker(x).
== See also ==
Bessel function
== References ==
Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 9". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 379. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
Olver, F. W. J.; Maximon, L. C. (2010), "Bessel functions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
== External links ==
Weisstein, Eric W. "Kelvin Functions." From MathWorld—A Wolfram Web Resource. [1]
GPL-licensed C/C++ source code for calculating Kelvin functions at codecogs.com: [2] | Wikipedia/Kelvin_functions |
The Woods Hole Oceanographic Institution (WHOI, acronym pronounced HOO-ee) is a private, nonprofit research and higher education facility dedicated to the study of marine science and engineering.
Established in 1930 in Woods Hole, Massachusetts, it is the largest independent oceanographic research institution in the U.S., with staff and students numbering about 1,000.
== Constitution ==
The institution is organized into six departments, the Cooperative Institute for Climate and Ocean Research, and a marine policy center. Its shore-based facilities are located in the village of Woods Hole, Massachusetts, United States and a mile and a half away on the Quissett Campus. The bulk of the institution's funding comes from grants and contracts from the National Science Foundation and other government agencies, augmented by foundations and private donations.
WHOI scientists, engineers, and students collaborate to develop theories, test ideas, build seagoing instruments, and collect data in diverse marine environments. Ships operated by WHOI carry research scientists throughout the world's oceans. The WHOI fleet includes two large research vessels (Atlantis and Neil Armstrong), the coastal craft Tioga, small research craft such as the dive-operation work boat Echo, the deep-diving human-occupied submersible Alvin, the tethered, remotely operated vehicle Jason/Medea, and autonomous underwater vehicles such as the REMUS and SeaBED.
WHOI offers graduate and post-doctoral studies in marine science. There are several fellowship and training programs, and graduate degrees are awarded through a joint program with the Massachusetts Institute of Technology (MIT). WHOI is accredited by the New England Association of Schools and Colleges. WHOI also offers public outreach programs and informal education through its Exhibit Center and summer tours. The institution has a volunteer program and a membership program, WHOI Associate.
WHOI shares a library, the MBLWHOI Library, with the Marine Biological Laboratory. The MBLWHOI Library holds print and electronic collections in the biological, biomedical, ecological, and oceanographic sciences. The library also conducts digitization, data preservation and informatics projects.
On October 1, 2020, Peter B. de Menocal became the institution's eleventh president and director.
== History ==
In 1927, a National Academy of Sciences committee concluded that it was time to "consider the share of the United States of America in a worldwide program of oceanographic research." The committee's recommendation for establishing a permanent independent research laboratory on the East Coast to "prosecute oceanography in all its branches" led to the founding in 1930 of the Woods Hole Oceanographic Institution.
A $2.5 million grant from the Rockefeller Foundation supported the summer work of a dozen scientists, construction of a laboratory building and commissioning of a research vessel, the 142-foot (43 m) ketch Atlantis, whose profile still forms the institution's logo.
WHOI grew substantially to support significant defense-related research during World War II, and later began a steady growth in staff, research fleet, and scientific stature. From 1950 to 1956, the director was Dr. Edward "Iceberg" Smith, an Arctic explorer, oceanographer and retired Coast Guard rear admiral.
In 1977 the institution appointed oceanographer John Steele as director, and he served until his retirement in 1989.
On 1 September 1985, a joint French-American expedition led by Jean-Louis Michel of IFREMER and Robert Ballard of the Woods Hole Oceanographic Institution identified the location of the wreck of RMS Titanic, which sank off the coast of Newfoundland 15 April 1912.
On 3 April 2011, within a week of resuming of the search operation for Air France Flight 447, a team led by WHOI, operating full ocean depth autonomous underwater vehicles (AUVs) owned by the Waitt Institute discovered, by means of sidescan sonar, a large portion of debris field from flight AF447.
In March 2017 the institution effected an open-access policy to make its research publicly accessible online.
In 2019, iDefense reported that China's hackers had launched cyberattacks on dozens of academic institutions in an attempt to gain information on technology being developed for the United States Navy. Some of the targets included the Woods Hole Oceanographic Institution. The attacks had been underway since at least April 2017.
In August 2024, institution researchers are scheduled, pending approval from the U.S. Environmental Protection Agency, to conduct a $10 million ocean alkalinity enhancement experiment partially funded by the National Oceanic and Atmospheric Administration that will release 6,000 gallons of a liquid solution of sodium hydroxide into the ocean 10 miles south of Martha's Vineyard in an attempt to remove 20 metric tons of carbon dioxide from the atmosphere.
== Military contracting ==
The Woods Hole Oceanographic Institution develops technology for the United States Navy, including ocean battlespace sensors, unmanned undersea vehicles, and acoustic navigation and communication systems for operations in the Arctic. The institution is also working on Project Sundance for the Office of Naval Research.
== Awards issued ==
=== B. H. Ketchum Award ===
The B. H. Ketchum award, established in 1983, is presented for innovative coastal/nearshore research and is named in honor of oceanographer Bostwick H. "Buck" Ketchum. The award is administered by the WHOI Coastal Ocean Institute and Rinehart Coastal Research Center.
Recipients:
2017: Don Anderson, Woods Hole Oceanographic Institution
2015: Candace Oviatt, Graduate School of Oceanography, University of Rhode Island
2010: James E. Cloern, United States Geological Survey
2007: Richard Garvine, University of Delaware
2003: John Farrington, Woods Hole Oceanographic Institution
2003: Nancy Rabalais, Louisiana Universities Marine Consortium
1999: Willard Moore, University of South Carolina
1996: Ronald Smith, Loughbororugh University
1995: Christopher Martens, University of North Carolina
1992: Scott Nixon, University of Rhode Island
1990: Daniel Lynch, Dartmouth College
1989: William Boicourt, University of Maryland
1988: Alasdair McIntyre, Aberdeen University (Emeritus)
1986: John S. Allen, Oregon State University
1985: Thomas H. Pearson, Oban, Argyll, Scotland
1985: Michael Moore, Plymouth, UK
1984: Edward D. Goldberg, Scripps Institution of Oceanography
=== Henry Bryant Bigelow Medal in Oceanography ===
The Henry Bryant Bigelow Medal in Oceanography was established in 1960 in honor of the first WHOI Director, biologist Henry Bryant Bigelow.
Recipients: Source:
2004 David M. Karl (Professor of Oceanography, University of Hawaii) – for "his contributions to microbial oceanography, especially the development and leadership of long-term, integrated studies of chemical, physical, and biological variations in oceanic environments."
1996 Bill J. Jenkins (Senior Scientist, Marine Chemistry & Geochemistry, WHOI) – for "his outstanding contributions to the development of the tritium-helium dating technique and its application to problems in ocean physics and biology and geochemistry, as well as his exceptional character and selfless dedication to the advance of science at WHOI."
1993 Robert Weller (Senior Scientist, Physical Oceanography; Director, CICOR; WHOI)
1992 Alice Louise Alldredge (University of California, Santa Barbara) and Mary Wilcox Silver (University of California, Santa Cruz) – for "their creative contributions to biological and chemical oceanography, particularly in demonstrating the importance of 'marine snow' as a major contributor to the vertical flux of particulate matter throughout the worlds oceans."
1988 Hans Thomas Rossby (University of Rhode Island) and Douglas Chester Webb (Webb Research) – for "Their creative contributions to ocean technology and oceanography, particularly in the development of the SOFAR float and advancing out knowledge of Lagrangian ocean dynamics."
1984 Arnold L. Gordon (Columbia University) for his "dedication in completing the Antarctic Circumpolar Survey"
1980 Holger W. Jannasch (WHOI) – for his "creative contributions to marine microbiology by providing us with an understanding of the fundamentals of microbial processes in the sea and the dynamics of oceanic food chains."
1979 Wolfgang Helmut Berger (Scripps Institution of Oceanography, University of California at San Diego) – for his "creative contributions to paleoceanography by opening the doors of perception on the controlling factors governing carbonate sedimentation in the oceans, and for providing us with a unifying conceptual model for interpreting the geological evolution of ocean basins."
1974 Henry M. Stommel (WHOI)
1970 Frederick J. Vine (WHOI) – In recognition of his "imaginative and sound contributions to man's understanding of the formative processes active within the earth."
1966 Columbus O'D. Iselin (WHOI)
1964 Bruce C. Heezen (WHOI)
1962 John C. Swallow (WHOI)
1960 Henry Bryant Bigelow
== Scientists ==
Over the years, WHOI scientists have made seminal discoveries about the ocean that have contributed to improving US commerce, health, national security, and quality of life. They have received awards and recognition from scientific societies such as The Oceanography Society, the American Geophysical Union, Association for the Sciences of Limnology and Oceanography, and several others.
Notable scientists include:
Amy Bower, senior scientist, blind oceanographer
Stan Hart, scientist emeritus, William Bowie Medal recipient
Elizabeth Kujawinski, American oceanographer, Woods Hole Senior Scientist
Loral O'Hara, research engineer, NASA astronaut
Christopher Reddy, senior scientist, oil spill researcher
Alfred C. Redfield (1890 – 1983), oceanographer. Discovered the Redfield ratio and served as WHOI senior biologist from 1930 to 1942, and associate director between 1942 and 1957. The Institute's Redfield Laboratory was named in his honor in 1971.
Mary Sears, senior scientist in marine biology who served at the Naval Hydrographic Office in World War II compiling oceanographic intelligence for the Pacific Campaign
Heidi Sosik, senior scientist in Biology, inventor
Klaus Hasselmann, Doherty Professor at Woods Hole Oceanographic Institution from 1970 to 1972
Robert Ballard, oceanographer, retired US Navy officer, explorer and maritime archeologist who found the wreck of the Titanic
Lisan Yu – known for serving on the Earth Science Advisory Committee (ESAC), and on the Federal Advisory Committee Act (FACA) committee of NASA.
== Research fleet ==
=== Ships ===
WHOI operates several research vessels, owned by the United States Navy, the National Science Foundation, or the institution:
R/V Atlantis (AGOR-25) – 274 feet long, mothership of the Alvin submarine
R/V Tioga (WHOI-owned) – 60 feet long
R/V Neil Armstrong (AGOR-27) – 238 feet long
WHOI formerly operated R/V Knorr, which was replaced by R/V Neil Armstrong in 2015.
=== Small boat fleet ===
WHOI operates many small boats used in inland harbors, ponds, rivers, and coastal bays. All are owned by the institution itself.
Motorboat Echo – 29 feet long (mainly used as a work boat to support dive operations, also the newest small research craft at WHOI)
Motorboat Mytilus – 24 feet long (mainly used in water too shallow for larger craft and is a versatile coastal research boat)
Motorboat Calanus – 21 feet long (mainly used in local water bodies such as Great Harbor, Vineyard Sound and Buzzards Bay)
Motorboat Limulus – 13 feet long (mainly used to shuttle equipment to larger craft and as a work platform for near-shore research tasks)
Rowboat Orzrus – 12 feet long (mainly used in harbors and ponds where motor craft are not permitted)
=== Underwater vehicles ===
WHOI also has developed numerous underwater autonomous and remotely operated vehicles for research:
Alvin (DSV-2) – human-occupied vehicle, the institution's most well-known equipment
Deepsea Challenger – human-occupied vehicle designed, field-tested, and later donated to the WHOI by Canadian film director James Cameron
Jason – a remotely operated vehicle (ROV)
Sentry – an autonomous underwater vehicle (AUV) and successor to ABE
Nereus – A hybrid remotely operated vehicle (HROV); lost on 5/10/14 while exploring the Kermadec Trench.
Remus – Remote Environment Monitoring UnitS, a family of autonomous underwater vehicles
Mesobot - an autonomous underwater vehicle built to track sea life in the mesopelagic zone
SeaBED – an autonomous underwater vehicle optimized for high-resolution seafloor imaging
Spray Glider – a remotely operated vehicle, used to collect data about the salinity, temperature, etc. about an area
Slocum Glider – another remotely operated vehicle, with functions similar to the functions of the Spray Glider
CAMPER – a towed vehicle used to collect samples from the seabed of the Arctic Ocean
Seasoar – a submarine towed by a ship
TowCam – a submarine with cameras that is towed by a ship along the ocean floor to take photographs
Video Plankton Recorder – a submarine with microscopic camera systems, towed along by a ship to take videos of plankton
Autonomous Benthic Explorer (ABE) – an autonomous underwater vehicle
== See also ==
52-hertz whale
Liquid Jungle Lab, a tropical research station in Pacific Panama operated by WHOI
Marine Biological Laboratory, a neighboring but administratively unrelated institution in Woods Hole
The Institute of Marine and Coastal Sciences, a smaller oceanographic facility located at Rutgers University in New Jersey
Harbor Branch Oceanographic Institute, a similar research facility associated with Florida Atlantic University and located in Fort Pierce, Florida
Hatfield Marine Science Center, a similar research facility associated with the Oregon State University and located in Newport, Oregon
Hopkins Marine Station, a similar research facility run by Stanford University in Monterey, California
Moss Landing Marine Laboratories, a multi-campus marine research consortium of the California State University System
Scripps Institution of Oceanography, a similar research facility associated with the University of California, San Diego and located in La Jolla, California
Ocean Frontier Institute, an ocean research centre located in Halifax, Canada
== References ==
== External links ==
Woods Hole Oceanographic Institution | Wikipedia/Woods_Hole_Oceanographic_Institution |
Scripps Institution of Oceanography (SIO) is the center for oceanography and Earth science at the University of California, San Diego. Its main campus is located in La Jolla, with additional facilities in Point Loma.
Founded in 1903 and incorporated into the University of California system in 1912, the institution has since broadened its research focus to encompass the physics, chemistry, geology, biology, and climate of the Earth. The institution awards the Nierenberg Prize annually to recognize researchers with exceptional contributions to science in public interest.
== History ==
=== Founding ===
Scripps Institution of Oceanography can trace its beginnings back to William Ritter, a biologist originally from Wisconsin. In 1891, Ritter was offered a job teaching biology at the University of California, Berkeley and married Mary Bennett. Their honeymoon and subsequent biological studies took them to San Diego, where Ritter met a local physician and naturalist, Fred Baker, who would later encourage him to build a marine biological laboratory in San Diego.
Ritter searched for eleven years for an appropriate place for a permanent marine biological laboratory. He spent summers at various places along the coast with students. His goal was frustrated by lack of money and lack of an appropriate place. During this time, research was being conducted at the boathouse of Hotel del Coronado on San Diego Bay.
In 1903, Ritter was introduced to newspaper magnate E. W. Scripps. Together with Scripps' half-sister Ellen Browning Scripps and Baker, they formed the Marine Biological Association of San Diego with Ritter as the Scientific Director. They fully funded the institution for its first decade. E. W. Scripps gave the biological association the use of his yacht, the Loma, in 1904 and served as the first research vessel in the history of the institution. In 1905, they moved to a small laboratory in La Jolla Cove until they arranged for the purchase of a 170-acre (0.69 km2) site in La Jolla, north of San Diego. The land was purchased for $1,000 at a public auction from the city of San Diego (the same site where the SIO main campus is today). However, construction cost estimates for a permeant building were around $50,000. Funding was secured through E. W. and E. B. Scripps, and the first permanent building (today known as the Old Scripps Building) was constructed in 1910.
The Marine Biological Association's first seafaring vessel, the Loma, would run aground in Point Loma in 1906 and prompted the search for a new one. With funds secured from Ellen Browning Scripps, the association was able to have a ship built by Lawrence Jensen strictly for oceanographic research - among the first for an American nongovernmental institution. The new vessel was acquired on April 21st, 1907 and was named the Alexander Agassiz after the Harvard biologist who had visited in 1905. The 85-foot Alexander Agassiz, a sailing vessel with twin gasoline engines, served the institution for ten years.
In 1912, the Biological Association became incorporated into the University of California and was renamed the Scripps Institution for Biological Research.
The first iteration of Scripps Pier, along with other buildings, was approved for construction in 1913, but was only completed in 1916 due to delays related to World War I. In 1915, the first building devoted solely to an aquarium was built on the Scripps campus. The small, wooden structure contained 19 tanks ranging in size from 96 to 228 U.S. gallons (360 to 860 L). The oceanographic museum was located in a nearby building. Since the pier was completed in 1916, measurements have been taken daily. The modern Scripps Pier was built as a replacement for the 1916 structure in 1988.
The institution's name changed to Scripps Institution of Oceanography (often shortened to just SIO) in October of 1925 to recognize the growing faculty's widened range of studies.
Easter Ellen Cupp would be the first woman to earn a Ph.D. in oceanography from SIO in 1934, studying diatoms under Wynfred Allen. She would stay with Scripps until 1939.
In 1935, SIO director T. Wayland Vaughan was the first Scripps member to be awarded the Alexander Agassiz Medal by the National Academy of Sciences. Harald Sverdrup would be awarded the medal 3 years later, beginning a long history of Scripps oceanographers being awarded the prize (Johnson in 1959, Revelle in 1963, and many more).
In November, 1936, the research vessel Scripps was sunk when there was an explosion in the galley, killing the cook and injuring the captain. The sinking of the Scripps left SIO without a research vessel, so SIO director Sverdrup approached the UC president Robert Gordon Sproul and Bob Scripps (son of E.W and Ellen) to acquire a new one. They found Bob's pleasure yacht, Novia Del Mar, ill-fitting for the science roles performed by the Scripps, and purchased a different yacht from actor Lewis Stone in April 1937. The Serena was rechristened E. W. Scripps and was presented to SIO in December 1937. The E. W. Scripps would be quintessential for Sverdrup to build datasets supporting simple theories of ocean circulation, including the Sverdrup balance.
=== Wartime ===
When World War II broke out Scripps created the University of California Division of War Research (UCDWR) in Point Loma, focusing on acoustics and waves to support the US Navy. Collaborative research between the UCDWR and the Navy led to the discovery of the deep scattering layer, a region from 300 - 500 m deep filled with organisms. The UCDWR would continue to research sound beacons and sonar until being absorbed into the Navy Electronics Laboratory and Scripps Marine Physical Laboratory between 1945 and 1948.
With Harald Sverdrup as the SIO director, recent graduate student Walter Munk was recalled from the army and together they were tasked with aiding Allied amphibious landings off the coast of Africa. The goal was to predict coastal surf and sea state for Allied landings in Africa, though their model was also applied to the Allied landings in Normandy, Sicily, and in the Pacific. SIO's UCDWR would train over 200 American and British military officers on swell forecasting techniques throughout the war. Though Sverdrup was initially intending on holding the position of SIO director for only 3 years until 1939, Nazi occupation of Norway prolonged his assumption of the role until 1948. Though Sverdrup's family became US citizens during the war, he struggled with Navy clearance which gave him an awkward relationship to the projects he was overseeing.
Wartime changed the funding dynamic for Scripps. Prior to the war, the only federal support for SIO came from the Navy seeking to protect the hulls of their ships. Threatened by German submarines, concepts within physical oceanography were researched for submarine warfare. By summer 1942, Roger Revelle was appointed as a Navy liaison for oceanography and the sonar head of the Navy Bureau of Ships. UCDWR research led to rapid development of bathythermographs, as well as the understanding of the thermocline and benthic sediments in the context of underwater warfare. Research on biofouling organisms were led by Dennis Fox and Claude ZoBell, with the goal to develop biological deterrents for seaplanes and vessels.
It was during 1942 that Sverdrup, along with Martin Johnson and Richard Fleming, completed the first comprehensive textbook of oceanography, The Oceans. The textbook was considered a first of its kind and of such military importance that it was forbidden from distribution outside of the United States.
SIO's first scientific diver was biologist Cheng Kwai Tseng, who used equipment to collect algae off the coast of San Diego in 1944. Tseng took red algae samples of Gelidium cartilagineum and cultured them to reduce the US dependence on Japanese agar, which was important to hospitals at the time.
=== The Golden Age of Oceanography ===
Following the war, Roger Revelle continued to act as a liaison for oceanographers and was consulted during Operation Crossroads in 1945. He noted significant difficulties during the project, stemming from the difficulty of civilian research to access naval research vessels and naval bureaucracy. To remedy this, Revelle championed joint research of the newly-established Office of Naval Research (ONR), the US Hydrographic Office, and Navy Bureau of Ships and Scripps was receiving around $900,000 annually from federal funding.
The Navy bestowed the operation of a number of vessels to SIO ushering in a "Golden Age" of oceanographic research and discoveries. Between 1947 and 1949 three post-war vessels were acquired and modified for scientific research: The Crest, Paolina-T, and Horizon. These vessels, combined with the overlap of expertise from the ONR in 1946, provided additional resources for ocean exploration. The three new vessels were put to work on the new Marine Life Research Program in 1950 (now CalCOFI), which sought to investigate the collapse of the California sardine population. In doing so, approximately 670,000 square miles (1,700,000 km2) of ocean would need to be surveyed.
When Aqua-Lung was made available in the US in 1948, UCLA graduates Conrad Limbaugh and Andy Rechnitzer were able to convince Boyd W. Walker, their marine biology advisor at the time, to purchase one. Together, they introduced the Aqua-Lung to SIO in 1950 (with Limbaugh studying under Carl Hubbs) and began the Scripps Diving Program. Roger Revelle took over the director role at SIO in 1951 from Carl Eckart and, following a diving fatality at La Jolla in 1950, requested that Limbaugh develop a scuba training program for SIO, which debuted in 1951 and was heavily influenced by practices of the U.S. Navy's Underwater Demolition Team. It was also during this time that Hugh Bradner, a physicist at UC Berkeley, became an advisor at SIO and developed the wetsuit in 1952. Bradner would go on to become a professor at SIO's Institute of Geophysics and Planetary Physics in 1961. The SIO Diving Program would continue to innovate and expand up to more than 160 affiliated divers in 2015.
The Vaughan Aquarium-Museum opened at the University's Charter Day in March 1951 to replace the prior aquarium, which had been in a consistent state of disrepair since at least 1925. Named to honor former institution director T. Wayland Vaughan, museum curator Percy S. Barnhart planned a replacement up until his retirement in 1946, passing the project along to Sam Hinton. Hinton would go on to collect specimens aboard the E. W. Scripps until the building was completed and occupied in 1950. While nearly three times the size of the previous aquarium, the building also housed the director's offices on the second floor and the preserved specimens in the basement. The seawater supply from Scripps Pier was renovated in 1964 to increase capacity and improve filtration.
In 1959, an additional administration building was constructed next to the original 1910 building, named the "New Scripps" building. Campus construction expanded with the completion of the Sumner Auditorium and Sverdrup Hall in 1960.
Scripps Institution of Oceanography director Revelle spearheaded the formation of the University of California, San Diego in 1960 on a bluff overlooking the Scripps Institution, with SIO acting as the nucleus. It was during the 1960s that SIO led the development of the Deep-Tow system, with oceanographer Fred Spiess as the lead of the Marine Physical Laboratory. The purpose was to map the oceans, most notably being used in Project FAMOUS between 1971 and 1974.
In 1965, Scripps began leasing 6 acres (2.4 ha) of land in Point Loma to tie up research vessels, including the RP Flip (launched in 1962), from the US Navy. The navy gave this land to Scripps in 1975 and the facility was named the Nimitz Marine Facility (or MarFac) after Chester Nimitz.
Also in 1965, Scripps assisted the Navy with the SEALAB project, where divers dwelled in a submersible habitat at 205 ft (62 m) in the nearby Scripps Canyon for 15 days at a time.
On October 25, 1973, California Sea Grant became a college (National Sea Grant College Program) administered by Scripps Institution of Oceanography at the University of California, San Diego.
From March to May of 1979, SIO directed the RISE project and oversaw the 1979 discovery of black smoker hydrothermal vents at the East Pacific Rise.
=== International projects and modern history ===
The Old Scripps Building, designed by Irving Gill, was declared a National Historic Landmark in 1982. Architect Barton Myers designed the current Scripps Building for the Institution of Oceanography in 1998.
In 2007, the family and wife of late Roger Revelle donated 2.5 million dollars toward the Roger Revelle Chair endowed position, which Shang-Ping Xie now holds.
In 2014, SIO received a grant from the U.S. Department of Transportation to test the use of biofuels on one of its ships, the Robert Gordon Sproul. The vessel operated from September 2014 to December 2015 on 100% biofuels which reduced nitrous oxide emissions, but increased particle emissions. However, the fuel source provided a proof of concept that research operations could be completed using biofuels rather than conventional diesel.
Also, 2014 was the first year of cruises for the international GO-SHIP program, a repeat hydrography program focusing on straight transects across major ocean basins and a follow-up to the World Ocean Circulation Experiment, which ran until 2002. Scripps, along with NOAA as the sole American members of the science committee, has overseen and advised many expeditions to contribute to the global data set.
In 2019, Scripps received $1.2 million of philanthropic funding for a 42-foot (13 m) research vessel, named after John Beyster and his wife Betty. Though the vessel was secured in spring of 2019, plans for the vessel's acquisition began in 2017.
From January to May of 2019, SIO directed a study at Imperial Beach to collect samples of sewage pollution from the Tijuana River and found elevated levels of harmful bacteria and aerosols. In 2024, Scripps was added to a task force including researchers from San Diego State University and regional doctors to better understand health impacts from the pollution. While collecting samples later in 2024, the task force had to evacuate the area due to elevated levels of toxic gases.
A campus report was published in 2022 describing campus lab, office, and storage spaces and found that women make up 26% of research scientists at SIO, yet occupy 17% of the space. The report highlighted that emeritus faculty on campus are 86% male and hold nearly 25% of all space at SIO.
==== 2023 graduate protests ====
In May 2023, the Scripps campus in La Jolla opened the Ted and Jean Scripps Marine Conservation and Technology Facility. The building required the razing of three older buildings originally constructed in 1963 and reinforcing of the nearby hillside in 2014. A month later, the building was vandalized in a protest against low graduate student wages. In June 2023, two SIO students and one recent graduate were arrested at their homes by University of California Police and held in custody overnight. The University alleged $12,000 in damages related to this incident. Union leadership in UAW 2865 and 5810, the local union chapters representing the arrested workers, accuse the University of California of retaliation and reneging on the contracts signed at the conclusion of the 2022 UC academic workers' strike. On July 10, 2023, hundreds of protesters gathered at San Diego's Central Courthouse to protest the arrests, however in a written statement the San Diego District Attorney's office said the arraignment would not move forward because the case had not been submitted to its office for review. However, university officials have up to three years to file charges. On July 18, 2023, UCPD obtained a warrant and searched a fourth student's house for evidence of chalk or union affiliation in relation to the May 30 incident.
== Campus ==
=== Main campus ===
The SIO main campus is located in La Jolla, situated between La Jolla Shores and Black's Beach. La Jolla Shores Drive provides access to greater La Jolla to the south, while continuing north through campus to the main UC San Diego campus.
Mass transit service to the main campus is handled by MTS line 30 (coming every 15 minutes) and UC San Diego's SIO bus route (every 10 minutes). Route 30 has stops exclusively on La Jolla Shores Drive, heading north to UTC Transit Center and south to Old Town Transit Center. The SIO route offers more comprehensive coverage of campus grounds, starting in Pawka Green, then La Jolla Shores Drive, Shellback Way, Birch Aquarium, and then north to Gilman Transit Center at UCSD's main campus.
Three sites on campus (the Seaside Forum, the Martin Johnson House, and Birch Aquarium) are available to the general public for rental.
==== Biological Grade ====
Biological Grade is the street running North to South parallel to La Jolla Shores drive, connecting a number of laboratories, libraries, and research halls. It was built between 1910 and 1912 with the original Old Scripps Building and was part of the main highway between San Diego and Los Angeles. As the campus grew, La Jolla Shores Drive was constructed to reroute through traffic for automobiles. Biological Grade connects to Shellback Way on the other side of La Jolla Shores Drive via the La Jolla Shores Pedestrian Bridge (also known as Scripps Crossing), erected in 1993.
The Scripps Coastal Meander trail (part of the California Coastal Trail) starts at the northern end of Biological Grade and connects to other trails, eventually terminating at Black's Beach.
==== Pawka Green and Naga Way ====
South of Biological Grade is the Pawka Green, named after Steven Pawka. The bordering Naga Way separates the labs from Biological Grade from the halls around Pawka Green, which are more oriented towards administration and instruction. The Naga Way street is named after the Naga Expedition, which took place in 1959 studying the Gulf of Thailand and South China Sea.
==== Shellback Way ====
Shellback Way connects a series of halls and labs on the east side of La Jolla Shores Drive, with greater emphasis on atmospheric science and fisheries. It connects to Biological Grade via the La Jolla Shores Pedestrian Bridge. Shellback Way is named after the Shellback Expedition which studied the deep Pacific off the coast of Peru, running from May to August 1952.
==== Downwind Way ====
Downwind Way connects La Jolla Shores Drive to Expedition Way, providing access to the rest of UCSD. This section of campus includes campus storage and facilities, Birch Aquarium, and Deep Sea Drilling Program. It is named after the first of three International Geophisical Year cruises, taking place from October 1957 to February 1958.
==== Campus flora and fauna ====
The main campus in La Jolla is situated next to the San Diego-Scripps Coastal Marine Conservation Area as well as Torrey Pines State Natural Reserve. The coastal chaparral biome has many plants also seen in the Torrey Pines reserve, such as lemonade berry, wild cucumber, coast spice bush, California sunflower, California buckwheat, and bladderpod.
Seabirds are a common sight near the campus, particularly seagulls, pelicans, plovers, egrets, and osprey. Peregrine falcons are also known to nest in the bluffs at the north end of campus.
===== Marine life =====
Marine life from La Jolla Shores to Black's Beach can be seen very shallow, making snorkeling a popular activity. Marine organisms include leopard sharks, Garibaldi, shovelnose guitarfish, round stingrays, and thornback rays. Due to the high concentration of stingrays, locals practice the "stingray shuffle" to help avoid being stung.
Connecting to La Jolla Canyon, Scripps Canyon is a popular spot for divers and marine research. Common fish within the canyon are species of poacher, sole, rockfish, and lizardfish.
=== Nimitz Marine Facility ===
The Nimitz Marine Facility is the home port of all SIO research vessels and is accessible by land via Rosecrans Street in Point Loma. The facility is serviced hourly by bus route 84 of the San Diego MTS, running from the Navy Base to Shelter Island and Cabrillo National Monument.
The facility borders the Point Loma Navy Base, operated by the NIWC. As of 2008, a TWIC card is required for access to the waterfront at MarFac as required by the United States Coast Guard.
Buildings at the Nimitz Marine Facility are numbered in increasing order from the waterfront approaching Rosecrans Street.
== Research programs ==
The institution's research programs encompass biological, physical, chemical, geological, and geophysical studies of the oceans and land. Scripps also studies the interaction of the oceans with both the atmospheric climate and environmental concerns on terra firma. Related to this research, Scripps offers undergraduate and graduate degrees.
Today, the Scripps staff of 1,300 includes approximately 235 faculty, 180 other scientists and some 350 graduate students, with an annual budget of more than $281 million. The institution operates a fleet of four oceanographic research vessels.
=== Research themes ===
Scripps follows a number of interdisciplinary research themes:
Climate change impacts and adaption
Resilience to hazards
Human health and the oceans
Innovative technology
Polar science
Biodiversity and conservation
National security
=== CalCOFI program ===
The California Cooperative Oceanic Fisheries Investigations (CalCOFI) program, established in 1949, is an ongoing partnership between SIO, NOAA Fisheries, and the California Department of Fish and Wildlife to study sardine population collapse and the marine environment off the coast of Southern California. Data are collected on routine research cruises and are able to be compared over many decades in a large service area.
=== The Keeling Curve ===
The Keeling Curve is the longest-running time series of atmospheric CO2, beginning in 1958. Spearheaded by Charles David Keeling, SIO established a research center in Mauna Loa, Hawaii to record atmospheric carbon dioxide levels. Since then, SIO researchers have expanded the dataset into numerous other sampling locations and analytical parameters to monitor climate change.
=== Argo program ===
The Argo program is an international effort to survey ocean temperature, salinity, and currents. The program was developed in the late 1990s and chaired by SIO's Dean Roemmich and SIO researchers helped design the SOLO and SOLO-II float designs. SIO is also involved in Argo-related programs, such as GO-BGC (biogeochemical) and SOCCOM, and hosts Argo data on the Argo Global Marine Atlas.
=== Oceanographic collections ===
SIO maintains a large collection of marine and benthic organism collections, tracing back to William Ritter's samples from 1902. When ichthyologist Carl Hubbs arrived at SIO in 1944, the collections grew rapidly and expanded by around 9,000 samples in 2014 when SIO inherited collections from UCLA's Department of Ecology. SIO also has a geological collection of thousands of ocean cores, sea dredge hauls, microfossil slides, and rock samples.
Collection samples are commonly used for instruction at SIO and for public outreach at Birch Aquarium.
== Organizational structure ==
=== Research sections ===
Scripps Oceanography is divided into three research sections, each with its own subdivisions:
Biology
Center for Marine Biotechnology & Biomedicine (CMBB)
Integrative Oceanography Division (IOD)
Marine Biology Research Division (MBRD)
Earth
Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics (IGPP)
Geosciences Research Division (GRD)
Oceans & Atmosphere
Climate, Atmospheric Science & Physical Oceanography (CASPO)
Marine Physical Laboratory (MPL)
=== Directors ===
Margaret Leinen took office as the director of Scripps Institution of Oceanography, Vice Chancellor for Marine Sciences, and Dean of the Graduate School of Marine Sciences on October 1, 2013.
List of SIO Directors
== Research vessels ==
Scripps owns and operates several research vessels and platforms:
RV Roger Revelle
RV Sally Ride
RV Robert Gordon Sproul
RV Bob and Betty Beyster
Current and previous vessels larger than 50 ft (15 m)
=== Hybrid Hydrogen Research Vessel ===
In 2021, Scripps was awarded $35 million for the development of a new coastal research vessel as a replacement for the RV Robert Gordon Sproul, in service since 1984. The proposed vessel would be 125 feet long and take 3 years to build, becoming the first hybrid-hydrogen research vessel in the UNOLS fleet and aiding in the University of California's Carbon Neutrality Initiative. Scripps chose Seattle-based architect Glosten as the ship's designer, having work experience from numerous other SIO vessels. It is expected that the research vessel will operate on hydrogen power for 75% of its operations.
== Birch Aquarium ==
Birch Aquarium, the public exploration center for the institution, features a Hall of Fishes with more than 60 tanks of Pacific fishes and invertebrates from the cold waters of the Pacific Northwest to the tropical waters of Mexico and the IndoPacific, a 13,000-gallon local shark and ray exhibit, interactive tide pools, and interactive science exhibits. In 2022, the aquarium opened a new exhibit for blue penguins.
== Notable faculty members (past and present) ==
== Notable alumni ==
== Awards by SIO ==
SIO confers a number of awards for scientific advancement or betterment of society.
== Popular culture ==
In 2014, the institution and its Keeling Curve measurement of atmospheric carbon dioxide levels were featured as a plot point in an episode of HBO's The Newsroom. In 2008, Scripps Institution of Oceanography was the subject of a category on the TV game show Jeopardy!.
== See also ==
Array Network Facility
RISE project
Scripps Research, a neighboring, but completely independent medical research institute
Monterey Bay Aquarium Research Institute, a private, non-profit oceanographic research center in Moss Landing, California
Moss Landing Marine Laboratories, a multi-campus marine research consortium of the California State University System
Hopkins Marine Station, a similar research facility run by Stanford University in Monterey, California
Hatfield Marine Science Center, a similar research facility associated with the Oregon State University and located in Newport, Oregon
Woods Hole Oceanographic Institution, a similar research facility located in Woods Hole, Massachusetts
== References ==
== Further reading ==
Scripps Institution of Oceanography; First Fifty Years Helen Raitt and Beatrice Moulton. Los Angeles : W. Ritchie Press, 1967.
Scripps Institution of Oceanography : Probing the Oceans, 1936 to 1976 Elizabeth Noble Shor. San Diego, Calif. : Tofua Press, 1978.
The Keeling Curve Turns 50
== External links ==
Official website | Wikipedia/Scripps_Institution_of_Oceanography |
Decompression theory is the study and modelling of the transfer of the inert gas component of breathing gases from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure. In all cases, the symptoms caused by decompression occur during or within a relatively short period of hours, or occasionally days, after a significant pressure reduction.
The term "decompression" derives from the reduction in ambient pressure experienced by the organism and refers to both the reduction in pressure and the process of allowing dissolved inert gases to be eliminated from the tissues during and after this reduction in pressure. The uptake of gas by the tissues is in the dissolved state, and elimination also requires the gas to be dissolved, however a sufficient reduction in ambient pressure may cause bubble formation in the tissues, which can lead to tissue damage and the symptoms known as decompression sickness, and also delays the elimination of the gas.
Decompression modeling attempts to explain and predict the mechanism of gas elimination and bubble formation within the organism during and after changes in ambient pressure, and provides mathematical models which attempt to predict acceptably low risk and reasonably practicable procedures for decompression in the field. Both deterministic and probabilistic models have been used, and are still in use.
Efficient decompression requires the diver to ascend fast enough to establish as high a decompression gradient, in as many tissues, as safely possible, without provoking the development of symptomatic bubbles. This is facilitated by the highest acceptably safe oxygen partial pressure in the breathing gas, and avoiding gas changes that could cause counterdiffusion bubble formation or growth. The development of schedules that are both safe and efficient has been complicated by the large number of variables and uncertainties, including personal variation in response under varying environmental conditions and workload.
== Physiology of decompression ==
The evidence that decompression sickness is caused by bubble formation and growth within the body tissues resulting from supersaturated dissolved gas is strong, but research results also suggest that the quantity of those bubbles alone is not enough to predict whether someone will experience symptoms of DCS.
Gas is breathed at ambient pressure, and some of this gas dissolves into the blood and other fluids. Inert gas continues to be taken up until the gas dissolved in the tissues is in a state of equilibrium with the gas in the lungs (see saturation diving), or the ambient pressure is reduced until the inert gases dissolved in the tissues are at a higher concentration than the equilibrium state, and start diffusing out again.
The absorption of gases in liquids depends on the solubility of the specific gas in the specific liquid, the concentration of gas, customarily measured by partial pressure, and temperature. In the study of decompression theory the behaviour of gases dissolved in the tissues is investigated and modeled for variations of pressure over time.
Once dissolved, distribution of the dissolved gas may be by diffusion, where there is no bulk flow of the solvent, or by perfusion where the solvent (blood) is circulated around the diver's body, where gas can diffuse to local regions of lower concentration. Given sufficient time at a specific partial pressure in the breathing gas, the concentration in the tissues will stabilise, or saturate, at a rate depending on the solubility, diffusion rate and perfusion.
If the concentration of the inert gas in the breathing gas is reduced below that of any of the tissues, there will be a tendency for gas to return from the tissues to the breathing gas. This is known as outgassing, and occurs during decompression, when the reduction in ambient pressure or a change of breathing gas reduces the partial pressure of the inert gas in the lungs.
The combined concentrations of gases in any given tissue will depend on the history of pressure and gas composition. Under equilibrium conditions, the total concentration of dissolved gases will be less than the ambient pressure, as oxygen is metabolised in the tissues, and the carbon dioxide produced is much more soluble. However, during a reduction in ambient pressure, the rate of pressure reduction may exceed the rate at which gas can be eliminated by diffusion and perfusion, and if the concentration gets too high, it may reach a stage where bubble formation can occur in the supersaturated tissues. When the pressure of gases in a bubble exceeds the combined external pressures of ambient pressure and the surface tension from the bubble - liquid interface, the bubble will grow, and this growth can cause damage to tissues. Symptoms caused by this damage are known as decompression sickness.
The actual rates of diffusion and perfusion and the solubility of gases in specific tissues are not generally known, and they vary considerably. However, mathematical models have been proposed which approximate the real situation to a greater or lesser extent, and these models are used to predict whether symptomatic bubble formation is likely to occur for a given pressure exposure profile.
Decompression involves a complex interaction of gas solubility, partial pressures and concentration gradients, diffusion, bulk transport and bubble mechanics in living tissues.
=== Dissolved phase gas dynamics ===
Solubility of gases in liquids is influenced by the nature of the solvent liquid and the solute, the temperature, pressure, and the presence of other solutes in the solvent. Diffusion is faster in smaller, lighter molecules of which helium is the extreme example. Diffusivity of helium is 2.65 times faster than nitrogen. The concentration gradient, can be used as a model for the driving mechanism of diffusion. In this context, inert gas refers to a gas which is not metabolically active. Atmospheric nitrogen (N2) is the most common example, and helium (He) is the other inert gas commonly used in breathing mixtures for divers. Atmospheric nitrogen has a partial pressure of approximately 0.78 bar at sea level. Air in the alveoli of the lungs is diluted by saturated water vapour (H2O) and carbon dioxide (CO2), a metabolic product given off by the blood, and contains less oxygen (O2) than atmospheric air as some of it is taken up by the blood for metabolic use. The resulting partial pressure of nitrogen is about 0,758 bar.
At atmospheric pressure the body tissues are therefore normally saturated with nitrogen at 0.758 bar (569 mmHg). At increased ambient pressures due to depth or habitat pressurisation, a diver's lungs are filled with breathing gas at the increased pressure, and the partial pressures of the constituent gases will be increased proportionately. The inert gases from the breathing gas in the lungs diffuse into blood in the alveolar capillaries and are distributed around the body by the systemic circulation in the process known as perfusion. Dissolved materials are transported in the blood much faster than they would be distributed by diffusion alone. From the systemic capillaries the dissolved gases diffuse through the cell membranes and into the tissues, where it may eventually reach equilibrium. The greater the blood supply to a tissue, the faster it will reach equilibrium with gas at the new partial pressure. This equilibrium is called saturation. Ingassing appears to follow a simple inverse exponential equation. The time it takes for a tissue to take up or release 50% of the difference in dissolved gas capacity at a changed partial pressure is called the half-time for that tissue and gas.
Gas remains dissolved in the tissues until the partial pressure of that gas in the lungs is reduced sufficiently to cause a concentration gradient with the blood at a lower concentration than the relevant tissues. As the concentration in the blood drops below the concentration in the adjacent tissue, the gas will diffuse out of the tissue into the blood, and will then be transported back to the lungs where it will diffuse into the lung gas and then be eliminated by exhalation. If the ambient pressure reduction is limited, this desaturation will take place in the dissolved phase, but if the ambient pressure is lowered sufficiently, bubbles may form and grow, both in blood and other supersaturated tissues. When the partial pressure of all gas dissolved in a tissue exceeds the total ambient pressure on the tissue it is supersaturated, and there is a possibility of bubble formation.
The sum of partial pressures of the gas that the diver breathes must necessarily balance with the sum of partial pressures in the lung gas. In the alveoli the gas has been humidified and has gained carbon dioxide from the venous blood. Oxygen has also diffused into the arterial blood, reducing the partial pressure of oxygen in the alveoli. As the total pressure in the alveoli must balance with the ambient pressure, this dilution results in an effective partial pressure of nitrogen of about 758 mb (569 mmHg) in air at normal atmospheric pressure. At a steady state, when the tissues have been saturated by the inert gases of the breathing mixture, metabolic processes reduce the partial pressure of the less soluble oxygen and replace it with carbon dioxide, which is considerably more soluble in water. In the cells of a typical tissue, the partial pressure of oxygen will drop, while the partial pressure of carbon dioxide will rise. The sum of these partial pressures (water, oxygen, carbon dioxide and nitrogen) is less than the total pressure of the respiratory gas. This is a significant saturation deficit, and it provides a buffer against supersaturation and a driving force for dissolving bubbles. Experiments suggest that the degree of unsaturation increases linearly with pressure for a breathing mixture of fixed composition, and decreases linearly with fraction of inert gas in the breathing mixture. As a consequence, the conditions for maximising the degree of unsaturation are a breathing gas with the lowest possible fraction of inert gas – i.e. pure oxygen, at the maximum permissible partial pressure. This saturation deficit is also referred to as inherent unsaturation, the "Oxygen window". or partial pressure vacancy.
The location of micronuclei or where bubbles initially form is not known. The incorporation of bubble formation and growth mechanisms in decompression models may make the models more biophysical and allow better extrapolation. Flow conditions and perfusion rates are dominant parameters in competition between tissue and circulation bubbles, and between multiple bubbles, for dissolved gas for bubble growth.
=== Bubble mechanics ===
Equilibrium of forces on the surface is required for a bubble to exist. The sum of the Ambient pressure and pressure due to tissue distortion, exerted on the outside of the surface, with surface tension of the liquid at the interface between the bubble and the surroundings must be balanced by the pressure on the inside of the bubble. This is the sum of the partial pressures of the gases inside due to the net diffusion of gas to and from the bubble. The force balance on the bubble may be modified by a layer of surface active molecules which can stabilise a microbubble at a size where surface tension on a clean bubble would cause it to collapse rapidly, and this surface layer may vary in permeability, so that if the bubble is sufficiently compressed it may become impermeable to diffusion. If the solvent outside the bubble is saturated or unsaturated, the partial pressure will be less than in the bubble, and the surface tension will be increasing the internal pressure in direct proportion to surface curvature, providing a pressure gradient to increase diffusion out of the bubble, effectively "squeezing the gas out of the bubble", and the smaller the bubble the faster it will get squeezed out. A gas bubble can only grow at constant pressure if the surrounding solvent is sufficiently supersaturated to overcome the surface tension or if the surface layer provides sufficient reaction to overcome surface tension. Clean bubbles that are sufficiently small will collapse due to surface tension if the supersaturation is low. Bubbles with semipermeable surfaces will either stabilise at a specific radius depending on the pressure, the composition of the surface layer, and the supersaturation, or continue to grow indefinitely, if larger than the critical radius. Bubble formation can occur in the blood or other tissues.
A solvent can carry a supersaturated load of gas in solution. Whether it will come out of solution in the bulk of the solvent to form bubbles will depend on a number of factors. Something which reduces surface tension, or adsorbs gas molecules, or locally reduces solubility of the gas, or causes a local reduction in static pressure in a fluid may result in a bubble nucleation or growth. This may include velocity changes and turbulence in fluids and local tensile loads in solids and semi-solids. Lipids and other hydrophobic surfaces may reduce surface tension (blood vessel walls may have this effect). Dehydration may reduce gas solubility in a tissue due to higher concentration of other solutes, and less solvent to hold the gas. Another theory presumes that microscopic bubble nuclei always exist in aqueous media, including living tissues. These bubble nuclei are spherical gas phases that are small enough to remain in suspension yet strong enough to resist collapse, their stability being provided by an elastic surface layer consisting of surface-active molecules which resists the effect of surface tension.
Once a micro-bubble forms it may continue to grow if the tissues are sufficiently supersaturated. As the bubble grows it may distort the surrounding tissue and cause damage to cells and pressure on nerves resulting in pain, or may block a blood vessel, cutting off blood flow and causing hypoxia in the tissues normally perfused by the vessel.
If a bubble or an object exists which collects gas molecules this collection of gas molecules may reach a size where the internal pressure exceeds the combined surface tension and external pressure and the bubble will grow. If the solvent is sufficiently supersaturated, the diffusion of gas into the bubble will exceed the rate at which it diffuses back into solution, and if this excess pressure is greater than the pressure due to surface tension the bubble will continue to grow. When a bubble grows, the surface tension decreases, and the interior pressure drops, allowing gas to diffuse in faster, and diffuse out slower, so the bubble grows or shrinks in a positive feedback situation. The growth rate is reduced as the bubble grows because the surface area increases as the square of the radius, while the volume increases as the cube of the radius. If the external pressure is reduced due to reduced hydrostatic pressure during ascent, the bubble will also grow, and conversely, an increased external pressure will cause the bubble to shrink, but may not cause it to be eliminated entirely if a compression-resistant surface layer exists.
Decompression bubbles appear to form mostly in the systemic capillaries where the gas concentration is highest, often those feeding the veins draining the active limbs. They do not generally form in the arteries provided that ambient pressure reduction is not too rapid, as arterial blood has recently had the opportunity to release excess gas into the lungs. The bubbles carried back to the heart in the veins may be transferred to the systemic circulation via a patent foramen ovale in divers with this septal defect, after which there is a risk of occlusion of capillaries in whichever part of the body they end up in.
Bubbles which are carried back to the heart in the veins will pass into the right side of the heart, and from there they will normally enter the pulmonary circulation and pass through or be trapped in the capillaries of the lungs, which are around the alveoli and very near to the respiratory gas, where the gas will diffuse from the bubbles though the capillary and alveolar walls into the gas in the lung. If the number of lung capillaries blocked by these bubbles is relatively small, the diver will not display symptoms, and no tissue will be damaged (lung tissues are adequately oxygenated by diffusion). The bubbles which are small enough to pass through the lung capillaries may be small enough to be dissolved due to a combination of surface tension and diffusion to a lowered concentration in the surrounding blood, though the Varying Permeability Model nucleation theory implies that most bubbles passing through the pulmonary circulation will lose enough gas to pass through the capillaries and return to the systemic circulation as recycled but stable nuclei. Bubbles which form within the tissues must be eliminated in situ by diffusion, which implies a suitable concentration gradient.
=== Isobaric counterdiffusion (ICD) ===
Isobaric counterdiffusion is the diffusion of gases in opposite directions caused by a change in the composition of the external ambient gas or breathing gas without change in the ambient pressure. During decompression after a dive this can occur when a change is made to the breathing gas, or when the diver moves into a gas filled environment which differs from the breathing gas. While not strictly speaking a phenomenon of decompression, it is a complication that can occur during decompression, and that can result in the formation or growth of bubbles without changes in the environmental pressure. Two forms of this phenomenon have been described by Lambertsen:
Superficial ICD (also known as Steady State Isobaric Counterdiffusion) occurs when the inert gas breathed by the diver diffuses more slowly into the body than the inert gas surrounding the body. An example of this would be breathing air in an heliox environment. The helium in the heliox diffuses into the skin quickly, while the nitrogen diffuses more slowly from the capillaries to the skin and out of the body. The resulting effect generates supersaturation in certain sites of the superficial tissues and the formation of inert gas bubbles.
Deep Tissue ICD (also known as Transient Isobaric Counterdiffusion) occurs when different inert gases are breathed by the diver in sequence. The rapidly diffusing gas is transported into the tissue faster than the slower diffusing gas is transported out of the tissue. This can occur as divers switch from a nitrogen mixture to a helium mixture or when saturation divers breathing hydreliox switch to a heliox mixture.
Doolette and Mitchell's study of Inner Ear Decompression Sickness (IEDCS) shows that the inner ear may not be well-modelled by common (e.g. Bühlmann) algorithms. Doolette and Mitchell propose that a switch from a helium-rich mix to a nitrogen-rich mix, as is common in technical diving when switching from trimix to nitrox on ascent, may cause a transient supersaturation of inert gas within the inner ear and result in IEDCS. They suggest that breathing-gas switches from helium-rich to nitrogen-rich mixtures should be carefully scheduled either deep (with due consideration to nitrogen narcosis) or shallow to avoid the period of maximum supersaturation resulting from the decompression. Switches should also be made during breathing of the largest inspired oxygen partial pressure that can be safely tolerated with due consideration to oxygen toxicity.
=== Causative role of oxygen ===
Although it is commonly held that DCS is caused by inert gas supersaturation, Hempleman has stated: ...This did not lead to a sufficient cut-back in the permitted decompression ratio and an allowance in the calculations is now made for high oxygen partial pressures. Whenever the partial pressure of oxygen in air (or mixture) exceeds 0.6 bar then it is considered that significant amounts of dissolved oxygen are present in the tissues and that there is an increased decompression risk. This is estimated by adding 25% to the dive depth, and proceeding with the calculations as just outlined using assumption (1). An oxygen first stop depth is thus obtained, and 5 min is spent at this depth to allow for metabolic use of the excess dissolved oxygen gas. Following this 'oxygen stop' the calculations proceed as outlined above.
== Decompression sickness ==
Vascular bubbles formed in the systemic capillaries may be trapped in the lung capillaries, temporarily blocking them. If this is severe, the symptom called "chokes" may occur. If the diver has a patent foramen ovale (or a shunt in the pulmonary circulation), bubbles may pass through it and bypass the pulmonary circulation to enter the arterial blood. If these bubbles are not absorbed in the arterial plasma and lodge in systemic capillaries they will block the flow of oxygenated blood to the tissues supplied by those capillaries, and those tissues will be starved of oxygen. Moon and Kisslo (1988) concluded that "the evidence suggests that the risk of serious neurological DCI or early onset DCI is increased in divers with a resting right-to-left shunt through a PFO. There is, at present, no evidence that PFO is related to mild or late onset bends."
Bubbles form within other tissues as well as the blood vessels. Inert gas can diffuse into bubble nuclei between tissues. In this case, the bubbles can distort and permanently damage the tissue. As they grow, the bubbles may also compress nerves as they grow causing pain.
Extravascular or autochthonous[a] bubbles usually form in slow tissues such as joints, tendons and muscle sheaths. Direct expansion causes tissue damage, with the release of histamines and their associated affects. Biochemical damage may be as important as, or more important than mechanical effects.
The exchange of dissolved gases between the blood and tissues is controlled by perfusion and to a lesser extent by diffusion, particularly in heterogeneous tissues.
The distribution of blood flow to the tissues is variable and subject to a variety of influences. When the flow is locally high, that area is dominated by perfusion, and by diffusion when the flow is low. The distribution of flow is controlled by the mean arterial pressure and the local vascular resistance, and the arterial pressure depends on cardiac output and the total vascular resistance. Basic vascular resistance is controlled by the sympathetic nervous system, and metabolites, temperature, and local and systemic hormones have secondary and often localised effects, which can vary considerably with circumstances. Peripheral vasoconstriction in cold water decreases overall heat loss without increasing oxygen consumption until shivering begins, at which point oxygen consumption will rise, though the vasoconstriction can persist.
The composition of the breathing gas during pressure exposure and decompression is significant in inert gas uptake and elimination for a given pressure exposure profile. Breathing gas mixtures for diving will typically have a different gas fraction of nitrogen to that of air. The partial pressure of each component gas will differ from that of nitrogen in air at any given depth, and uptake and elimination of each inert gas component is proportional to the actual partial pressure over time. The two foremost reasons for use of mixed breathing gases are the reduction of nitrogen partial pressure by dilution with oxygen, to make Nitrox mixtures, primarily to reduce the rate of nitrogen uptake during pressure exposure, and the substitution of helium (and occasionally other gases) for the nitrogen to reduce the narcotic effects under high partial pressure exposure. Depending on the proportions of helium and nitrogen, these gases are called Heliox, if there is no nitrogen, or Trimix, if there is nitrogen and helium along with the essential oxygen. The inert gases used as substitutes for nitrogen have different solubility and diffusion characteristics in living tissues to the nitrogen they replace. For example, the most common inert gas diluent substitute for nitrogen is helium, which is significantly less soluble in living tissue, but also diffuses faster due to the relatively small size and mass of the He atom in comparison with the N2 molecule.
Blood flow to skin and fat are affected by skin and core temperature, and resting muscle perfusion is controlled by the temperature of the muscle itself. During exercise increased flow to the working muscles is often balanced by reduced flow to other tissues, such as kidneys spleen and liver. Blood flow to the muscles is also lower in cold water, but exercise keeps the muscle warm and flow elevated even when the skin is chilled. Blood flow to fat normally increases during exercise, but this is inhibited by immersion in cold water. Adaptation to cold reduces the extreme vasoconstriction which usually occurs with cold water immersion. Variations in perfusion distribution do not necessarily affect respiratory inert gas exchange, though some gas may be locally trapped by changes in perfusion. Rest in a cold environment will reduce inert gas exchange from skin, fat and muscle, whereas exercise will increase gas exchange. Exercise during decompression can reduce decompression time and risk, providing bubbles are not present, but can increase risk if bubbles are present. Inert gas exchange is least favourable for the diver who is warm and exercises at depth during the ingassing phase, and rests and is cold during decompression.
Other factors which can affect decompression risk include oxygen concentration, carbon dioxide levels, body position, vasodilators and constrictors, positive or negative pressure breathing. and dehydration (blood volume). Individual susceptibility to decompression sickness has components which can be attributed to a specific cause, and components which appear to be random. The random component makes successive decompressions a poor test of susceptibility. Obesity and high serum lipid levels have been implicated by some studies as risk factors, and risk seems to increase with age. Another study has also shown that older subjects tended to bubble more than younger subjects for reasons not yet known, but no trends between weight, body fat, or gender and bubbles were identified, and the question of why some people are more likely to form bubbles than others remains unclear.
== Decompression model concepts ==
Two rather different concepts have been used for decompression modelling. The first assumes that dissolved gas is eliminated while in the dissolved phase, and that bubbles are not formed during asymptomatic decompression. The second, which is supported by experimental observation, assumes that bubbles are formed during most asymptomatic decompressions, and that gas elimination must consider both dissolved and bubble phases.
Early decompression models tended to use the dissolved phase models, and adjusted them by more or less arbitrary factors to reduce the risk of symptomatic bubble formation. Dissolved phase models are of two main groups. Parallel compartment models, where several compartments with varying rates of gas absorption (half time), are considered to exist independently of each other, and the limiting condition is controlled by the compartment which shows the worst case for a specific exposure profile. These compartments represent conceptual tissues and are not intended to represent specific organic tissues, merely to represent the range of possibilities for the organic tissues. The second group uses serial compartments, where gas is assumed to diffuse through one compartment before it reaches the next. A recent variation on the serial compartment model is the Goldman interconnected compartment model (ICM).
More recent models attempt to model bubble dynamics, also by simplified models, to facilitate the computation of tables, and later to allow real time predictions during a dive. The models used to approximate bubble dynamics are varied, and range from those which are not much more complex that the dissolved phase models, to those which require considerably greater computational power.
None of the decompression models can be shown to be an accurate representation of the physiological processes, although interpretations of the mathematical models have been proposed which correspond with various hypotheses. They are all approximations which predict reality to a greater or lesser extent, and are acceptably reliable only within the bounds of calibration against collected experimental data.
=== Range of application ===
The ideal decompression profile creates the greatest possible gradient for inert gas elimination from a tissue without causing bubbles to form, and the dissolved phase decompression models are based on the assumption that bubble formation can be avoided. However, it is not certain whether this is practically possible: some of the decompression models assume that stable bubble micronuclei always exist. The bubble models make the assumption that there will be bubbles, but there is a tolerable total gas phase volume or a tolerable gas bubble size, and limit the maximum gradient to take these tolerances into account.
Decompression models should ideally accurately predict risk over the full range of exposure from short dives within the no-stop limits, decompression bounce dives over the full range of practical applicability, including extreme exposure dives and repetitive dives, alternative breathing gases, including gas switches and constant PO2, variations in dive profile, and saturation dives. This is not generally the case, and most models are limited to a part of the possible range of depths and times. They are also limited to a specified range of breathing gases, and sometimes restricted to air.
A fundamental problem in the design of decompression tables is that the simplified rules that govern a single dive and ascent do not apply when some tissue bubbles already exist, as these will delay inert gas elimination and equivalent decompression may result in decompression sickness. Repetitive diving, multiple ascents within a single dive, and surface decompression procedures are significant risk factors for DCS. These have been attributed to the development of a relatively high gas phase volume which may be partly carried over to subsequent dives or the final ascent of a sawtooth profile.
The function of decompression models has changed with the availability of Doppler ultrasonic bubble detectors, and is no longer merely to limit symptomatic occurrence of decompression sickness, but also to limit asymptomatic post-dive venous gas bubbles. A number of empirical modifications to dissolved phase models have been made since the identification of venous bubbles by Doppler measurement in asymptomatic divers soon after surfacing.
=== Tissue compartments ===
One attempt at a solution was the development of multi-tissue models, which assumed that different parts of the body absorbed and eliminated gas at different rates. These are hypothetical tissues which are designated as fast and slow to describe the rate of saturation. Each tissue, or compartment, has a different half-life. Real tissues will also take more or less time to saturate, but the models do not need to use actual tissue values to produce a useful result. Models with from one to 16 tissue compartments have been used to generate decompression tables, and dive computers have used up to 20 compartments.
For example: Tissues with a high lipid content can take up a larger amount of nitrogen, but often have a poor blood supply. These will take longer to reach equilibrium, and are described as slow, compared to tissues with a good blood supply and less capacity for dissolved gas, which are described as fast.
Fast tissues absorb gas relatively quickly, but will generally release it quickly during ascent. A fast tissue may become saturated in the course of a normal recreational dive, while a slow tissue may have absorbed only a small part of its potential gas capacity. By calculating the levels in each compartment separately, researchers are able to construct more effective algorithms. In addition, each compartment may be able to tolerate more or less supersaturation than others. The final form is a complicated model, but one that allows for the construction of algorithms and tables suited to a wide variety of diving. A typical dive computer has an 8–12 tissue model, with half times varying from 5 minutes to 400 minutes. The Bühlmann tables use an algorithm with 16 tissues, with half times varying from 4 minutes to 640 minutes.
Tissues may be assumed to be in series, where dissolved gas must diffuse through one tissue to reach the next, which has different solubility properties, in parallel, where diffusion into and out of each tissue is considered to be independent of the others, and as combinations of series and parallel tissues, which becomes computationally complex.
=== Ingassing model ===
The half time of a tissue is the time it takes for the tissue to take up or release 50% of the difference in dissolved gas capacity at a changed partial pressure. For each consecutive half time the tissue will take up or release half again of the cumulative difference in the sequence ½, ¾, 7/8, 15/16, 31/32, 63/64 etc. Tissue compartment half times range from 1 minute to at least 720 minutes. A specific tissue compartment will have different half times for gases with different solubilities and diffusion rates. Ingassing is generally modeled as following a simple inverse exponential equation where saturation is assumed after approximately four (93.75%) to six (98.44%) half-times depending on the decompression model.
This model may not adequately describe the dynamics of outgassing if gas phase bubbles are present.
=== Outgassing models ===
For optimised decompression the driving force for tissue desaturation should be kept at a maximum, provided that this does not cause symptomatic tissue injury due to bubble formation and growth (symptomatic decompression sickness), or produce a condition where diffusion is retarded for any reason.
There are two fundamentally different ways this has been approached. The first is based on an assumption that there is a level of supersaturation which does not produce symptomatic bubble formation and is based on empirical observations of the maximum decompression rate which does not result in an unacceptable rate of symptoms. This approach seeks to maximise the concentration gradient providing there are no symptoms, and commonly uses a slightly modified exponential half-time model. The second assumes that bubbles will form at any level of supersaturation where the total gas tension in the tissue is greater than the ambient pressure and that gas in bubbles is eliminated more slowly than dissolved gas. These philosophies result in differing characteristics of the decompression profiles derived for the two models: The critical supersaturation approach gives relatively rapid initial ascents, which maximize the concentration gradient, and long shallow stops, while the bubble models require slower ascents, with deeper first stops, but may have shorter shallow stops. This approach uses a variety of models.
==== The critical supersaturation approach ====
J.S. Haldane originally used a critical pressure ratio of 2 to 1 for decompression on the principle that the saturation of the body should at no time be allowed to exceed about double the air pressure. This principle was applied as a pressure ratio of total ambient pressure and did not take into account the partial pressures of the component gases of the breathing air. His experimental work on goats and observations of human divers appeared to support this assumption. However, in time, this was found to be inconsistent with incidence of decompression sickness and changes were made to the initial assumptions. This was later changed to a 1.58:1 ratio of nitrogen partial pressures.
Further research by people such as Robert Workman suggested that the criterion was not the ratio of pressures, but the actual pressure differentials. Applied to Haldane's work, this would suggest that the limit is not determined by the 1.58:1 ratio but rather by the critical pressure difference of 0.58 atmospheres between tissue pressure and ambient pressure. Most Haldanean tables since the mid 20th century, including the Bühlmann tables, are based on the critical difference assumption .
The M-value is the maximum value of absolute inert gas pressure that a tissue compartment can take at a given ambient pressure without presenting symptoms of decompression sickness. M-values are limits for the tolerated gradient between inert gas pressure and ambient pressure in each compartment. Alternative terminology for M-values include "supersaturation limits", "limits for tolerated overpressure", and "critical tensions".
Gradient factors are a way of modifying the M-value to a more conservative value for use in a decompression algorithm. The gradient factor is a percentage of the M-value chosen by the algorithm designer, and varies linearly between the maximum depth of the specific dive and the surface. They are expressed as a two number designation, where the first number is the percentage of the deep M-value, and the second is a percentage of the shallow M-value. The gradient factors are applied to all tissue compartments equally and produce an M-value which is linearly variable in proportion to ambient pressure.
For example: A 30/85 gradient factor would limit the allowed supersaturation at depth to 30% of the designer's maximum, and to 85% at the surface.
In effect the user is selecting a lower maximum supersaturation than the designer considered appropriate. Use of gradient factors will increase decompression time, particularly in the depth zone where the M-value is reduced the most. Gradient factors may be used to force deeper stops in a model which would otherwise tend to produce relatively shallow stops, by using a gradient factor with a small first number. Several models of dive computer allow user input of gradient factors as a way of inducing a more conservative, and therefore presumed lower risk, decompression profile. Forcing a low gradient factor at the deep M-value can have the effect of increasing ingassing during the ascent, generally of the slower tissues, which must then release a larger gas load at shallower depths. This has been shown to be an inefficient decompression strategy.
The Variable Gradient Model adjusts the gradient factors to fit the depth profile on the assumption that a straight line adjustment using the same factor on the deep M-value regardless of the actual depth is less appropriate than using an M-value linked to the actual depth. (the shallow M-value is linked to actual depth of zero in both cases)
==== The no-supersaturation approach ====
According to the thermodynamic model of Hugh LeMessurier and Brian Andrew Hills, this condition of optimum driving force for outgassing is satisfied when the ambient pressure is just sufficient to prevent phase separation (bubble formation).
The fundamental difference of this approach is equating absolute ambient pressure with the total of the partial gas tensions in the tissue for each gas after decompression as the limiting point beyond which bubble formation is expected.
The model assumes that the natural unsaturation in the tissues due to metabolic reduction in oxygen partial pressure provides the buffer against bubble formation, and that the tissue may be safely decompressed provided that the reduction in ambient pressure does not exceed this unsaturation value. Clearly any method which increases the unsaturation would allow faster decompression, as the concentration gradient would be greater without risk of bubble formation.
The natural unsaturation increases with depth, so a larger ambient pressure differential is possible at greater depth, and reduces as the diver surfaces. This model leads to slower ascent rates and deeper first stops, but shorter shallow stops, as there is less bubble phase gas to be eliminated.
==== The critical volume approach ====
The critical-volume criterion assumes that whenever the total volume of gas phase accumulated in the tissues exceeds a critical value, signs or symptoms of DCS will appear. This assumption is supported by doppler bubble detection surveys. The consequences of this approach depend strongly on the bubble formation and growth model used, primarily whether bubble formation is practicably avoidable during decompression.
This approach is used in decompression models which assume that during practical decompression profiles, there will be growth of stable microscopic bubble nuclei which always exist in aqueous media, including living tissues.
Efficient decompression will minimize the total ascent time while limiting the total accumulation of bubbles to an acceptable non-symptomatic critical value. The physics and physiology of bubble growth and elimination indicate that it is more efficient to eliminate bubbles while they are very small. Models which include bubble phase have produced decompression profiles with slower ascents and deeper initial decompression stops as a way of curtailing bubble growth and facilitating early elimination, in comparison with the models which consider only dissolved phase gas.
=== Bounce dives ===
A bounce dive is any dive where the exposure to pressure is not long enough for all the tissues to reach equilibrium with the inert gases in the breathing gas.
=== Saturation dives ===
A saturation exposure is where the time exposed to pressure is sufficient for all tissues to reach equilibrium with the inert gases in the breathing mixture. For practical purposes this is usually taken as 6 times the half time of the slowest tissue in the model.
=== No-stop limits ===
A no-stop limit, also called no decompression limit (NDL) is the theoretical maximum dissolved gas content of each tissue compartment of the whole body, which can be decompressed directly to surface pressure at the chosen ascent rate used by the model, without a need to stop to outgas at any depth, which has an acceptable risk of developing symptomatic decompression sickness. No decompression limit is a misnomer as the ascent at the specified ascent rate is decompression, but the term has historical inertia and continues to be used.
=== Decompression ceiling ===
Once the gas loading of one or more tissue compartments exceeds the maximum level accepted for the no-stop limit, there is a minimum depth to which the diver can ascend at the appropriate ascent rate, at an acceptable risk for decompression sickness. This depth is known as the decompression ceiling. It may be considered a soft overhead, in that it is physically trivial to ascend above it, but that increases the risk of developing symptomatic decompression sickness according to the decompression model. The tissue that reaches its decompression ceiling first is called the limiting tissue.
=== Decompression obligation ===
A decompression obligation is the presence in the tissues of sufficient dissolved gas that the risk of symptomatic decompression sickness is unacceptable if a direct ascent to surface pressure is made at the prescribed ascent rate for the decompression model in use. A diver with a decompression ceiling can be said to have a decompression obligation, meaning that time must be spent outgassing during the ascent additional to the time spent ascending at the appropriate ascent rate. This time is nominally and most efficiently spent at decompression stops, though outgassing will occur at any depth where the arterial blood and lung gas have a lower partial pressure of the inert gas than the limiting tissue.
=== Time to surface ===
Time to surface (TTS) is the estimated total time required for a diver to surface from a given point on a dive profile, using a given set of decompression gases, ascending at the nominal ascent rate, and doing all the stops at the specifies depths. This value may be an estimate calculated from a dive plan, and followed by the diver as the ascent schedule, or shown on the screen of a dive computer as updated in real time. It may be based on the current gas selected, or the optimum gas selection from all gases set as active gases on the computer.
=== Staged decompression ===
Staged decompression is done with stops as specified depths based on an easily followed series. For most tables this has historically been a convenient 3 metres (10 ft) interval, but any arbitrary spacing may be used provided the computation of decompression stops uses it. The diver must stay at the prescribed stop depth until the ceiling decreases to the next shallower stop depth, at which point the diver ascends to that depth for the next stop.
The calculation of stop time can also be done to follow the decompression ceiling, which will give a maximised pressure gradient for inert gas washout, and reduces the overall decompression duration by about 4 to 12% This strategy can be approximately followed when using a dive computer with the option enabled. The effect on decompression risk with this strategy is unknown, as no testing has been done as of 2022.
=== Residual inert gas ===
Gas bubble formation has been experimentally shown to significantly inhibit inert gas elimination.
A considerable amount of inert gas will remain in the tissues after a diver has surfaced, even if no symptoms of decompression sickness occur. This residual gas may be dissolved or in sub-clinical bubble form, and will continue to outgas while the diver remains at the surface. If a repetitive dive is made, the tissues are preloaded with this residual gas which will make them saturate faster.
In repetitive diving, the slower tissues can accumulate gas day after day, if there is insufficient time for the gas to be eliminated between dives. This can be a problem for multi-day multi-dive situations. Multiple decompressions per day over multiple days can increase the risk of decompression sickness because of the build up of asymptomatic bubbles, which reduce the rate of off-gassing and are not accounted for in most decompression algorithms. Consequently, some diver training organisations make extra recommendations such as taking "the seventh day off".
== Decompression models in practice ==
=== Deterministic models ===
Deterministic decompression models are a rule based approach to calculating decompression. These models work from the idea that "excessive" supersaturation in various tissues is "unsafe" (resulting in decompression sickness). The models usually contain multiple depth and tissue dependent rules based on mathematical models of idealised tissue compartments. There is no objective mathematical way of evaluating the rules or overall risk other than comparison with empirical test results. The models are compared with experimental results and reports from the field, and rules are revised by qualitative judgment and curve fitting so that the revised model more closely predicts observed reality, and then further observations are made to assess the reliability of the model in extrapolations into previously untested ranges. The usefulness of the model is judged on its accuracy and reliability in predicting the onset of symptomatic decompression sickness and asymptomatic venous bubbles during ascent.
It may be reasonably assumed that in reality, both perfusion transport by blood circulation, and diffusion transport in tissues where there is little or no blood flow occur. The problem with attempts to simultaneously model perfusion and diffusion is that there are large numbers of variables due to interactions between all of the tissue compartments and the problem becomes intractable. A way of simplifying the modelling of gas transfer into and out of tissues is to make assumptions about the limiting mechanism of dissolved gas transport to the tissues which control decompression. Assuming that either perfusion or diffusion has a dominant influence, and the other can be disregarded, can greatly reduce the number of variables.
==== Perfusion limited tissues and parallel tissue models ====
The assumption that perfusion is the limiting mechanism leads to a model comprising a group of tissues with varied rates of perfusion, but supplied by blood of approximately equivalent gas concentration. It is also assumed that there is no gas transfer between tissue compartments by diffusion. This results in a parallel set of independent tissues, each with its own rate of ingassing and outgassing dependent on the rate of blood flowing through the tissue. Gas uptake for each tissue is generally modelled as an exponential function, with a fixed compartment half-time, and gas elimination may also be modelled by an exponential function, with the same or a longer half time, or as a more complex function, as in the exponential-linear elimination model.
The critical ratio hypothesis predicts that the development of bubbles will occur in a tissue when the ratio of dissolved gas partial pressure to ambient pressure exceeds a particular ratio for a given tissue. The ratio may be the same for all tissue compartments or it may vary, and each compartment is allocated a specific critical supersaturation ratio, based on experimental observations.
John Scott Haldane introduced the concept of half times to model the uptake and release of nitrogen into the blood. He suggested 5 tissue compartments with half times of 5, 10, 20, 40 and 75 minutes. In this early hypothesis it was predicted that if the ascent rate does not allow the inert gas partial pressure in each of the hypothetical tissues to exceed the environmental pressure by more than 2:1 bubbles will not form. Basically this meant that one could ascend from 30 m (4 bar) to 10 m (2 bar), or from 10 m (2 bar) to the surface (1 bar) when saturated, without a decompression problem. To ensure this a number of decompression stops were incorporated into the ascent schedules. The ascent rate and the fastest tissue in the model determine the time and depth of the first stop. Thereafter the slower tissues determine when it is safe to ascend further. This 2:1 ratio was found to be too conservative for fast tissues (short dives) and not conservative enough for slow tissues (long dives). The ratio also seemed to vary with depth. Haldane's approach to decompression modeling was used from 1908 to the 1960s with minor modifications, primarily changes to the number of compartments and half times used. The 1937 US Navy tables were based on research by O. D. Yarbrough and used 3 compartments: the 5- and 10-minute compartments were dropped. In the 1950s the tables were revised and the 5- and 10-minute compartments restored, and a 120-minute compartment added.
In the 1960s Robert D. Workman of the U.S. Navy Experimental Diving Unit (NEDU) reviewed the basis of the model and subsequent research performed by the US Navy. Tables based on Haldane's work and subsequent refinements were still found to be inadequate for longer and deeper dives. Workman proposed that the tolerable change in pressure was better described as a critical pressure difference, and revised Haldane's model to allow each tissue compartment to tolerate a different amount of supersaturation which varies with depth. He introduced the term "M-value" to indicate the maximum amount of supersaturation each compartment could tolerate at a given depth and added three additional compartments with 160, 200 and 240-minute half times. Workman presented his findings as an equation which could be used to calculate the results for any depth and stated that a linear projection of M-values would be useful for computer programming.
A large part of Albert A. Bühlmann's research was to determine the longest half time compartments for Nitrogen and Helium, and he increased the number of compartments to 16. He investigated the implications of decompression after diving at altitude and published decompression tables that could be used at a range of altitudes. Bühlmann used a method for decompression calculation similar to that proposed by Workman, which included M-values expressing a linear relationship between maximum inert gas pressure in the tissue compartments and ambient pressure, but based on absolute pressure, which made them more easily adapted for altitude diving. Bühlmann's algorithm was used to generate the standard decompression tables for a number of sports diving associations, and is used in several personal decompression computers, sometimes in a modified form.
B.A. Hills and D.H. LeMessurier studied the empirical decompression practices of Okinawan pearl divers in the Torres Strait and observed that they made deeper stops but reduced the total decompression time compared with the generally used tables of the time. Their analysis strongly suggested that bubble presence limits gas elimination rates, and emphasized the importance of inherent unsaturation of tissues due to metabolic processing of oxygen. This became known as the thermodynamic model. More recently, recreational technical divers developed decompression procedures using deeper stops than required by the decompression tables in use. These led to the RGBM and VPM bubble models. A deep stop was originally an extra stop introduced by divers during ascent, at a greater depth than the deepest stop required by their computer algorithm. There are also computer algorithms that are claimed to use deep stops, but these algorithms and the practice of deep stops have not been adequately validated.
A "Pyle stop" is a deep stop named after Richard Pyle, an early advocate of deep stops, at the depths halfway between the bottom and the first conventional decompression stop, and halfway between the previous Pyle stop and the deepest conventional stop, provided the conventional stop is more than 9 m shallower. A Pyle stop is about 2 minutes long. The additional ascent time required for Pyle stops is included in the dive profile before finalising the decompression schedule. Pyle found that on dives where he stopped periodically to vent the swim-bladders of his fish specimens, he felt better after the dive, and based the deep stop procedure on the depths and duration of these pauses. The hypothesis is that these stops provide an opportunity to eliminate gas while still dissolved, or at least while the bubbles are still small enough to be easily eliminated, and the result is that there will be considerably fewer or smaller venous bubbles to eliminate at the shallower stops as predicted by the thermodynamic model of Hills.
For example, a diver ascends from a maximum depth of 60 metres (200 ft), where the ambient pressure is 7 bars (100 psi), to a decompression stop at 20 metres (66 ft), where the pressure is 3 bars (40 psi). The first Pyle stop would take place at the halfway pressure, which is 5 bars (70 psi) corresponding to a depth of 40 metres (130 ft). The second Pyle stop would be at 30 metres (98 ft). A third would be at 25 metres (82 ft) which is less than 9 metres (30 ft) below the first required stop, and therefore is omitted.
The value and safety of deep stops additional to the decompression schedule derived from a decompression algorithm is unclear. Decompression experts have pointed out that deep stops are likely to be made at depths where ingassing continues for some slow tissues, and that the addition of deep stops of any kind should be included in the hyperbaric exposure for which the decompression schedule is computed, and not added afterwards, so that such ingassing of slower tissues can be taken into account. Deep stops performed during a dive where the decompression is calculated in real-time are simply part of a multi-level dive to the computer, and add no risk beyond that which is inherent in the algorithm.
There is a limit to how deep a "deep stop" can be. Some off-gassing must take place, and continued on-gassing should be minimised for acceptably effective decompression. The "deepest possible decompression stop" for a given profile can be defined as the depth where the gas loading for the leading compartment crosses the ambient pressure line. This is not a useful stop depth - some excess in tissue gas concentration is necessary to drive the outgassing diffusion, however this depth is a useful indicator of the beginning of the decompression zone, in which ascent rate is part of the planned decompression.
A study by DAN in 2004 found that the incidence of high-grade bubbles could be reduced to zero providing the nitrogen concentration of the most saturated tissue was kept below 80 percent of the allowed M value and that an added deep stop was a simple and practical way of doing this, while retaining the original ascent rate.
==== Diffusion limited tissues and the "Tissue slab", and series models ====
The assumption that diffusion is the limiting mechanism of dissolved gas transport in the tissues results in a rather different tissue compartment model. In this case a series of compartments has been postulated, with perfusion transport into one compartment, and diffusion between the compartments, which for simplicity are arranged in series, so that for the generalised compartment, diffusion is to and from only the two adjacent compartments on opposite sides, and the limit cases are the first compartment where the gas is supplied and removed via perfusion, and the end of the line, where there is only one neighbouring compartment. The simplest series model is a single compartment, and this can be further reduced to a one-dimensional "tissue slab" model.
==== Bubble models ====
Bubble decompression models are a rule based approach to calculating decompression based on the idea that microscopic bubble nuclei always exist in water and tissues that contain water and that by predicting and controlling the bubble growth, one can avoid decompression sickness. Most of the bubble models assume that bubbles will form during decompression, and that mixed phase gas elimination occurs, which is slower than dissolved phase elimination. Bubble models tend to have deeper first stops to get rid of more dissolved gas at a lower supersaturation to reduce the total bubble phase volume, and potentially reduce the time required at shallower depths to eliminate bubbles.
Decompression models that assume mixed phase gas elimination include:
The arterial bubble decompression model of the French Tables du Ministère du Travail 1992
The U.S. Navy Exponential-Linear (Thalmann) algorithm used for the 2008 US Navy air decompression tables (among others)
Hennessy's combined perfusion/diffusion model of the BSAC'88 tables
The Varying Permeability Model (VPM) developed by D.E. Yount and Hoffman (1986) at the University of Hawaii
The Reduced Gradient Bubble Model (RGBM) developed by Bruce Wienke in 1990 at Los Alamos National Laboratory
Michael Gernhardt proposed the Tissue Bubble Dynamics Model (1991)
Wayne Gerth and Richard Vann (1997) published the Probabilistic Gas and Bubble Dynamics Model.
Lewis and Crow introduced their Gas Formation Model (GFM) in 2008.
The Copernicus model of Gutvik and Brubakk (2009)
The most widely implemented model in dive computers is a simplified modification of the RGBM.
The models of Yount and Hoffman, and Wienke, assume that bubble formation is due to supersaturation, while Gernhardt, Gerth and Vann, and Gutvik and Brubakk assume pre-existing microscopic bubble nuclei, which grow when concentration of gases in the tissues is high enough. These models are more mathematically complex, and as of 2009 were unsuitable for real-time computation by dive computer.
==== Goldman Interconnected Compartment Model ====
In contrast to the independent parallel compartments of the Haldanean models, in which all compartments are considered risk bearing, the Goldman model posits a relatively well perfused "active" or "risk-bearing" compartment in series with adjacent relatively poorly perfused "reservoir" or "buffer" compartments, which are not considered potential sites for bubble formation, but affect the probability of bubble formation in the active compartment by diffusive inert gas exchange with the active compartment. During compression, gas diffuses into the active compartment and through it into the buffer compartments, increasing the total amount of dissolved gas passing through the active compartment. During decompression, this buffered gas must pass through the active compartment again before it can be eliminated. If the gas loading of the buffer compartments is small, the added gas diffusion through the active compartment is slow. The interconnected models predict a reduction in gas washout rate with time during decompression compared with the rate predicted for the independent parallel compartment model used for comparison.
The Goldman model differs from the Kidd-Stubbs series decompression model in that the Goldman model assumes linear kinetics, where the K-S model includes a quadratic component, and the Goldman model considers only the central well-perfused compartment to contribute explicitly to risk, while the K-S model assumes all compartments to carry potential risk. The DCIEM 1983 model associates risk with the two outermost compartments of a four compartment series. The mathematical model based on this concept is claimed by Goldman to fit not only the Navy square profile data used for calibration, but also predicts risk relatively accurately for saturation profiles. A bubble version of the ICM model was not significantly different in predictions, and was discarded as more complex with no significant advantages. The ICM also predicted decompression sickness incidence more accurately at the low-risk recreational diving exposures recorded in DAN's Project Dive Exploration data set. The alternative models used in this study were the LE1 (Linear-Exponential) and straight Haldanean models. The Goldman model predicts a significant risk reduction following a safety stop on a low-risk dive and significant risk reduction by using nitrox (more so than the PADI tables suggest).
=== Probabilistic models ===
Probabilistic decompression models are designed to calculate the risk (or probability) of decompression sickness (DCS) occurring on a given decompression profile. Statistical analysis is well suited to compressed air work in tunneling operations due to the large number of subjects undergoing similar exposures at the same ambient pressure and temperature, with similar workloads and exposure times, with the same decompression schedule. Large numbers of decompressions under similar circumstances have shown that it is not reasonably practicable to eliminate all risk of DCS, so it is necessary to set an acceptable risk, based on the other factors relevant to the application. For example, easy access to effective treatment in the form of hyperbaric oxygen treatment on site, or greater advantage to getting the diver out of the water sooner, may make a higher incidence acceptable, while interfering with work schedule, adverse effects on worker morale or a high expectation of litigation would shift acceptable incidence rate downward. Efficiency is also a factor, as decompression of employees occurs during working hours.
These methods can vary the decompression stop depths and times to arrive at a decompression schedule that assumes a specified probability of DCS occurring, while minimizing the total decompression time. This process can also work in reverse allowing one to calculate the probability of DCS for any decompression schedule, given sufficient reliable data.
In 1936 an incidence rate of 2% was considered acceptable for compressed air workers in the UK. The US Navy in 2000 accepted a 2% incidence of mild symptoms, but only 0.1% serious symptoms. Commercial diving in the North Sea in the 1990s accepted 0.5% mild symptoms, but almost no serious symptoms, and commercial diving in the Gulf of Mexico also during the 1990s, accepted 0.1% mild cases and 0.025% serious cases. Health and Safety authorities tend to specify the acceptable risk as as low as reasonably practicable taking into account all relevant factors, including economic factors. To analyse probability of mild and severe symptoms it is first necessary to define these classes of manifestation, as applicable to the analysis.
The necessary tools for probability estimation for decompression sickness are a biophysical model which describes the inert gas exchange and bubble formation during decompression, exposure data in the form of pressure/time profiles for the breathing gas mixtures, and the DCS outcomes for these exposures, statistical methods, such as survival analysis or Bayesian analysis to find a best fit between model and experimental data, after which the models can be quantitatively compared and the best fitting model used to predict DCS probability for the model. This process is complicated by the influence of environmental conditions on DCS probability. Factors that affect perfusion of the tissues during ingassing and outgassing, which affect rates of inert gas uptake and elimination respectively, include immersion, temperature and exercise. Exercise is also known to promote bubble formation during decompression.
The distribution of decompression stops is also known to affect DCS risk. A USN experiment using symptomatic decompression sickness as the endpoint, compared two models for dive working exposures on air using the same bottom time, water temperature and workload, with the same total decompression time, for two different depth distributions of decompression stops, also on air, and found the shallower stops to carry a statistically very significantly lower risk. The model did not attempt to optimise depth distribution of decompression time, or the use of gas switching, it just compared the effectiveness of two specific models, but for those models the results were convincing.
Another set of experiments was conducted for a series of increasing bottom time exposures at a constant depth, with varying ambient temperature. Four temperature conditions were compared: warm during the bottom sector and decompression, cold during bottom sector and decompression, warm at the bottom and cold during decompression, and cold at the bottom and warm during decompression. The effects were very clear that DCS incidence was much lower for divers that were colder during the ingassing phase and warmer during decompression than the reverse, which has been interpreted as indicating the effects of temperature on perfusion on gas uptake and elimination.
A retrospective statistical analysis of a large data set of case reports of air and nitrox dives published in 2017 indicated that for an acceptable risk of 2% for mild symptoms, and 0.1% for severe symptoms, using a linear-exponential degassing model, the severe symptom risk was the limiting factor. One of the factors complicating this analysis was the variability in methods for distinguishing between mild and severe cases.
=== Saturation decompression ===
Saturation decompression is a physiological process of transition from a steady state of full saturation with inert gas at raised pressure to standard conditions at normal surface atmospheric pressure. It is a long process during which inert gases are eliminated at a very low rate limited by the slowest affected tissues, and a deviation can cause the formation of gas bubbles which can produce decompression sickness. Most operational procedures rely on experimentally derived parameters describing a continuous slow decompression rate, which may depend on depth and gas mixture.
In saturation diving all tissues are considered saturated and decompression which is safe for the slowest tissues will theoretically be safe for all faster tissues in a parallel model. Direct ascent from air saturation at approximately 7 msw produces venous gas bubbles but not symptomatic DCS. Deeper saturation exposures require decompression to saturation schedules.
The safe rate of decompression from a saturation dive is controlled by the partial pressure of oxygen in the inspired breathing gas. The inherent unsaturation due to the oxygen window allows a relatively fast initial phase of saturation decompression in proportion to the oxygen partial pressure and then controls the rate of further decompression limited by the half-time of inert gas elimination from the slowest compartment. However, some saturation decompression schedules specifically do not allow an decompression to start with an upward excursion. Neither the excursions nor the decompression procedures currently in use (2016) have been found to cause decompression problems in isolation, but there appears to be significantly higher risk when excursions are followed by decompression before non-symptomatic bubbles resulting from excursions have totally resolved. Starting decompression while bubbles are present appears to be the significant factor in many cases of otherwise unexpected decompression sickness during routine saturation decompression.
Application of a bubble model in 1985 allowed successful modelling of conventional decompressions, altitude decompression, no-stop thresholds, and saturation dives using one setting of four global nucleation parameters.
Research continues on saturation decompression modelling and schedule testing. In 2015 a concept named Extended Oxygen Window was used in preliminary tests for a modified saturation decompression model. This model allows a faster rate of decompression at the start of the ascent to utilise the inherent unsaturation due to metabolic use of oxygen, followed by a constant rate limited by oxygen partial pressure of the breathing gas. The period of constant decompression rate is also limited by the allowable maximum oxygen fraction, and when this limit is reached, decompression rate slows down again as the partial pressure of oxygen is reduced. The procedure remains experimental as of May 2016. The goal is an acceptably safe reduction of overall decompression time for a given saturation depth and gas mixture.
=== Validation of models ===
It is important that any theory be validated by carefully controlled testing procedures. As testing procedures and equipment become more sophisticated, researchers learn more about the effects of decompression on the body. Initial research focused on producing dives that were free of recognizable symptoms of decompression sickness (DCS). With the later use of Doppler ultrasound testing, it was realized that bubbles were forming within the body even on dives where no DCI signs or symptoms were encountered. This phenomenon has become known as "silent bubbles".
The presence of venous gas emboli is considered a low specificity predictor of decompression sickness, but their absence is recognised to be a sensitive indicator of low risk decompression, therefore the quantitative detection of VGE is thought to be useful as an indicator of decompression stress when comparing decompression strategies, or assessing the efficiency of procedures.
The US Navy 1956 tables were based on limits determined by external DCS signs and symptoms. Later researchers were able to improve on this work by adjusting the limitations based on Doppler testing. However the US Navy CCR tables based on the Thalmann algorithm also used only recognisable DCS symptoms as the test criteria. Since the testing procedures are lengthy and costly, and there are ethical limitations on experimental work on human subjects with injury as an endpoint, it is common practice for researchers to make initial validations of new models based on experimental results from earlier trials. This has some implications when comparing models.
==== Efficiency of stop depth distribution ====
Deep, short duration dives require a long decompression in comparison to the time at depth, which is inherently inefficient in comparison with saturation diving. Various modifications to decompression algorithms with reasonably validated performance in shallower diving have been used in the effort to develop shorter or safer decompression, but these are generally not supported by controlled experiment and to some extent rely on anecdotal evidence. A widespread belief developed that algorithms based on bubble models and which distribute decompression stops over a greater range of depths are more efficient than the traditional dissolved gas content models by minimising early bubble formation, based on theoretical considerations, largely in the absence of evidence of effectiveness, though there were low incidences of symptomatic decompression sickness. Some evidence relevant to some of these modifications exists and has been analysed, and generally supports the opposite view, that deep stops may lead to greater rates of bubble formation and growth compared to the established systems using shallower stops distributed over the same total decompression time for a given deep profile.
The integral of supersaturation over time may be an indicator of decompression stress, either for a given tissue group or for all the tissue groups. Comparison of this indicator calculated for the combined Bühlmann tissue groups for a range of equal duration decompression schedules for the same depth, bottom time, and gas mixtures, has suggested greater overall decompression stress for dives using deep stops, at least partly due to continued ingassing of slower tissues during the deep stops.
==== Effects of inert gas component changes ====
Gas switching during decompression on open circuit is done primarily to increase the partial pressure of oxygen to increase the oxygen window effect, while keeping below acute toxicity levels. It is well established both in theory and practice, that a higher oxygen partial pressure facilitates a more rapid and effective elimination of inert gas, both in the dissolved state and as bubbles.
In closed circuit rebreather diving the oxygen partial pressure throughout the dive is maintained at a relatively high but tolerable level to reduce the ongassing as well as to accelerate offgassing of the diluent gas. Changes from helium-based diluents to nitrogen during ascent are desirable for reducing the use of expensive helium, but have other implications. It is unlikely that changes to nitrogen based decompression gas will accelerate decompression in typical technical bounce dive profiles, but there is some evidence that decompressing on helium-oxygen mixtures is more likely to result in neurological DCS, while nitrogen based decompression is more likely to produce other symptom if DCS occurs. However, switching from helium rich to nitrogen rich decompression gas is implicated in inner ear DCS, connected with counter-diffusion effects. This risk can be reduced by sufficient initial decompression, using high oxygen partial pressure and making the helium to nitrogen switch relatively shallow.
==== Altitude exposure, altitude diving and flying after diving ====
The USAF conducted experiments on human subjects in 1982 to validate schedules for air diving no-decompression limits before immediate excursions to altitude and for altitude diving allowing immediate flying after the dive to an altitude of 8,500 feet (2,600 m). Another test series in 2004 was made to validate predictions of a bubble-model for altitude decompression using previously untested exposure profiles. Parameters included exertion, altitudes from 18,000 to 35,000 feet (5,500 to 10,700 m), prebreathe time and exposure time, but these exposures did not include recent dives.
Experiments with an endpoint of DCS symptoms using profiles near the no-decompression exposure limits for recreational diving were carried out to determine how DCS occurrence during or after flight relates to the length of pre-flight surface interval (PFSI). The dives and PFSI were followed by a four-hour exposure at 75 kPa, equivalent to the maximum permitted commercial aircraft cabin altitude of 8,000 feet (2,400 m). DCS incidence decreased as surface interval increased, with no incidence for a 17 hour surface interval. Repetitive dives profiles usually needed longer surface intervals than single dives to minimise incidence. These tests have helped inform recommendations on time to fly.
In-flight transthoracic echocardiography has shown that there is a low but non-zero probability of decompression sickness in commercial pressurised aircraft after a 24 hour pre-flight surface interval following a week of multiple repetitive recreational dives, indicated by detection of venous gas bubbles in a significant number of the divers tested.
== Current research ==
Research on decompression continues. Data is not generally available on the specifics, however Divers Alert Network (DAN) has an ongoing citizen science based programme run by DAN (Europe) which gathers data from volunteer recreational divers for analysis by DAN research staff and other researchers. This research is funded by subscription fees of DAN Europe members. The Diving Safety Laboratory is a database to which members can upload dive profiles from a wide range of dive computers converted to a standard format and other data about the dive. Data on hundreds of thousands of real dives is analysed to investigate aspects of diving safety. The large amounts of data gathered is used for probabilistic analysis of decompression risk. The data donors can get immediate feedback in the form of a simple risk analysis of their dive profiles rated as one of three nominal levels of risk (high, medium and low) based on comparison with Bühlmann ZH16c M-values computed for the same profile.
Listed projects (not all directly related to decompression) include:
Gathering data on vascular gas bubbles and analysis of the data
Identification of optimised ascent profile
Investigating the causes of unexplained diving incidents
Stress in recreational diving
Correlation between patent foramen ovale (PFO) and risk of decompression illness
Diving with asthma and diabetes and managing the associated risk
Physiology and pathophysiology of breath-hold
Hypothermia and diving
Headache and diving
Blood changes associated with diving
Decompression risk of air travel after diving
Physiological effects of rebreather diving
Effects of decompression stress on endothelial stem cells and blood cells
Early decompression stress biomarkers
The effects of normobaric oxygen on blood and in DCI first aid
=== Practical effectiveness of models ===
Bubble models for decompression were popular among technical divers in the early 2000s, although there was little data to support the effectiveness of the models in practice. Since then, several comparative studies have indicated relatively larger numbers of venous gas emboli after decompression based on bubble models, and one study reported a higher rate of decompression sickness. The deeper decompression stops earlier in the ascent appear to be less effective at controlling bubble formation than the hypotheses suggested. This failure may be due to continued ingassing of slower tissues during the extended time at greater depth, resulting in these tissues being more supersaturated at shallower depths. The optimal decompression strategy for deep bounce dives remains unknown (2016).
The practical efficacy of gas switches from helium-based diluent to nitrox for accelerating decompression has not been demonstrated convincingly. These switches increase risk of inner ear decompression sickness due to counterdiffusion effects.
Besides the basic dive profile and gas mixes, and the residual gas load from previous dives, three groups of factors are considered likely to have significant influence on decompression stress, the evolution of bubbles in the diver, and development of symptoms. These are exercise, before, during and after the dive, Thermal status, during and after the dive, including the effects on perfusion distribution and changes during the dive, and the set of factors grouped under the label "predisposition", such as the state of hydration, physical fitness, age, biological health, and other characteristics which could affect the uptake and release of gases in the diver. Currently these factors cannot be used to make reproducible predictions about decompression risk, and some cannot be numerically evaluated in real time.
== Teaching of decompression theory ==
Decompression is an area where you discover that, the more you learn, the more you know that you really don't know what is going on. For behind the "black-and-white" exactness of table entries, the second-by-second countdowns of dive computers, and beneath the mathematical purity of decompression models, lurks a dark and mysterious physiological jungle that has barely been explored.
— Karl E. Huggins, 1992
Exposure to the various theories, models, tables and algorithms is needed to allow the diver to make educated and knowledgeable decisions regarding their personal decompression needs. Basic decompression theory and use of decompression tables is part of the theory component of training for commercial divers, and dive planning based on decompression tables, and the practice and field management of decompression is a significant part of the work of the diving supervisor. Recreational divers are trained in the theory and practice of decompression to the extent that the certifying agency specifies in the training standard for each certification. This may vary from a rudimentary overview sufficient to allow the diver to avoid decompression obligation for entry level divers, to competence in the use of several decompression algorithms by way of personal dive computers, decompression software, and tables for advanced technical divers. The detailed understanding of decompression theory is not generally required of either commercial or recreational divers.
== See also ==
Decompression (diving) – Pressure reduction and its effects during ascent from depth
Decompression practice – Techniques and procedures for safe decompression of divers
Decompression sickness – Disorder caused by dissolved gases forming bubbles in tissues
Dive computer – Instrument to calculate decompression status in real time
Equivalent air depth – Method of comparing decompression requirements for air and a given nitrox mix
Equivalent narcotic depth – Method for comparing the narcotic effects of a mixed diving gas with air
History of decompression research and development – Chronological list of notable events in the history of diving decompression.
Hyperbaric treatment schedules – Planned hyperbaric exposure using a specified breathing gas as medical treatment
Oxygen window – Physiological effect of oxygen metabolism on the total dissolved gas concentration in venous blood
Physiology of decompression – The physiological basis for decompression theory and practice
Decompression models:
Bühlmann decompression algorithm – Mathematical model of tissue inert gas uptake and release with pressure change
Haldane's decompression model – Decompression model developed by John Scott Haldane
Reduced gradient bubble model – Decompression algorithm
Thalmann algorithm – Mathematical model for diver decompression
Thermodynamic model of decompression – Early model in which decompression is controlled by volume of gas bubbles forming in tissues
Varying Permeability Model – Decompression model and algorithm based on bubble physics
== Notes ==
1. ^a autochthonous: formed or originating in the place where found
== References ==
=== Sources ===
Hamilton, Robert W.; Thalmann, Edward D. (2003). "10.2: Decompression Practice". In Brubakk, Alf O.; Neuman, Tom S. (eds.). Bennett and Elliott's physiology and medicine of diving (5th Revised ed.). United States: Saunders. pp. 455–500. ISBN 978-0-7020-2571-6. OCLC 51607923.
Huggins, Karl E. (1992). Dynamics of decompression workshop. Course Taught at the University of Michigan (Report).
Thalmann, E.D. (1984). Phase II testing of decompression algorithms for use in the U.S. Navy underwater decompression computer. Navy Exp. Diving Unit Res. Report (Report). Vol. 1–84.
Thalmann, E.D. (1985). Development of a Decompression Algorithm for Constant Oxygen Partial Pressure in Helium Diving. Navy Experimental Diving Unit Research Report (Report). Vol. 1–85.
US Navy (2008). US Navy Diving Manual, 6th revision. United States: US Naval Sea Systems Command. Retrieved 15 June 2008.
Wienke, Bruce R.; O'Leary, Timothy R. (13 February 2002). "Reduced gradient bubble model: Diving algorithm, basis and comparisons" (PDF). Tampa, Florida: NAUI Technical Diving Operations. Retrieved 25 January 2012.
Yount, D.E. (1991). Hans-Jurgen, K.; Harper Jr, D.E. (eds.). "Gelatin, bubbles, and the bends". International Pacifica Scientific Diving..., (Proceedings of the American Academy of Underwater Sciences Eleventh Annual Scientific Diving Symposium Held 25–30 September 1991. University of Hawaii, Honolulu, Hawaii).
== Further reading ==
Ball, R; Himm, J; Homer, LD; Thalmann, ED (1995). "Does the time course of bubble evolution explain decompression sickness risk?". Undersea and Hyperbaric Medicine. 22 (3): 263–280. ISSN 1066-2936. PMID 7580767.
Gerth, Wayne A; Doolette, David J. (2007). "VVal-18 and VVal-18M Thalmann Algorithm – Air Decompression Tables and Procedures". Navy Experimental Diving Unit, TA 01-07, NEDU TR 07-09.
Gribble, M. de G. (1960); A comparison of the High-Altitude and High-Pressure syndromes of decompression sickness, Br. J. Ind. Med., 1960, 17, 181.
Hills. B. (1966); A thermodynamic and kinetic approach to decompression sickness. Thesis
Lippmann, John; Mitchell, Simon (2005). Deeper into Diving (2nd ed.). Melbourne, Australia: J L Publications. ISBN 0-9752290-1-X.
Parker, E. C.; S.S. Survanshi; P.K. Weathersby & E.D. Thalmann (1992). "Statistically Based Decompression Tables VIII: Linear Exponential Kinetics". Naval Medical Research Institute Report. 92–73.
Salama, Asser (2018). Deep into Deco. Florida: Best Pub. ISBN 978-1-947239-09-8.
Powell, Mark (2008). Deco for Divers. Southend-on-Sea: Aquapress. ISBN 978-1-905492-07-7. | Wikipedia/Decompression_theory |
The science of underwater diving includes those concepts which are useful for understanding the underwater environment in which diving takes place, and its influence on the diver. It includes aspects of physics, physiology and oceanography. The practice of scientific work while diving is known as Scientific diving. These topics are covered to a greater or lesser extent in diver training programs, on the principle that understanding the concepts may allow the diver to avoid problems and deal with them more effectively when they cannot be avoided.
A basic understanding of the physics of the underwater environment is foundational to the understanding of the short and long term physiological effects on the diver, and the associated hazards of the diving environment and their consequences which are inherent to diving.
== Physics ==
Diving physics are the aspects of physics which directly affect the underwater diver and explain the effects that divers and their equipment are subject to underwater which differ from the normal human experience out of water.
These effects are mostly consequences of immersion in water; buoyancy, the hydrostatic pressure of depth, the effects of the pressure on breathing gases and gas spaces in the diver and equipment, the inertial and viscous effects on diver movement, and the heat transfer effects. Other effects are the physical influences of the underwater environment on human sensory perception. An understanding of the physics are useful when considering the physiological effects of diving, the hazards and risks of diving, the working of underwater breathing apparatus, buoyancy control and buoyant lifting.
Other foundational knowledge of physics for diving includes the properties of gases and breathing gas mixtures under variations of absolute pressure and temperature, and the solubility of gases in fluids.
== Physiology ==
The human physiology of underwater diving is the physiological influences of the underwater environment on human divers, and adaptations to operating underwater, both during breath-hold dives and while breathing at ambient pressure from a suitable breathing gas supply. It, therefore, includes both the physiology of breath-hold diving in humans, and the range of physiological effects generally limited to human ambient pressure divers either freediving or using underwater breathing apparatus. Several factors affect the diver, including immersion, exposure to the water, the limitations of breath-hold endurance, variations in ambient pressure, the effects of breathing gases at raised ambient pressure, effects caused by the use of breathing apparatus, and sensory impairment. All of these may affect diver performance and safety.
Immersion affects fluid balance, circulation and work of breathing. Exposure to cold water can result in the harmful cold shock response, the helpful diving reflex and excessive loss of body heat. Breath-hold duration is limited by oxygen reserves, and the risk of hypoxic blackout, which has a high associated risk of drowning.
Large or sudden changes in ambient pressure have the potential for injury known as barotrauma. Breathing under pressure involves several effects. Metabolically inactive gases are absorbed by the tissues and may have narcotic or other undesirable effects, and must be released slowly to avoid the formation of bubbles during decompression. Metabolically active gases have a greater effect in proportion to their concentration, which is proportional to their partial pressure, which for contaminants is increased in proportion to absolute ambient pressure.
Work of breathing is increased by increased density of the breathing gas, artifacts of the breathing apparatus, and hydrostatic pressure variations due to posture in the water. High work of breathing and large combinations of physiological and mechanical dead space can lead to hypercapnia, which may induce a panic response.
The underwater environment also affects sensory input, which can impact on safety and the ability to function effectively at depth.
Other physiological effects become apparent at greater depths and where alternative breathing gas mixtures are used to mitigate some of these effects. Nitrogen narcosis occurs under high partial pressures of nitrogen, and helium is substituted to avoid or reduce this effect. High pressure nervous syndrome affects divers breathing helium mixes during rapid compression to high pressures, Compression arthralgia can also affect divers during rapid compression to high pressures. Long decompression times can be reduced by higher oxygen content of breathing gas, but this can expose the diver to oxygen toxicity effects, and changing from helium to nitrogen diluted gases during decompression can cause isobaric counterdiffusion problems. Toxicity of breathing gas contaminants is proportional to partial pressure, and a gas which may have no effect at the surface can be dangerously toxic at higher ambient pressure.
Hypoxia of ascent can affect freedivers and rebreather divers, and in occasional circumstances scuba and surface-supplied divers, and can be a killer, as the diver can lose consciousness without warning and consequently drown or asphyxiate.
== Environment ==
The ocean and aquatic environment is described by oceanography and limnology. These are directly influenced by aspects of geology, weather and climate. The underwater environment is inhabited by organisms of great diversity, some of which may be hazardous to the diver, or affect the dive in some way.
Sufficient knowledge and a basic understanding of the expected environment for an intended dive allow the diver to predict the conditions which may reasonably be expected during the dive, and allow reasonable estimation of hazards and associated risk, which allows effective dive planning. There are a range of environmental hazards which should be considered during dive planning.
The other side of understanding of the environment by divers is the impact of diving activity on the environment. The environmental impact of recreational diving on the popular tropical coral reef environment has been extensively studied, and there are known adverse effects due to poor diving skills and lack of environmental awareness, which can be addressed by training and education. While commercial diving operations can also have significant environmental impact, they are less frequent, and where environmental impact is expected to be an issue it should be considered in the environmental impact study for the specific contract or project. Similarly, scientific diving environmental impact should be estimated during planning, and be subject to acceptance by the relevant ethics committee.
A basic understanding of the practical relevance of some environmental factors that influence diving operations is useful, such as:
Algal bloom – Spread of planktonic algae in water
Current (stream) – Flow of water in a natural watercourse due to gravity
Longshore drift – Sediment moved by the longshore current
Ocean current – Directional mass flow of oceanic water
Rip current – Water current moving away from shore
Tidal race – Fast-moving tidal flow passing through a constriction, forming waves, eddies and strong currents
Undertow (water waves) – Return flow below nearshore water waves.
Upwelling – Oceanographic phenomenon of wind-driven motion of ocean water
Ekman transport – Net transport of surface water perpendicular to wind direction
Halocline – Stratification of a body of water due to salinity differences
Reef – Shoal of rock, coral, or other material lying beneath the surface of water
Coral reef – Outcrop of rock in the sea formed by the growth and deposit of stony coral skeletons
Stratification (water) – Layering of a body of water due to density variations
Thermocline – Distinct layer of temperature change in a body of water
Tide – Rise and fall of the sea level under astronomical gravitational influences
Turbidity – Cloudiness of a fluid
Wind wave – Surface waves generated by wind on open water
Breaking wave, also known as Surf – Wave that becomes unstable as a consequence of excessive steepness
Surge (wave action) – The component of wave motion close to and parallel with the bottom
Swell (ocean) – Series of waves generated by distant weather systems
Wave shoaling – Effect by which surface waves entering shallower water change in wave height
== References == | Wikipedia/Science_of_underwater_diving |
Oxygen therapy, also referred to as supplemental oxygen, is the use of oxygen as medical treatment. Supplemental oxygen can also refer to the use of oxygen enriched air at altitude. Acute indications for therapy include hypoxemia (low blood oxygen levels), carbon monoxide toxicity and cluster headache. It may also be prophylactically given to maintain blood oxygen levels during the induction of anesthesia. Oxygen therapy is often useful in chronic hypoxemia caused by conditions such as severe COPD or cystic fibrosis. Oxygen can be delivered via nasal cannula, face mask, or endotracheal intubation at normal atmospheric pressure, or in a hyperbaric chamber. It can also be given through bypassing the airway, such as in ECMO therapy.
Oxygen is required for normal cellular metabolism. However, excessively high concentrations can result in oxygen toxicity, leading to lung damage and respiratory failure. Higher oxygen concentrations can also increase the risk of airway fires, particularly while smoking. Oxygen therapy can also dry out the nasal mucosa without humidification. In most conditions, an oxygen saturation of 94–96% is adequate, while in those at risk of carbon dioxide retention, saturations of 88–92% are preferred. In cases of carbon monoxide toxicity or cardiac arrest, saturations should be as high as possible. While air is typically 21% oxygen by volume, oxygen therapy can increase O2 content of air up to 100%.
The medical use of oxygen first became common around 1917, and is the most common hospital treatment in the developed world. It is currently on the World Health Organization's List of Essential Medicines. Home oxygen can be provided either by oxygen tanks or oxygen concentrator.
== Medical uses ==
Oxygen is widely used by hospitals, EMS, and first-aid providers in a variety of conditions and settings. A few indications frequently requiring high-flow oxygen include resuscitation, major trauma, anaphylaxis, major bleeding, shock, active convulsions, and hypothermia.
=== Acute conditions ===
In context of acute hypoxemia, oxygen therapy should be titrated to a target level based on pulse oximetry (94–96% in most patients, or 88–92% in people with COPD). This can be performed by increasing oxygen delivery, described as FIO2(fraction of inspired oxygen). In 2018, the British Medical Journal recommended that oxygen therapy be stopped for saturations greater than 96% and not started for saturations above 90 to 93%. This may be due to an association between excessive oxygenation in the acutely ill and increased mortality. Exceptions to these recommendations include carbon monoxide poisoning, cluster headaches, sickle cell crisis, and pneumothorax.
Oxygen therapy has also been used as emergency treatment for decompression sickness for years. Recompression in a hyperbaric chamber with 100% oxygen is the standard treatment for decompression illness. The success of recompression therapy is greatest if given within four hours after resurfacing, with earlier treatment associated with a decreased number of recompression treatments required for resolution. It has been suggested in literature that heliox may be a better alternative to oxygen therapy.
In the context of stroke, oxygen therapy may be beneficial as long as hyperoxic environments are avoided.
People receiving outpatient oxygen therapy for hypoxemia following acute illness or hospitalization should be re-assessed by a physician prior to prescription renewal to gauge the necessity of ongoing oxygen therapy. If the initial hypoxemia has resolved, additional treatment may be an unnecessary use of resources.
=== Chronic conditions ===
Common conditions which may require a baseline of supplementary oxygen include chronic obstructive pulmonary disease (COPD), chronic bronchitis, and emphysema. Patients may also require additional oxygen during acute exacerbations. Oxygen may also be prescribed for breathlessness, end-stage cardiac failure, respiratory failure, advanced cancer, or neurodegenerative disease in spite of relatively normal blood oxygen levels. Physiologically, it may be indicated in people with arterial oxygen partial pressure PaO2 ≤ 55mmHg (7.3kPa) or arterial oxygen saturation SaO2 ≤ 88%.
Careful titration of oxygen therapy should be considered in patients with chronic conditions predisposing them to carbon dioxide retention (e.g., COPD, emphysema). In these instances, oxygen therapy may decrease respiratory drive, leading to accumulation of carbon dioxide (hypercapnia), acidemia, and increased mortality secondary to respiratory failure. Improved outcomes have been observed with titrated oxygen treatment largely due to gradual improvement of the ventilation/perfusion ratio. The risks associated with loss of respiratory drive are far outweighed by the risks of withholding emergency oxygen, so emergency administration of oxygen is never contraindicated. Transfer from the field to definitive care with titrated oxygen typically occurs long before significant reductions to the respiratory drive are observed.
=== Contraindications ===
There are certain situations in which oxygen therapy has been shown to negatively impact a person's condition.
Oxygen therapy can exacerbate the effects of paraquat poisoning and should be withheld unless severe respiratory distress or respiratory arrest is present. Paraquat poisoning is rare, with about 200 deaths globally from 1958 to 1978.
Oxygen therapy is not recommended for people with pulmonary fibrosis or bleomycin-associated lung damage.
ARDS caused by acid aspiration may be exacerbated with oxygen therapy according to some animal studies.
Hyperoxic environments should be avoided in cases of sepsis.
=== Adverse effects ===
In some instances, oxygen delivery can lead to particular complications in population subsets.
In infants with respiratory failure, administration of high levels of oxygen can sometimes promote overgrowth of new blood vessels in the eye leading to blindness. This phenomenon is known as retinopathy of prematurity (ROP).
In rare instances, people receiving hyperbaric oxygen therapy have had seizures, which has been previously attributed to oxygen toxicity.
There is some evidence that extended HBOT can accelerate development of cataracts.
=== Alternative medicine ===
Some practitioners of alternative medicine have promoted "oxygen therapy" as a cure for many human ailments including AIDS, Alzheimer's disease and cancer. According to the American Cancer Society, "available scientific evidence does not support claims that putting oxygen-releasing chemicals into a person's body is effective in treating cancer", and some of these treatments can be dangerous.
== Physiologic effects ==
Oxygen supplementation has a variety of physiologic effects on the human body. Whether or not these effects are adverse to a patient is dependent upon clinical context. Cases in which an excess amount of oxygen is available to organs is known as hyperoxia. While the following effects may observed with noninvasive high-dose oxygen therapy (i.e., not ECMO), delivery of oxygen at higher pressures is associated with exacerbation of the following associated effects.
=== Absorption atelectasis ===
It has been hypothesized that oxygen therapy may promote accelerated development of atelectasis (partial or complete lung collapse), as well as denitrogenation of gas cavities (e.g., pneumothorax, pneumocephalus). This concept is based on the idea that oxygen is more quickly absorbed compared to nitrogen within the body, leading oxygen-rich areas that are poorly ventilated to be rapidly absorbed, leading to atelectasis. It is thought that higher fractions of inhaled oxygen (FIO2) are associated with increasing rates of atelectasis in the clinical scenario. In clinically healthy adults, it is believed that absorption atelectasis typically does not have any significant implications when managed properly.
=== Airway inflammation ===
In regard to the airway, both tracheobronchitis and mucositis have been observed with high levels of oxygen delivery (typically >40% O2). Within the lungs, these elevated concentrations of oxygen have been associated with increased alveolar toxicity (coined the Lorrain-Smith effect). Mucosal damage is observed to increase with elevated atmospheric pressure and oxygen concentrations, which may result in the development of ARDS and possibly death.
=== Central nervous system effects ===
Decreased cerebral blood flow and intracranial pressure (ICP) have been reported in hyperoxic conditions, with mixed results regarding impact on cognition. Hyperoxia as also been associated with seizures, cataract formation, and reversible myopia.
=== Hypercapnea ===
Among CO2 retainers, excess exposure to oxygen in context of the Haldane effect causes decreased binding of deoxyhemoglobin to CO2 in the blood. This unloading of CO2 may contribute to the development of acid-base disorders due to the associated increase in PaCO2 (hypercapnea). Patients with underlying lung disease such as COPD may not be able to adequately clear the additional CO2 produced by this effect, worsening their condition. In addition, oxygen therapy has also been shown to decrease respiratory drive, further contributing to possible hypercapnea.
=== Immunological effects ===
Hyperoxic environments have been observed to decrease granulocyte rolling and diapedesis in specific circumstances in humans. In regard to anaerobic infections, cases of necrotizing fasciitis have been observed to require fewer debridement operations and have improvement in regard to mortality in patients treated with hyperbaric oxygen therapy. This may stem from oxygen intolerance of otherwise anaerobic microorganisms.
=== Oxidative stress ===
Sustained exposure to oxygen may overwhelm the body's capacity to deal with oxidative stress. Rates of oxidative stress appears to be influenced by both oxygen concentration and length of exposure, with general toxicity observed to occur within hours in certain hyperoxic conditions.
=== Reduction in erythropoiesis ===
Hyperoxia is observed to result in a serum reduction in erythropoietin, resulting in reduced stimulus for erythropoiesis. Hyperoxia at normobaric environments does not appear to be able to halt erythropoiesis completely.
=== Pulmonary vasodilation ===
Within the lungs, hypoxia is observed to be a potent pulmonary vasoconstrictor, due to inhibition of an outward potassium current and activation of inward sodium current leading to pulmonary vascular muscular contraction. However, the effects of hyperoxia do not seem to have a particularly strong vasodilatory effect from the few studies that have been performed on patients with pulmonary hypertension. As a result, an effect appears to be present but minor.
=== Systemic vasoconstriction ===
In the systemic vasculature, oxygen serves as a vasoconstrictor, leading to mildly increased blood pressure and decreased cardiac output and heart rate. Hyperbaric conditions do not seem to have a significant impact on these overall physiologic effects. Clinically, this may lead to increased left-to-right shunting in certain patient populations, such as those with atrial septal defect. While the mechanism of the vasoconstriction is unknown, one proposed theory is that increased reactive oxygen species from oxygen therapy accelerates the degradation of endothelial nitric oxide, a vasodilator. These vasoconstrictive effects are thought to be the underlying mechanism helping to abort cluster headaches.
Dissolved oxygen in hyperoxic conditions may make also a significant contribution to total gas transport.
== Storage and sources ==
Oxygen can be separated by a number of methods (e.g., chemical reaction, fractional distillation) to enable immediate or future use. The main methods utilized for oxygen therapy include:
Liquid storage – Liquid oxygen is stored in insulated tanks at low temperature and allowed to boil (at a temperature of 90.188 K (−182.96 °C)) during use, releasing gaseous oxygen. This method is widely utilized at hospitals due to high oxygen requirements. See Vacuum Insulated Evaporator for more information on this method of storage.
Compressed gas storage – Oxygen gas is compressed in a gas cylinder, which provides a convenient storage method (refrigeration not required). Large oxygen cylinders hold a volume of 6,500 litres (230 cu ft) and can last about two days at a flow rate of 2 litres per minute (LPM). A small portable M6 (B) cylinder holds 164 or 170 litres (5.8 or 6.0 cu ft) and weighs about 1.3 to 1.6 kilograms (2.9 to 3.5 lb). These tanks can last 4–6 hours with a conserving regulator, which adjust flow based on a person's breathing rate. Conserving regulators may not be effective for patients who breathe through their mouth.
Instant usage – The use of an electrically powered oxygen concentrator or a chemical reaction based unit can create sufficient oxygen for immediate personal use. These units (especially the electrically powered versions) are widely used for home oxygen therapy as portable personal oxygen. One particular advantage includes continuous supply without need for bulky oxygen cylinders.
=== Hazards and risk ===
Highly concentrated sources of oxygen also increase risk for rapid combustion. Oxygen itself is not flammable, but the addition of concentrated oxygen to a fire greatly increases its intensity, and can aid the combustion of materials that are relatively inert under normal conditions. Fire and explosion hazards exist when concentrated oxidants and fuels are brought together in close proximity, although an ignition event (e.g., heat or spark) is needed to trigger combustion.
Concentrated oxygen will allow combustion to proceed rapidly and energetically. Steel pipes and storage vessels used to store and transmit both gaseous and liquid oxygen will act as a fuel; and therefore the design and manufacture of oxygen systems requires special training to ensure that ignition sources are minimized. Highly concentrated oxygen in a high-pressure environment can spontaneously ignite hydrocarbons such as oil and grease, resulting in a fire or explosion. The heat caused by rapid pressurization serves as the ignition source. For this reason, storage vessels, regulators, piping and any other equipment used with highly concentrated oxygen must be "oxygen-clean" prior to use to ensure the absence of potential fuels. This does not only apply to pure oxygen; any concentration significantly higher than atmospheric (approximately 21%) carries a potential ignition risk.
Some hospitals have instituted "no-smoking" policies which can help keep ignition sources away from medically piped oxygen. These policies do not eliminate the risk of injury among patients with portable oxygen systems, especially among smokers. Other potential sources of ignition include candles, aromatherapy, medical equipment, cooking, and deliberate vandalism.
== Delivery ==
Various devices are used for oxygen administration. In most cases, the oxygen will first pass through a pressure regulator, used to control the high pressure of oxygen delivered from a cylinder (or other source) to a lower pressure. This lower pressure is then controlled by a flowmeter (which may be preset or selectable) which controls the flow at a measured rate (e.g., litres per minute [LPM]). The typical flowmeter range for medical oxygen is between 0 and 15 LPM with some units capable of obtaining up to 25 LPM. Many wall flowmeters using a Thorpe tube design are able to be dialed to "flush" oxygen which is beneficial in emergency situations.
=== Low-dose oxygen ===
Many people only require slight increases in inhaled oxygen, rather than pure or near-pure oxygen. These requirements can be met through a number of devices dependent on situation, flow requirements, and personal preference.
A nasal cannula (NC) is a thin tube with two small nozzles inserted into a person's nostrils. It can provide oxygen at low flow rates, 1–6 litres per minute (LPM), delivering an oxygen concentration of 24–40%.
There are also a number of face mask options, such as the simple face mask, often used at between 5 and 10 LPM, capable of delivering oxygen concentrations between 35% and 55%. This is closely related to the more controlled air-entrainment masks, also known as Venturi masks, which can accurately deliver a predetermined oxygen concentration from 24 to 50%.
In some instances, a partial rebreathing mask can be used, which is based on a simple mask, but features a reservoir bag, which can provide oxygen concentrations of 40–70% at 5–15 LPM.
Demand oxygen delivery systems (DODS) or oxygen resuscitators deliver oxygen only when the person inhales or the caregiver presses a button on the mask (e.g., nonbreathing patient). These systems greatly conserve oxygen compared to steady-flow masks, and are useful in emergency situations when a limited supply of oxygen is available and there is a delay in transporting the person to higher care. Due to utilization of a variety of methods for oxygenation requirements performance differences arise. They are very useful in CPR, as the caregiver can deliver rescue breaths composed of 100% oxygen with the press of a button. Care must be taken not to over-inflate the person's lungs, for which some systems employ safety valves. These systems may not be appropriate for people who are unconscious or in respiratory distress because of the required respiratory effort.
=== High flow oxygen delivery ===
For patients requiring high concentrations of oxygen, a number of devices are available. The most commonly utilized device is the non-rebreather mask (or reservoir mask). Non-rebreather masks draw oxygen from attached reservoir bags with one-way valves that direct exhaled air out of the mask. If flow rate is not sufficient (~10L/min), the bag may collapse on inspiration. This type of mask is indicated for acute medical emergencies. The delivered FIO2 (Inhalation volumetric fraction of molecular oxygen) of this system is 60–80%, depending on oxygen flow and breathing pattern.
Another type of device is a humidified high flow nasal cannula which enables flows exceeding a person's peak inspiratory flow demand to be delivered via nasal cannula, thus providing FIO2 of up to 100% because there is no entrainment of room air. This also allows the person to continue to talk, eat, and drink while still receiving therapy. This type of delivery method is associated with greater overall comfort, improved oxygenation, respiratory rates and reduced sputumstatis compared with face mask oxygen.
In specialist applications such as aviation, tight-fitting masks can be used. These masks also have applications in anaesthesia, carbon monoxide poisoning treatment and in hyperbaric oxygen therapy.
=== Positive pressure delivery ===
Patients who are unable to breathe on their own will require positive pressure to move oxygen into their lungs for gaseous exchange to take place. Systems for delivery vary in complexity and cost, starting with a basic pocket mask adjunct which can be used to manually deliver artificial respiration with supplemental oxygen delivered through a mask port.
Many emergency medical service members, first aid personnel, and hospital staff may use a bag-valve-mask (BVM), which is a malleable bag attached to a face mask (or invasive airway such as an endotracheal tube or laryngeal mask airway), usually with a reservoir bag attached, which is manually manipulated by the healthcare professional to push oxygen (or air) into the lungs. This is the only procedure allowed for initial treatment of cyanide poisoning in the UK workplace.Automated versions of the BVM system, known as a resuscitator or pneupac can also deliver measured and timed doses of oxygen directly to people through a facemask or airway. These systems are related to the anaesthetic machines used in operations under general anaesthesia that allow a variable amount of oxygen to be delivered, along with other gases including air, nitrous oxide and inhalational anaesthetics.
=== Drug delivery ===
Oxygen and other compressed gases are used in conjunction with a nebulizer to allow delivery of medications to the upper and/or lower airways. Nebulizers use compressed gas to propel liquid medication into therapeutically sized aerosol droplets for deposition to the appropriate portion of the airway. A typical compressed gas flow rate of 8–10 L/min is used to nebulize medications, saline, sterile water, or a combination these treatments into a therapeutic aerosol for inhalation. In the clinical setting, room air (ambient mix of several gasses), molecular oxygen, and Heliox are the most common gases used to nebulize a bolus treatment or a continuous volume of therapeutic aerosols.
=== Exhalation filters for oxygen masks ===
Filtered oxygen masks have the ability to prevent exhaled particles from being released into the surrounding environment. These masks are normally of a closed design such that leaks are minimized and breathing of room air is controlled through a series of one-way valves. Filtration of exhaled breaths is accomplished either by placing a filter on the exhalation port or through an integral filter that is part of the mask itself. These masks first became popular in the Toronto (Canada) healthcare community during the 2003 SARS Crisis. SARS was identified as being respiratory based, and it was determined that conventional oxygen therapy devices were not designed for the containment of exhaled particles. In 2003, the HiOx80 oxygen mask was released for sale. The HiOx80 mask is a closed design mask that allows a filter to be placed on the exhalation port. Several new designs have emerged in the global healthcare community for the containment and filtration of potentially infectious particles. Other designs include the ISO-O2 oxygen mask, the Flo2Max oxygen mask, and the O-Mask.
Typical oxygen masks allow a person to breathe in a mixture of room air and therapeutic oxygen. However, as filtered oxygen masks use a closed design that minimizes or eliminates the person's contact with and ability to inhale room air, delivered oxygen concentrations in such devices have been found to be elevated, approaching 99% using adequate oxygen flows. Because all exhaled particles are contained within the mask, nebulized medications are also prevented from releasing into the surrounding atmosphere, decreasing the occupational exposure to healthcare staff and other people.
=== Aircraft ===
In the United States, most airlines restrict the devices allowed on board an aircraft. As a result, passengers are restricted in what devices they can use. Some airlines will provide cylinders for passengers with an associated fee. Other airlines allow passengers to carry on approved portable concentrators. However, the lists of approved devices varies by airline so passengers may need to check with any airline they are planning to fly on. Passengers are generally not allowed to carry on personal cylinders. In all cases, passengers need to notify the airline in advance of their equipment.
Effective May 13, 2009, the Department of Transportation and FAA ruled that a select number of portable oxygen concentrators are approved for use on all commercial flights. FAA regulations require larger airplanes to carry D-cylinders of oxygen for use in case of an emergency.
=== Oxygen conserving devices ===
Since the 1980s, devices have been available which conserve stored oxygen by delivering it during the portion of the breathing cycle when it is more effectively used. This has the effect of stored oxygen lasting longer, or a smaller, and therefore lighter, portable oxygen delivery system being practicable. This class of device can also be used with portable oxygen concentrators, making them more efficient.
The delivery of supplemental oxygen is most effective if it is made at a point in the breathing cycle when it will be inhaled to the alveoli, where gas transfer occurs. oxygen delivered later in the cycle will be inhaled into physiological dead space, wher it serves no useful purpose as it cannot diffuse into the blood. Oxygen delivered during stages of the breathing cycle in which it is not inhaled is also wasted.
A continuous constant flow rate uses a simple regulator, but is inefficient as a high percentage of the delivered gas does not reach the alveoli, and over half is not inhaled at all. A system which accumulates free-flow oxygen during resting and exhalation stages, (reservoir cannulas) makes a larger part of the oxygen available for inhalation, and it will be selectively inhaled during the initial part of inhalation, which reaches furthest into the lungs. A similar function is provided by a mechanical demand regulator which provides gas only during inhalation, but requires some physical effort by the user, and also ventilates dead space with oxygen. A third class of system (pulse dose oxygen conserving device, or demand pulse devices) senses the start of inhalation and provides a metered bolus, which if correctly matched to requirements, will be sufficient and effectively inhaled into the alveoli.Such systems can be pneumatically or electrically controlled.
Adaptive demand systems
A development in pulse demand delivery are devices that automatically adjust the volume of the pulsed bolus to suit the activity level of the user. This adaptive response in intended to reduce desaturation responses caused by exercise rate variation.
Pulsed delivery devices are available as stand alone modules or integrated into a system specifically designed to use compressed gas, liquid oxygen or oxygen concentrator sources. Integrated design usually allows optimisation of the system for the source type at the cost of versatility.
Transtracheal oxygen catheters are inserted directly into the trachea through a small opening in the front of the neck for that purpose. The opening is directed downward, towards the bifurcation of the bronchi. Oxygen introduced through the catheter bypasses the dead spaces of the nose, pharynx and upper trachea during inhalation, and during continuous flow, will accumulate in the anatomic dead space at the end of exhalation and be available for immediate inhalation to the alveoli on the following inhalation. This reduces wastage and provides efficiency roughly three times greater than with external continuous flow. This is roughly equivalent to a reservoir cannula. Transtracheal catheters have been found to be effective during rest, exercise and sleep.
== See also ==
Bottled oxygen (climbing) – Equipment which allows the user to breathe at hypoxic altitudesPages displaying short descriptions of redirect targets
Breathing gas – Gas used for human respiration
Emergency medical services – Services providing acute medical care
Hyperbaric oxygen therapy – Treatment using oxygen at raised ambient pressure
Mechanical ventilation – Method to mechanically assist or replace spontaneous breathing
Nebulizer – Drug delivery device
Oxygen bar – Establishment that sells oxygen for on-site recreational use
Oxygen firebreak – Safety mechanism designed to extinguish a fire in a medical oxygen delivery tube
Oxygen tent – Canopy over a patient to provide supplemental oxygen
Respiratory therapist – Practitioner in cardio-pulmonary medicine
Redento D. Ferranti - Early use of oxygen therapy in the U.S. as an effective approach to rehabilitation for COPD patients.
== References ==
== Further reading ==
Cahill Lambert AE (November 2005). "Adult domiciliary oxygen therapy: a patient's perspective". The Medical Journal of Australia. 183 (9): 472–3. doi:10.5694/j.1326-5377.2005.tb07125.x. PMID 16274348. S2CID 77689244.
Kallstrom TJ (June 2002). "AARC Clinical Practice Guideline: oxygen therapy for adults in the acute care facility--2002 revision & update". Respiratory Care. 47 (6): 717–20. PMID 12078655.
"Study: Change in how medics use oxygen could reduce deaths". Lexipol. November 5, 2010. Retrieved 2025-03-17. (see comments for study meta-analysis) | Wikipedia/Oxygen_therapy |
A diving weighting system is ballast weight added to a diver or diving equipment to counteract excess buoyancy. They may be used by divers or on equipment such as diving bells, submersibles or camera housings.
Divers wear diver weighting systems, weight belts or weights to counteract the buoyancy of other diving equipment, such as diving suits and aluminium diving cylinders, and buoyancy of the diver. The scuba diver must be weighted sufficiently to be slightly negatively buoyant at the end of the dive when most of the breathing gas has been used, and needs to maintain neutral buoyancy at safety or obligatory decompression stops. During the dive, buoyancy is controlled by adjusting the volume of air in the buoyancy compensation device (BCD) and, if worn, the dry suit, in order to achieve negative, neutral, or positive buoyancy as needed. The amount of weight required is determined by the maximum overall positive buoyancy of the fully equipped but unweighted diver anticipated during the dive, with an empty buoyancy compensator and normally inflated dry suit. This depends on the diver's mass and body composition, buoyancy of other diving gear worn (especially the diving suit), water salinity, weight of breathing gas consumed, and water temperature. It normally is in the range of 2 kilograms (4.4 lb) to 15 kilograms (33 lb). The weights can be distributed to trim the diver to suit the purpose of the dive.
Surface-supplied divers may be more heavily weighted to facilitate underwater work, and may be unable to achieve neutral buoyancy, and rely on the diving stage, bell, umbilical, lifeline, shotline or jackstay for returning to the surface.
Freedivers may also use weights to counteract buoyancy of a wetsuit. However, they are more likely to weight for neutral buoyancy at a specific depth, and their weighting must take into account not only the compression of the suit with depth, but also the compression of the air in their lungs, and the consequent loss of buoyancy. As they have no decompression obligation, they do not have to be neutrally buoyant near the surface at the end of a dive.
If the weights have a method of quick release, they can provide a useful rescue mechanism: they can be dropped in an emergency to provide an instant increase in buoyancy which should return the diver to the surface. Dropping weights increases the risk of barotrauma and decompression sickness due to the possibility of an uncontrollable ascent to the surface. This risk can only be justified when the emergency is life-threatening or the risk of decompression sickness is small, as is the case in freediving and scuba diving when the dive is well short of the no-decompression limit for the depth. Often divers take great care to ensure the weights are not dropped accidentally, and heavily weighted divers may arrange their weights so subsets of the total weight can be dropped individually, allowing for a somewhat more controlled emergency ascent.
The weights are generally made of lead because of its high density, reasonably low cost, ease of casting into suitable shapes, and resistance to corrosion. The lead can be cast in blocks, cast shapes with slots for straps, or shaped as pellets known as "shot" and carried in bags. There is some concern that lead diving weights may constitute a toxic hazard to users and environment, but little evidence of significant risk.
== Function and use of weights ==
Diver weighting systems have two functions; ballast, and trim adjustment.
=== Ballast ===
The primary function of diving weights is as ballast, to prevent the diver from floating at times when he or she wishes to remain at depth.
==== Freediving ====
In freediving (breathhold) the weight system is almost exclusively a weight belt with quick release buckle, as the emergency release of the weights will usually allow the diver to float to the surface even if unconscious, where there is at least a chance of rescue. The weights are used mainly to neutralise the buoyancy of the exposure suit, as the diver is nearly neutral in most cases, and there is little other equipment carried. The weights required depend almost entirely on the buoyancy of the suit. Most freedivers will weight themselves to be positively buoyant at the surface, and use only enough weight to minimise the effort required to swim down against the buoyancy at the start of a dive, while retaining sufficient buoyancy at maximum depth to not require too much effort to swim back up to where the buoyancy becomes positive again. As a corollary to this practice, freedivers will use as thin a wetsuit as comfortably possible, to minimise buoyancy changes with depth due to suit compression.
==== Scuba diving ====
Buoyancy control is considered both an essential skill and one of the most difficult for the novice to master. Lack of proper buoyancy control increases the risk of disturbing or damaging the surroundings, and is a source of additional and unnecessary physical effort to maintain precise depth, which also increases stress.
The scuba diver generally has an operational need to control depth without resorting to a line to the surface or holding onto a structure or landform, or resting on the bottom. This requires the ability to achieve neutral buoyancy at any time during a dive, otherwise the effort expended to maintain depth by swimming against the buoyancy difference will both task load the diver and require an otherwise unnecessary expenditure of energy, increasing air consumption, and increasing the risk of loss of control and escalation to an accident. Maintaining depth by finning necessarily directs part of fin thrust upwards or downwards, and when near the bottom, downward thrust can disturb the benthos and stir up silt. The risk of fin-strike damage is also significant.
A further requirement for scuba diving in most circumstances, is the ability to achieve significant positive buoyancy at any point of a dive. When at the surface, this is a standard procedure to enhance safety and convenience, and underwater it is generally a response to an emergency.
The average human body with a relaxed lungful of air is close to neutral buoyancy. If the air is exhaled, most people will sink in fresh water, and with full lungs, most will float in seawater. The amount of weight required to provide neutral buoyancy to the naked diver is usually trivial, though there are some people who require several kilograms of weight to become neutral in seawater due to low average density and large size. This is usually the case with people with a large proportion of body fat. As the diver is nearly neutral, most ballasting is needed to compensate for the buoyancy of the diver's equipment.
The main components of the average scuba diver's equipment which are positively buoyant are the components of the exposure suit. The two most commonly used exposure suit types are the dry suit and the wet suit. Both of these types of exposure suit use gas spaces to provide insulation, and these gas spaces are inherently buoyant. The buoyancy of a wet suit will decrease significantly with an increase in depth as the ambient pressure causes the volume of the gas bubbles in the neoprene to decrease. Measurements of volume change of neoprene foam used for wetsuits under hydrostatic compression show that about 30% of the volume, and therefore 30% of surface buoyancy, is lost in about the first 10 m, another 30% by about 60 m, and the volume appears to stabilise at about 65% loss by about 100 m. The total buoyancy loss of a wetsuit is proportional to the initial uncompressed volume. An average person has a surface area of about 2 m2, so the uncompressed volume of a full one piece 6 mm thick wetsuit will be in the order of 1.75 x 0.006 = 0.0105 m3, or roughly 10 litres. The mass will depend on the specific formulation of the foam, but will probably be in the order of 4 kg, for a net buoyancy of about 6 kg at the surface. Depending on the overall buoyancy of the diver, this will generally require 6 kg of additional weight to bring the diver to neutral buoyancy to allow reasonably easy descent The volume lost at 10 m is about 3litres, or 3 kg of buoyancy, rising to about 6 kg buoyancy lost at about 60 m. This could nearly double for a large person wearing a two-piece suit for cold water. This loss of buoyancy must be balanced by inflating the buoyancy compensator to maintain neutral buoyancy at depth.
A dry suit will also compress with depth, but the air space inside is continuous and can be topped up from a cylinder or vented to maintain an approximately constant volume. A large part of the ballast used by a diver is to balance the buoyancy of this gas space, but if the dry suit has a catastrophic flood, much of this buoyancy may be lost, and some way to compensate is necessary.
Another significant issue in open circuit scuba diver weighting is that the breathing gas is used up during a dive, and this gas has weight, so the total weight of the cylinder decreases, while its volume remains almost unchanged. As the diver needs to be neutral at the end of the dive, particularly at shallow depths for obligatory or safety decompression stops, sufficient ballast weight must be carried to allow for this reduction in weight of gas supply. (the density of air at normal atmospheric pressure is approximately 1.2 kg/m3, or approximately 0.075 lb/ft3) The amount of weight needed to compensate for gas use is easily calculable once the free gas volume and density are known.
Most of the rest of the diver's equipment is negatively buoyant or nearly neutral, and more importantly, does not change in buoyancy during a dive, so its overall influence on buoyancy is static.
While it is possible to calculate the required ballast given the diver and all his or her equipment, this is not done in practice, as all the values would have to be measured accurately. The practical procedure is known as a buoyancy check, and is done by wearing all the equipment, with the tank(s) nearly empty, and the buoyancy compensator empty, in shallow water, and adding or removing weight until the diver is neutrally buoyant. The weight should then be distributed on the diver to provide correct trim, and a sufficient part of the weight should be carried in such a way that it can be removed quickly in an emergency to provide positive buoyancy at any point in the dive. This is not always possible, and in those cases an alternative method of providing positive buoyancy should be used.
A diver ballasted by following this procedure will be negatively buoyant during most of the dive unless the buoyancy compensator is used, to an extent which depends on the amount of breathing gas carried. A recreational dive using a single cylinder may use between 2 and 3 kg of gas during the dive, which is easy to manage, and provided that there is no decompression obligation, end-dive buoyancy is not critical. A long or deep technical dive may use 6 kg of back gas and another 2 to 3 kg of decompression gas. If there is a problem during the dive and reserves must be used, this could increase by up to 50%, and the diver must be able to stay down at the shallowest decompression stop. The extra weight and therefore negative buoyancy at the start of the dive could easily be as much as 13 kg for a diver carrying four cylinders. The buoyancy compensator is partially inflated when needed to support this negative buoyancy, and as breathing gas is used up during the dive, the volume of the buoyancy compensator will be reduced, by venting as required. The inconvenience of additional weight and managing the gas required to compensate for it in a dive that goes according to plan is the price that must be paid for the ability to decompress after an emergency which uses up most of the gas. There is little value in having enough gas to avoid drowning if the diver is killed or crippled by decompression sickness instead.
Examples:
The common 80 ft3 (11 litre, 207 bar) cylinder carries about 6 pounds (2.7 kg) of air when full, so the diver should start the dive about 6 pounds (2.7 kg) negative and use about 1/10 ft3 (2.7 L)of air in the BCD to compensate at the start of a dive.
A twin 12.2 litre 230 bar set carries about 6.7 kilograms (15 lb) of Nitrox when full, so the diver should start the dive about 6.7 kilograms (15 lb) negative and use about 6.7 liters (0.24 cu ft) of gas in the BCD at the start of the dive.
A twin 12.2 litre 230 bar with an 11 litre 207 bar deep deco mix and a 5.5 litre 207 bar shallow deco gas will carry 10.7 kilograms (24 lb) of gas, and while it is unlikely that all will be used on the dive, it is possible, and the diver should be able to remain at the correct depth for decompression until all the gas is used up.
==== Optimum weighting ====
Optimum weighting for scuba allows the diver to achieve neutral buoyancy at any time during a dive while there is still usable breathing gas in any of the cylinders carried, using the least amount of ballast. Deviations from this optimum either make the diver buoyant while there is still usable breathing gas, which is a disadvantage in emergencies where decompression stops are required, or make the diver more negatively buoyant than necessary at the start of the dive with full cylinders, necessitating more gas in the buoyancy compensator for most of the dive, which is more sensitive to buoyancy changes with change in depth, and may make a larger buoyancy compensator necessary. These disadvantages can be compensated by skill, but more attention and effort is required throughout the dive.
==== Surface-supplied diving ====
In surface-supplied diving, and particularly in saturation diving, the loss of weights followed by positive buoyancy can expose the diver to potentially fatal decompression injury. Consequently, weight systems for surface-supplied diving where the diver is transported to the worksite by a diving bell or stage, are usually not provided with a quick-release system.
Much of the work done by surface-supplied divers is on the bottom, and weighted boots may be used to allow the diver to walk upright on the bottom. When working in this mode, several kilograms beyond the requirement for neutralising buoyancy may be useful, so that the diver is reasonably steady on the bottom and can exert useful force when working.
The lightweight demand helmets in general use by surface-supplied divers are integrally ballasted for neutral buoyancy in the water, so they do not float off the diver's head or pull upwards on the neck, but the larger volume free-flow helmets would be too heavy and cumbersome if they had all the required weight built in. Therefore, they are either ballasted after dressing the diver by fastening weights to the lower parts of the helmet assembly, so the weight is carried on the shoulders when out of the water, or the helmet may be held down by a jocking strap and the harness weights provide the ballast.
The traditional copper helmet and corselet were generally weighted by suspending a large weight from support points on the front and back of the corselet, and the diver often also wore weighted boots to assist in remaining upright. The US Navy Mk V standard diving system used a heavy weighted belt buckled around the waist, suspended by shoulder straps which crossed over the breastplate of the helmet, directly transferring the load to the buoyant helmet when immersed, but with a relatively low centre of gravity. Combined with lacing of the suit legs and heavy weighted shoes, this reduced the risk of inversion accidents.
=== Trim ===
Trim is the diver's attitude in the water, in terms of balance and alignment with the direction of motion. Optimum trim depends on the task at hand. For recreational divers this is usually swimming horizontally or observing the environment without making contact with benthic organisms. Ascent and descent at neutral buoyancy can be controlled well in horizontal or head-up trim, and descent can be most energy efficient head down, if the diver can effectively equalise the ears in this position. Freediving descents are usually head down, as the diver is usually buoyant at the start of the dive, and must fin downwards. Professional divers usually have work to do at the bottom, often in a fixed location, which is usually easier in upright trim, and some diving equipment is more comfortable and safer to use when relatively upright.
Accurately controlled trim reduces horizontal swimming effort, as it reduces the sectional area of the diver passing through the water. A slight head down trim is recommended to reduce downward directed fin thrust during finning, and this reduces silting and fin impact with the bottom.
Trim weighting is mainly of importance to the free-swimming diver, and within this category is used extensively by scuba divers to allow the diver to remain horizontal in the water without effort. This ability is of great importance for both convenience and safety, and also reduces the environmental impact of divers on fragile benthic communities.
The free-swimming diver may need to trim erect or inverted at times, but in general, a horizontal trim has advantages both for reduction of drag when swimming horizontally, and for observing the bottom. A horizontal trim allows the diver to direct propulsive thrust from the fins directly to the rear, which minimises disturbance of sediments on the bottom, and reduces the risk of striking delicate benthic organisms with the fins. A stable horizontal trim requires that diver's centre of gravity is directly below the centre of buoyancy (the centroid). Small errors can be compensated fairly easily, but large offsets may make it necessary for the diver to constantly exert significant effort towards maintaining the desired attitude, if it is actually possible.
The position of the centre of buoyancy is largely beyond the control of the diver, though some control of suit volume is possible, the cylinder(s) may be shifted in the harness by a small amount, and the volume distribution of the buoyancy compensator has a large influence when inflated. Most of the control of trim available to the diver is in the positioning of ballast weights. The main ballast weights therefore should be placed as far as possible to provide an approximately neutral trim, which is usually possible by wearing the weights around the waist or just above the hips on a weight belt, or in weight pockets provided in the buoyancy compensator jacket or harness for this purpose. Fine tuning of trim can be done by placing smaller weights along the length of the diver to bring the centre of gravity to the desired position. There are several ways this can be done.
Ankle weights provide a large lever arm for a small amount of weight and are very effective at correcting head-down trim problems, but the addition of mass to the feet increases the work of propulsion significantly. This may not be noticed on a relaxed dive, where there is no need to swim far or fast, but if there is an emergency and the diver needs to swim hard, ankle weights will be a significant handicap, particularly if the diver is marginally fit for the conditions.
Tank bottom weights provide a much shorter lever arm, so need to be a much larger proportion of the total ballast, but do not interfere with propulsive efficiency the way ankle weights do. There are not really any other convenient places below the weight belt to add trim weights, so the most effective option is to carry the main weights as low as necessary, by using a suitable harness or integrated weight pocket buoyancy compensator which actually allows the weights to be placed correctly, so there is no need for longitudinal trim correction.
A less common problem is found when rebreathers have a counterlung towards the top of the torso. In this case there may be a need to attach weights near the counterlung. This is usually not a problem, and weight pockets for this purpose are often built into the rebreather harness or casing, and if necessary weights can be attached to the harness shoulder straps.
== Types of weight ==
All or part of the weighting system may be carried in such a way that it can be quickly and easily jettisoned by the diver to increase buoyancy, the rest is usually attached more securely.
=== Ditchable weights ===
Breathhold and scuba divers generally carry some or all of their weights in a way that can be quickly and easily removed while under water. Removal of these weights should ensure that the diver can surface and remain positively buoyant at the surface. The technique for shedding weights in an emergency is a basic skill of scuba diving, which is trained at entry level. Research performed in 1976 analyzing diving accidents noted that in majority of diving accidents, divers failed to release their weight belts. Later evaluations in 2003 and 2004 both showed that failure to ditch the weight remained a problem.
==== Weight belt ====
Weight belts are the most common weighting system currently in use for recreational diving. Weight belts are often made of tough nylon webbing, but other materials such as rubber can be used. Weight belts for scuba and breathhold diving are generally fitted with a quick release buckle to allow the dumping of weight rapidly in an emergency.
A belt made of rubber with traditional pin buckle is called a Marseillaise belt. These belts are popular with freedivers as the rubber contracts on descent as the diving suit and lungs are compressed, keeping the belt tight throughout the dive.
The most common design of weight used with a belt consists of rectangular lead blocks with rounded edges and corners and two slots in them threaded onto the belt. These blocks can be coated in plastic, which further increases corrosion resistance. Coated weights are often marketed as being less abrasive to wetsuits. The weights may be constrained from sliding along the webbing by the use of metal or plastic belt sliders. This style of weight is generally about 1 to 4 pounds (0.45 to 1.81 kg). Larger "hip weights" are usually curved for a better fit, and tend to be 6 to 8 pounds (2.7 to 3.6 kg).
Another popular style has a single slot through which the belt can be threaded. These are sometimes locked in position by squeezing the weight to grip the webbing, but this makes them difficult to remove when less weight is needed.
There are also weight designs which may be added to the belt by clipping on when needed.
Some weightbelts contain pouches to contain lead weights or round lead shot: this system allows the diver to add or remove weight more easily than with weights threaded onto the belt. The use of shot can also be more comfortable, as the shot conforms to the diver's body. Weight belts using shot are called shot belts. Each shot pellet should be coated to prevent corrosion by sea water, as use of uncoated shotgun shot for sea diving would result in the lead eventually corroding into powdery lead chloride
==== BCD integrated weights ====
These are stored in pockets built into the buoyancy control device. Often a velcro flap or plastic clip holds the weights in place. The weights may also be contained in zippered or velcroed pouches that slot into special pockets in the BCD. The weight pouches often have handles, which must be pulled to drop the weights in an emergency or to remove the weights when exiting the water. Some designs also have smaller "trim pouches" located higher in the BCD, which may help the diver maintain neutral attitude in the water. Trim pouches typically can not be ditched quickly, and are designed to hold only 1-2 pounds (0.5–1 kg) each. Many integrated systems cannot carry as much weight as a separate weight belt: a typical capacity is 6 kg per pocket, with two pockets available. This may not be sufficient to counteract the buoyancy of dry suits with thick undergarments used in cold water.
Some BCD harness systems include a crotch strap to prevent the BCD from sliding up the wearer when inflated, or down when inverted, due to the weights.
==== Weight harness ====
A weight harness usually consists of a belt around the waist holding pouches for the weights, with shoulder straps for extra support and security. Often a velcro flap holds the weights in place. They have handles, which must be pulled to drop the weights in an emergency or to remove the weights when exiting the water. A weight harness allows the weights to be comfortably carried lower on the body than a weight belt, which must be high enough to be supported by the hips. This is an advantage for divers who have no discernible waist, or whose waist is too high to trim correctly if a weight belt is worn. These advantages may also be available on some styles of integrated BC weights. A weight harness may also incorporate a crotch strap or straps to prevent weight shift if the diver is in a steep head down posture.
==== Clip-on weights ====
These are weights which attach to the harness directly, but are removable by disengaging the clip mechanism. They can also be used to temporarily increase the weight of a conventional weight belt. Various sizes have been available, ranging from around 0.5 to 5 kg or more. The larger models are intended as ditchable primary weights, and are used in the same way as BCD integral weights or weight harness weighs, but clipped to the backplate or sidemount harness webbing, and the smaller versions are also useful at trim weights.
==== Backpack weight pouch ====
Some rebreathers (e.g. the Siebe Gorman CDBA) have a pouch containing lead balls each a bit over an inch diameter. The diver can release them by pulling a cord.
=== Fixed weights ===
Surface-supplied divers often carry their weights securely attached to reduce the risk of accidentally dropping them during a dive and losing control of their buoyancy. These may be carried on a weight belt with a secure buckle, supported by a weight harness, connected directly to the diving safety harness, or suspended from the corselet of the helmet. Heavily weighted footwear may also be used to stabilise the diver in an upright position.
In addition to the weight that can be dropped easily ('ditched'), some scuba divers add additional fixed weights to their gear, either to reduce the weight placed on the belt, which can cause lower back pain, or to shift the diver's center of mass to achieve the optimum position in the water.
Tank weights are attached to the diving cylinder to shift the center of mass backward and towards the head or feet, depending on placement.
V-weights are long, narrow, weights which are carried in the groove between twinned cylinders. They may be carried singly or as a pair. Traditionally wedge sectioned lead castings, but also found in solid cylindrical format and as long narrow webbing weight pockets filled with shot.
Tank trim weights are smaller weights , usually strapped towards the base of an aluminium cylinder to prevent it from trimming base-upward in seawater when side- or sling-mounted, when the gas is used up.
Ankle weights, which are typically about 1 lb./0.5 kg of shot, are used to counteract the positive buoyancy of diving suit leggings, made worse in drysuits by the migration of the internal bubble of air to the feet, and positively buoyant fins. Some divers prefer negatively buoyant fins. The additional effort needed when finning with ankle weights or heavy fins increases the diver's gas consumption.
Metal backplates made from stainless steel, which may be used with wing style buoyancy compensators, move the center of mass upward and backward. Some backplates are fitted with an additional weight, often mounted in the central channel, also called a keel weight or a p-weight.
Steel diving cylinders are preferred over aluminium cylinders by some divers—particularly cold water divers who must wear a suit that increases their overall buoyancy—because of their negative buoyancy. Most steel tanks stay negatively buoyant even when empty, aluminium tanks may become positively buoyant as the gas they contain is used. High-pressure (300bar) steel tanks are significantly negative.
== Hazards ==
There are several operational hazards associated with diving weights:
Over-weighting leading to inability to ascend or remain at the surface, or difficulties in ascent and buoyancy control. If severe, it may be necessary to ditch weights to get to the surface.
Under-weighting leading to inability to descend or remain at a required depth. While inability to descend at the start of a dive may be considered an inconvenience, the inability to maintain depth at a required decompression stop at the end of the dive may put the diver at a severe risk of decompression sickness.
Inability or failure to ditch weight to establish buoyancy in an emergency. In an out of air emergency there may not be gas available to inflate the buoyancy compensator if it has been allowed to be insufficiently inflated. The only option left to reach the surface may be to ditch weights. A similar need may arise at the surface if there is a major loss of buoyancy. Occasionally a diver at the side of the boat will remove the scuba set with buoyancy compensator before passing up their weight belt, and then find it impossible to remain afloat because they are over-weighted. If they fail to grab the boat or ditch the belt the risk of drowning is high.
Loss of weight at depth at the wrong time. Ditching weights at depth to establish positive buoyancy will generally prevent a properly controlled ascent. The risk of drowning due to running out of breathing gas is exchanged for the risk of decompression sickness. Accidental loss of weights when there is no emergency will cause an emergency if there is a decompression obligation.
Loss, damage or injury caused by mishandling. When passing the weights to a person on the boat, there is a risk that the weights may be dropped, and may hit the diver, or someone's foot, demand valve, mask or camera, or may drop overboard to be lost, or possibly hit a diver under the boat.
Discomfort or stress injury related to weight distribution and support. A weight belt hanging from the small of the back of a horizontal diver to counteract suit buoyancy spread over the full length of the diver can cause lower back pain. When walking on land before and after a dive, the weight belt may exert painful pressure on the hip joints.
Additional work load due to sub-optimal distribution. The work of finning will generally be increased by using ankle weights which must be accelerated for every kick. When this is combined with other effects increasing the workload on the diver, it may cumulatively exceed the work capacity of the diver and result in a positive feedback loop of buildup of carbon dioxide.
Buoyancy and weighting problems have been implicated in a relatively high proportion of scuba diving fatalities. A relatively large number of bodies have been recovered with all weights still in place.
== Materials ==
The most common material for personal dive weights is cast lead. The primary reason for using lead is its high density, as well as its relatively low melting point, low cost and easy availability compared to other high density materials. It is also resistant to corrosion in fresh and salt water. Most dive weights are cast by foundries and sold by dive shops to divers in a range of sizes, but some are made by divers for their own use. Scrap lead from sources such as fishing sinkers and wheel balance weights can be easily cast by a hobbyist in relatively cheap re-usable moulds, though this may expose them to vaporized lead fumes.
=== Heavy metal toxicity ===
Although lead is the least expensive dense (SG=11.34) material available, it is a toxic substance causing biological damage to wildlife and humans. The Centers for Disease Control has stated that no safe level of lead exposure in children has been determined, and that once lead has been absorbed into the body, its effects cannot be corrected. Even a very small amount of exposure causes a permanent reduction in intelligence, ability to focus attention, and academic ability. Lead can be inhaled or ingested as either a metal powder or powdered corrosion products, however most lead salts have very low solubility in water, and pure lead corrodes very slowly in seawater. Absorption through skin is not likely for metallic lead and inorganic corrosion products.
Although it is inexpensive to recycle lead from other sources into homemade dive weights, pure lead melts at 327.46 °C (621.43 °F) and releases fumes at 482 °C (900 °F). The fumes will form oxides in the air and settle as dust on nearby surfaces. Even with good ventilation there will be lead oxide dust in the lead melting area.
Solid block weights can corrode and be damaged when dropped or impacting other weights. In flexible bag weights, the small pieces of lead shot will rub together when handled and used, releasing lead dust and corrosion products into the water. The amount of lead lost to the water is roughly proportional to the total surface area of the weights, and the amount of motion between contact surfaces and is greater for smaller sizes of shot.
Solubility of lead salts in seawater is low, though there is a significant role played by natural organic matter in complexing dissolved lead, and oceanic lead concentrations typically range from 1 to 36 ng/L, with from 50 to 300 ng/L in coastal waters affected by anthropogenic activities.
Diving is also sometimes practiced in swimming pools for training and exercise. Swimming pools can be contaminated by lead weights. Many divers using the same pool with lead weights will over time increase the lead contamination of the pool water until the water is changed.
There are no published studies on lead absorption by divers or diving support personnel due to handling weights, which suggests that it has not been considered a problem by diving medical experts or the occupational health and safety authorities.
=== Alternative materials ===
Other heavy metals have been considered as an alternative to lead. One example is bismuth which has a similar density (SG=9.78) and a low melting point. It is less toxic, and its salts are highly insoluble which limits absorption by the body. Tungsten (SG=19.25) is another possible replacement for lead, but it is very expensive by comparison, both as a material and to manufacture in suitable shapes.
Non-toxic materials such as iron (SG=7.87) can be used in place of lead and would not cause poisoning and contamination. However, the density of most such materials is significantly lower, so the dive weight needs to be of larger volume and therefore greater mass, to equal the negative buoyancy of the mass of lead it replaces. A lead weight of 1 kg would be replaced[1] by an iron weight of 1 × (7.87/11.34) × ((11.34-1)/(7.87-1)) = 1.044 kg, a 4.4% additional load for the diver when out of the water.
Iron is also corroded much more easily in seawater than lead, and would need some form of protection to prevent rusting. Alloys of stainless steel are more resistant to corrosion, but, for the cheaper grades, need to be rinsed with freshwater after use to prevent corrosion in storage. The cost of shaping alternative materials may be considerably greater, particularly for small quantities. Stainless steel and tungsten dive weights for example are currently only obtainable by milling down a solid metal stock material in block or cylinder form, into the required shape. Direct casting of some of these materials in a foundry is possible, but would require high volume production for the casting processes to be cost effective.
=== Encapsulation of lead weights ===
Lead weights can be coated with a protective outer layer such as plastic or paint, and this is commonly used for lead abatement. This prevents the lead from corroding or being ground into dust by rubbing, and helps to cushion impacts. However the protection is reduced if the coating is cracked or otherwise damaged. Soft plastics may become brittle over time due to UV degradation from sunlight and loss of plasticizers, leading to cracking and shattering. Encapsulation materials are usually of near neutral buoyancy in water, and reduce the average density of the weights, making the weights slightly less effective, and increasing the overall weight in air of the diving equipment.
== Ballast on other diving and support equipment ==
Clump weights for bells and stages:– A clump weight is a large ballast weight suspended from a cable which runs down from one side of the launch and recovery gantry, through a pair of sheaves on the sides of the weight, and up the other side back to the gantry, where it is fastened. The weight hangs freely between the two parts of the cable, and due to its weight, hangs horizontally and keeps the cable under tension with the vertical parts parallel. The bell hangs between the vertical parts of the cable, and has a fairlead on each side which slides along the cable as it is lowered or lifted. Deployment of the bell is by a primary lifting cable attached to the top. As the bell is lowered, the fairleads prevent it from rotating on the deployment cable, which would put twist into the umbilical and risk loops or snagging. The clump weight cables therefore function as guidelines or rails along which the bell is lowered to the workplace, and raised back to the platform.
Releasable ballast on closed bells, atmospheric diving suits, remotely operated underwater vehicles and submersibles:– Solid weights which can be released by the operator, or automatically release in a power failure, to achieve positive buoyancy in an emergency, allowing the unit to float back to the surface.
Trim weights on atmospheric diving suits, remotely operated underwater vehicles, and submersibles, used to compensate for variations in payload.
Ballast and trim weights on camera equipment and diver propulsion vehicles. Camera and light assemblies are often ballasted or provided with rigid buoyancy to provide neutral buoyancy and reasonably stable trim, as this makes it easier to hold the camera in place when setting up a shot. Similar considerations apply to video cameras, which must often be kept steady and in focus for relatively long periods. Diver propulsion vehicles are ballasted to neutral buoyancy and level trim to make it easier to steer them for long periods and at varying speeds, a procedure which is generally done using only one hand, so that the other is available for other work.
== See also ==
Archimedes' principle – Buoyancy principle in fluid dynamics
Buoyancy – Upward force that opposes the weight of an object immersed in fluid
Buoyancy compensator (diving) – Equipment for controlling the buoyancy of a diver
Emergency ascent – Ascent to the surface by a diver in an emergency
Human factors in diving equipment design – Influence of the interaction between the user and the equipment on design
== References ==
=== Notes ===
^ Derivation of formula for equivalent apparent weight in water.
Density = mass/volume, ρ = m/V so m = ρ × V
Buoyancy in water: B = (ρ - ρwater) × V × g, where g = gravitational acceleration at earth' surface
For two objects of different densities but the same buoyancy in water: B1 = B2 so (ρ1 - ρwater) × V1 × g = (ρ2 - ρwater) × V2 × g (g can be dropped from both sides)
therefore: V1 = V2 × (ρ2 - ρwater) ÷ (ρ1 - ρwater)
Also, for the same two objects in air (ignoring the buoyancy of the air): m1 = ρ1 × V1 and m2 = ρ2 × V2
by substitution: m1 ÷ m2 = (ρ1 ÷ ρ2) × ((ρ2 - ρwater) ÷ (ρ1 - ρwater))
so: m1 = (ρ1 ÷ ρ2) × ((ρ2 - ρwater) ÷ (ρ1 - ρwater)) × m2
And the same works with SG in place of density: m1 = (SG1 ÷ SG2) × ((SG2 - SGwater) ÷ (SG1 - SGwater)) × m2
And since SGwater = 1: m1 = (SG1 ÷ SG2) × ((SG2 - 1) ÷ (SG1 - 1)) × m2
Substituting values for 1 kg lead, iron gives: 1kg lead × (7.87/11.34) × ((11.34-1)/(7.87-1)) = 1.044kg iron
=== Sources === | Wikipedia/Integrated_weights |
Hyperbaric treatment schedules or hyperbaric treatment tables, are planned sequences of events in chronological order for hyperbaric pressure exposures specifying the pressure profile over time and the breathing gas to be used during specified periods, for medical treatment. Hyperbaric therapy is based on exposure to pressures greater than normal atmospheric pressure, and in many cases the use of breathing gases with oxygen content greater than that of air.
A large number of hyperbaric treatment schedules are intended primarily for treatment of underwater divers and hyperbaric workers who present symptoms of decompression illness during or after a dive or hyperbaric shift, but hyperbaric oxygen therapy may also be used for other conditions.
Most hyperbaric treatment is done in hyperbaric chambers where environmental hazards can be controlled, but occasionally treatment is done in the field by in-water recompression when a suitable chamber cannot be reached in time. The risks of in-water recompression include maintaining gas supplies for multiple divers and people able to care for a sick patient in the water for an extended period of time.
== Background ==
Recompression of diving casualties presenting symptoms of decompression sickness has been the treatment of choice since the late 1800s. This acceptance was primarily based on clinical experience.
John Scott Haldane's decompression procedures and the associated tables developed in the early 1900s greatly reduced the incidence of decompression sickness, but did not eliminate it entirely. It was, and remains, necessary to treat incidences of decompression sickness.
=== Hyperbaric chamber recompression ===
During the building of the Brooklyn Bridge, workers with decompression sickness were recompressed in an iron chamber built for this purpose. They were recompressed to the same pressure they had been exposed to while working, and when the pain was relieved, decompressed slowly to atmospheric pressure.
Although recompression and slow decompression were the accepted treatment, there was not yet a standard for either the recompression pressure or the rate of decompression. This changed when the first standard table for recompression treatment with air was published in the US Navy Diving Manual in 1924. These tables were not entirely successful – there was a 50% relapse rate, and the treatment, though fairly effective for mild cases, was less effective in serious cases.
==== 1945 series of human experiments ====
Field results showed that the 1944 oxygen treatment table was not yet satisfactory, so a series of tests were conducted by staff from the Navy Medical Research Institute and the Navy Experimental Diving Unit using human subjects to verify and modify the treatment tables.
Tests were conducted using the 100-foot air-oxygen treatment table and the 100-foot air treatment table, which were found to be satisfactory. Other tables were extended until they produced satisfactory results. The resulting tables were used as the standard treatment for the next 20 years, and these tables and slight modifications were adopted by other navies and industry. Over time, evidence accumulated that the success of these table for severe decompression sickness was not very good.
These low success rates led to the development of the oxygen treatment table by Goodman and Workman in 1965, variations of which are still in general use as the definitive treatment for most cases of decompression sickness.
=== In water recompression ===
Treatment of DCS utilizing the US Navy Treatment Table 6 with oxygen at 18 m is a standard of care. Significant delay to treatment, difficult transport, and facilities with limited experience may lead one to consider on site treatment. Surface oxygen for first aid has been proven to improve the efficacy of recompression and decreased the number of recompression treatments required when administered within four hours post dive. IWR to 9 m breathing oxygen is one option that has shown success over the years. IWR is not without risk and should be undertaken with certain precautions. IWR would only be suitable for an organised and disciplined group of divers with suitable equipment and practical training in the procedure.
== Applications ==
Treatment of decompression sickness, arterial gas embolism, and other medical applications.
== Equipment ==
=== Recompression chamber ===
The type of chamber which can be used depends on the maximum pressure required for the schedule, and what gases are used for treatment. Most treatment protocols for diving injuries require an attendant in the chamber, and a medical lock to transfer medical supplies into the chamber while under pressure.
==== Monoplace chambers ====
Outside of the diving industry, most chambers are intended for a single occupant, and not all of them are fitted with built-in breathing systems (BIBS). This limits the schedules which can be safely used in them. Some schedules have been developed specifically for hyperbaric oxygen treatment in monoplace chambers, and some hyperbaric treatment schedules nominally intended for chambers with BIBS have been shown to be acceptable for use without air breaks if the preferred facilities are not available.
=== Treatment gases ===
Originally therapeutic recompression was done using air as the only breathing gas, and this is reflected in several of the tables detailed below. However, work by Yarbrough and Behnke showed that use of oxygen as a treatment gas is usually beneficial and this has become the standard of care for treatment of DCS. Pure oxygen can be used at pressures up to 60 fsw (18 msw) with acceptable risk of CNS oxygen toxicity, which generally has acceptable consequences in the chamber environment when an inside tender is at hand. At greater pressures, treatment gas mixtures using Nitrogen or Helium as a diluent to limit partial pressure of oxygen to 3 ata (3 bar) or less are preferred to air as they are more effective both at elimination of inert gases and oxygenating injured tissues in comparison with air. Nitrox and Heliox mixtures are recommended by the US Navy for
treatment gases at pressures exceeding 60 fsw (18 msw), and Heliox is preferred at pressures exceeding 165 fsw (50 msw) to reduce nitrogen narcosis.
High oxygen fraction gas mixtures may also be substituted for pure oxygen at pressures less than 60 fsw if the patient does not tolerate 100% oxygen.
=== Built in breathing system ===
Treatment gases are generally oxygen or oxygen rich mixtures which would constitute an unacceptable fire hazard if used as the chamber gas. Chamber oxygen concentration is limited due to fire hazard and the high risk of fatality or severe injury in the event of a chamber fire. US Navy specifications for oxygen content of chamber air allow a range from 19% to 25%. If the oxygen fraction rises above this limit the chamber must be ventilated with air to bring the concentration to an acceptable level. To minimize the requirement for venting, oxygen-rich treatment gases are usually provided to the patient by built in breathing system (BIBS) masks, which vent exhaled gas outside the chamber. BIBS masks are provided with straps to hold them in place over the mouth and nose, but are often held in place manually, so they will fall away if the user has an oxygen toxicity convulsion.
BIBS masks provide gas on demand (inhalation), much like a diving regulator, and use a similar system to control outflow to the normobaric environment. They are connected to supply lines plumbed through the pressure hull of the chamber, valved on both sides, and supplied from banks of storage cylinders, usually kept near the chamber. The BIBS system is normally used with medical oxygen, but can be connected to other breathing gases as required. Chamber gas oxygen content is usually monitored by bleeding chamber gas past an electro-galvanic oxygen sensor cell.
== Units of measurement used in hyperbaric treatment ==
The commonly used units of pressure for hyperbaric treatment are metres of sea water (msw) and feet of sea water (fsw) which indicate the pressure of treatment in terms of the height of water column that would be supported in a manometer. These units are also used for measuring the depth of a surface supplied diver using a pneumofathometer and directly relate the pressure to an equivalent depth. The pressure gauges used on diving chambers are often calibrated in both of these units. Elapsed time of treatment is usually recorded in minutes, or hours and minutes, and may be measured from the start of pressurisation, or from the time when treatment pressure is reached.
== Hyperbaric chamber treatment schedules ==
The schedules listed here include both historical procedures and schedules currently in use. As a general rule, more recent tables from the same source have a greater success rate than the superseded schedules. Some of the older procedures are now considered to be dangerous.
=== US Navy 1943 100-foot Air Treatment Table ===
Use: Treatment of decompression sickness where relief is obtained at or less than 66 fsw.
Obsolete
Oxygen is not used
Maximum pressure 100 fsw (30 msw)
Run time 3 hours 37 minutes
=== US Navy 1943 150-foot Air Treatment Table ===
Use: Treatment of decompression sickness where relief is obtained at or less than 116 fsw.
Obsolete
Oxygen is not used
Maximum pressure 150 fsw (46 msw)
Run time 4 hours 55 minutes
=== US Navy 1943 200-foot Air Treatment Table ===
Use: Treatment of decompression sickness where relief is obtained at or less than 166 fsw.
Obsolete
Oxygen is not used
Maximum pressure 200 fsw (61 msw)
Run time 5 hours 58 minutes
=== US Navy 1943 250-foot Air Treatment Table ===
Use: Treatment of decompression sickness where relief is obtained at or less than 216 fsw.
Obsolete
Oxygen is not used
Maximum pressure 250 fsw (76 msw)
Run time 6 hours 46 minutes
=== US Navy 1943 300-foot Air Treatment Table ===
Use: Treatment of decompression sickness where relief is obtained at or less than 266 fsw.
Obsolete
Oxygen is not used
Maximum pressure 300 fsw (91 msw)
Run time 7 hours 29 minutes
=== US Navy 1944 Long Air Recompression Treatment Table ===
Use: Treatment of moderate to severe decompression sickness when oxygen is not available or the patient cannot tolerate the elevated oxygen partial pressure.
Oxygen is not used
Maximum pressure 165 fsw (50 msw)
Run time 5 hours 39 minutes
=== US Navy 1944 Long Air Recompression Treatment Table with Oxygen ===
Use: Treatment of moderate to severe decompression sickness when oxygen is available.
Oxygen is used
Maximum pressure 165 fsw (50 msw)
Run time 3 hours 0 minutes
=== US Navy 1944 Short Air Recompression Treatment Table ===
Use: Treatment of mild decompression sickness when oxygen is not available or the patient cannot tolerate the elevated oxygen partial pressure.
Oxygen is not used
Maximum pressure 100 fsw (30 msw)
Run time 5 hours 5 minutes
=== US Navy 1944 Short Oxygen Recompression Treatment Table ===
Use: Treatment of mild decompression sickness.
Oxygen is used
Maximum pressure 100 fsw (30 msw)
Run time 2 hours 17 minutes
=== US Navy Recompression Treatment Table 1 ===
Use: Treatment of pain only decompression sickness.
Pain is relieved at less than 66 fsw (20 msw)
Oxygen is available
Maximum pressure 100 fsw (100 msw)
Run time 2 hours 21 minutes
Omitted from the US Navy Diving Manual since Revision 6
=== US Navy Air Treatment Table 1A ===
Table 1A is included in the US Navy Diving Manual Revision 6 and is authorized for use as a last resort when oxygen is not available. This table has been revised by decreasing the ascent rate from 1 minute between stops to 1 fsw per minute since the original was published in 1958.
Use: For treatment of pain only decompression sickness.
Pain is relieved at less than 66 fsw. (20 msw)
Air only, No oxygen.
Maximum pressure 100 fsw (30 msw)
Run time 7 hours 52 minutes
=== US Navy Recompression Treatment Table 2 ===
Use: Treatment of pain-only decompression sickness.
Pain is relieved at greater than 66 fsw (20 msw)
Oxygen available
Maximum pressure 165 fsw (50 msw)
Run time 4 hours 1 minute
=== US Navy Air Treatment Table 2a ===
Table 2A is included in the US Navy Diving Manual Revision 6 and is authorized for use as a last resort when oxygen is not available. This table has been revised by decreasing the ascent rate from 1 minute between stops to 1 fsw per minute since the original was published in 1958.
Use: Treatment of pain only decompression sickness when oxygen cannot be used.
Pain is relieved at a depth greater than 66 fsw (20 msw).
Oxygen not available
Maximum pressure 165 fsw (50 msw)
Run time 13 hours 33 minutes
=== US Navy Air Treatment Table 3 ===
Table 3 is included in the US Navy Diving Manual Revision 6 and is authorized for use as a last resort when oxygen is not available. This table has been revised by decreasing the ascent rate from 1 minute between stops to 1 fsw per minute since the original was published in 1958.
Use: Treatment of serious symptoms when oxygen cannot be used and symptoms are relieved within 30 minutes at 165 feet.
Oxygen not available
Maximum pressure 165 fsw (50 msw)
Run time 21 hours 33 minutes
=== US Navy Recompression Treatment Table 4 ===
This table is in the US Navy Diving Manual Revision 6 and is currently authorized for use.
Use: Treatment of serious symptoms when oxygen can be used and symptoms are not relieved within 30 minutes at 165 fsw (50 msw).
Oxygen enriched treatment gases and Oxygen may be used. Air may be used if nothing better is available. If oxygen breathing is interrupted no compensation to the times is required. Oxygen partial pressure may not exceed 3 ata (3 bar).
Maximum depth 165 fsw (50 msw)
Time at 165 fsw optional from 30 minutes to 2 hours including compression
Total run time 39 hours 6 minutes to 40 hours 36 minutes
=== US Navy Recompression Treatment Table 5 ===
Use: Treatment of pain-only decompression sickness when oxygen can be used and symptoms are relieved within 10 minutes at 60 ft.
Treatment Table 5 is currently included in the US Navy Diving Manual and is approved for use.
Oxygen treatment
Maximum pressure 60 fsw (18 msw)
Standard run time 2 hours 16 minutes
The table may be extended by two oxygen-breathing periods at the 30 fsw (9 msw) stop
=== US Navy Recompression Treatment Table 5a ===
Use: Treatment of gas embolism when oxygen can be used and symptoms are relieved within 15 minutes at 165 fsw (50 msw).
Treatment table 5a is not currently included in the US Navy Diving Manual (Revision 6).
Oxygen treatment
Maximum pressure 165 fsw (50 msw)
Run time 2 hours 34 minutes
=== US Navy Recompression Treatment Table 6 ===
Use: Treatment of pain-only decompression sickness when oxygen can be used and symptoms are not relieved within 10 minutes at 60 fsw (18 msw).
Oxygen treatment
Maximum pressure 60 fsw (18 msw)
Run time 4 hours 45 minutes
==== Catalina modification ====
The Catalina treatment table is a modification of Treatment Table 6. Oxygen cycles are 20 minutes, and air breaks 5 minutes. The full Catalina Table allows for up to 5 extensions at 60 fsw.
Shorter versions include:
3 oxygen cycles at 60 fsw followed by a minimum of 6 oxygen cycles at 30 fsw. (equivalent to USN Table 6)
4 oxygen cycles at 60 fsw followed by a minimum of 9 oxygen cycles at 30 fsw.
5 to 8 oxygen cycles at 60 fsw followed by a minimum of 12 oxygen cycles at 30 fsw.
Tenders breathe oxygen for 60 minutes at 30 fsw. Further treatments may follow after at least 12 hours on air at the surface.
=== US Navy Recompression Treatment Table 6a ===
Use: Treatment of gas embolism when oxygen can be used and symptoms moderate to a major extent within 30 minutes at 165 ft.
This treatment table is included in the US Navy Diving Manual Revision 6 and is currently authorized for use. It has been updated since original publication.
Oxygen treatment
Optional treatment with oxygen enriched gases (Heliox or Nitrox) not exceeding 3.0 ata (3 bar) partial pressure of oxygen if available
Maximum pressure 165 fsw (50 msw)
Nominal run time 5 hours 50 minutes from reaching full pressure
At 50msw (absolute pressure 6 bar) an oxygen fraction of 50% will produce a partial pressure of 3 bar, This could be a nitrox, heliox or trimix blend with 50% oxygen.
=== US Navy Treatment Table 7 ===
Use: Treatment of non-responding severe gas embolism or life-threatening decompression sickness. It is used when loss of life may result from decompression from 60 fsw. It is not used to treat residual symptoms that do not improve at 60 fsw, or to treat residual pain.
Treatment table 7 is included in the US Navy Diving Manual Revision 6 and is currently authorized for use.
Oxygen is used if practicable
Maximum pressure 60 fsw (18 msw)
Minimum time at 60 fsw is 12 hours. Decompression following this length of exposure is generally considered decompression from saturation, so the decompression profile is not affected by longer exposure at 60 fsw. Use of this table may be preceded by initial treatment on table 6, 6A or 4. Table 7 treatment begins on arrival at 60 fsw.
Duration of decompression is 36 hours
Decompression comprises an approximated continuous ascent with stops every 2 fsw as shown in the graphic profile, with a stop at 4 fsw for 4 hours to avoid inadvertent loss of pressure due to seal failure at low pressure differences.
=== US Navy Treatment Table 8 ===
Use: Mainly for treating deep uncontrolled ascents when more than 60 minutes of decompression have been omitted.
Treatment table 8 is included in the US Navy Diving Manual Revision 6 and is currently authorized for use.
Adapted from Royal Navy Treatment Table 65.
Patient is recompressed to pressure of symptomatic relief but not to exceed 225 fsw and treatment initiated
Once begun, decompression is continuous, but may be interrupted at 60 fsw or shallower.
Heliox mixtures may be used at pressures exceeding 165 fsw to reduce nitrogen narcosis. Heliox 64/36 is the preferred treatment gas.
Heliox or Nitrox with partial pressure not exceeding 3 ata may be used as treatment gas at pressures less than 165 fsw
100% oxygen may be used as treatment gas at pressures less than 60 fsw
Decompression is done by 2 fsw pressure decrements unless the start depth is an odd number, in which case the first stop is at a 3 fsw reduction in pressure. Stop times vary according to the depth range of the stop. Shorter stops are done at greater pressures, and the stop time increases as the stops get shallower.
Nominal total ascent time from 225 fsw is 56 hours 29 minutes.
=== US Navy Treatment Table 9 ===
Use: Hyperbaric oxygen treatment as prescribed by Diving Medical Officer for:
Residual symptoms after treatment for AGE/DCS
Cases of carbon monoxide or cyanide poisoning
Smoke inhalation
Initial treatment of patients urgently needing definitive medical care for severe injuries.
Maximum pressure 45 fsw (13.5 msw)
Nominal elapsed time excluding pressurization 102 minutes
Treatment depth may be reduced to 30 fsw (9 msw) if patient cannot tolerate oxygen at 45 fsw (13.5 msw).
Table may be extended to a maximum of 4 hours oxygen breathing time.
=== US Navy Treatment Table for decompression sickness occurring on saturation dives ===
Use: For treatment of decompression sickness manifested as musculoskeletal pains only, during decompression from saturation.
Maximum pressure specified is 1600 fsw
Recompression in increments of 10 fsw at 5 fsw per minute until diver reports improvement. It is not usually necessary or desirable to recompress by more than 30 fsw.
Treatment gas with oxygen partial pressure of up to 2.5 atm may be administered by BIBS mask for periods of 20 minutes, with breaks of 5 minutes on chamber gas during recompression and holding periods. Pure oxygen may be used at pressures less than 60 fsw.
Use: For treatment of serious decompression sickness resulting from upward excursion.
Recompression immediately at 30 fsw per minute to at least the depth from which the excursion started.
If this does not provide complete relief compression should continue until relief is reported.
Hold at relief depth for at least 2 hours for pain only symptoms and at least 12 hours for serious symptoms.
Decompress after treatment according to normal saturation decompression schedule from the treatment depth.
=== Tektite I and II Treatment and emergency decompression schedule for a 42 to 50-foot saturation dive ===
Treatment of Tektite aquanauts after emergency surfacing.
Saturation gas mixture Nitrox 9%
Oxygen available
Maximum pressure 60 fsw (18 msw)
Run time 14 hours 40 minutes
=== Tektite II Treatment and emergency decompression schedule for the 100-foot saturation dive ===
Treatment of Tektite aquanauts after emergency surfacing.
Oxygen available
Maximum pressure up to 200 fsw
Run time variable depending on circumstances
=== Royal Navy 1943 Recompression Treatment Procedure ===
Treatment of any decompression sickness symptoms.
Oxygen not used
Maximum pressure variable up to 225 fsw (68 msw)
Run time 4 hours 57 minutes to 5 hours 57 minutes
=== Royal Navy Table 51 – Air Recompression Therapy ===
Use: Treatment of pain-only decompression sickness when oxygen is not available and pain is relieved within 10 minutes at or less than 20 msw (667 fsw)
Oxygen not used
Maximum pressure 30 msw (98 fsw)
Run time 7 hours 5 minutes
=== Royal Navy Table 52 – Air Recompression Therapy ===
Use: Treatment of pain-only decompression sickness when oxygen is not available and pain is not relieved within 10 minutes at or less than 20 msw (66 fsw) but does have relief within 10 minutes at 50 msw (165 fsw).
Oxygen not used
Maximum pressure 50 msw (164 fsw)
Run time 9 hours 58 minutes
=== Royal Navy Table 53 – Air Recompression Therapy ===
Use: Treatment of joint pain plus a more serious symptom of decompression sickness when oxygen is not available and symptoms are relieved within 30 minutes at or less than 50 msw (164 fsw)
Oxygen not used
Maximum pressure 50msw (164 fsw)
Run time 19 hours 48 minutes
=== Royal Navy Table 54 – Air Recompression Therapy ===
Use: Treatment of joint pain plus a more serious symptom of decompression sickness when oxygen is available and symptoms are not relieved within 30 minutes at or less than 50 metres (164 ft)
Oxygen available
Maximum pressure 50 msw (164 fsw)
Run time 39 hours 0 minutes
=== Royal Navy Table 55 – Air Recompression Therapy ===
Use: Treatment of joint pain plus a more serious symptom of decompression sickness when oxygen is not available and symptoms are not relieved within 30 minutes at or less than 50msw (164 fsw)
Oxygen not available
Maximum pressure 50 msw (164 fsw)
Run time 43 hours 0 minutes
=== Royal Navy Table 61 – Oxygen Recompression Therapy ===
Use: Treatment of pain only decompression sickness when oxygen is available and pain is relieved within 10 minutes or at less than 18 msw (59 fsw), or for serious symptoms where a specialist medical officer is present.
Oxygen treatment
Maximum pressure 18 msw (59 fsw)
Run time 2 hours 17 minutes
=== Royal Navy Table 62 – Oxygen Recompression Therapy ===
Use: Treatment of pain only decompression sickness when oxygen is available and pain is not relieved within 10 minutes at 18 msw (59 fsw), or for serious symptoms where a specialist medical officer is present.
Oxygen treatment
Maximum pressure 18 msw (59 fsw)
Run time 4 hours 47 minutes
=== Royal Navy Table 71 – Modified Air Recompression Table ===
Use: Treatment of any decompression symptom if a specialist medical officer is present.
Oxygen not available
Maximum pressure 70 msw (230 fsw)
Run time 47 hours 44 minutes
=== Royal Navy Table 72 – Modified Air Recompression Therapy ===
Use: Treatment of any decompression symptom if a specialist medical officer is present. Applicable for multiple recompression of submarine survivors.
Oxygen not available
Maximum pressure 50 msw (164 fsw)
Run time 46 hours 45 minutes
=== RNPL Therapeutic Decompression from a Helium-Oxygen Recompression ===
Use: Treatment of decompression sickness occurring during decompression from a Heliox dive.
Oxygen not used
Maximum pressure variable. May be greater than 137 msw (450 fsw)
Run time depends on treatment depth
=== French Navy Recompression Treatment Table 1 (GERS 1962) ===
Use: Treatment of mild decompression sickness.
Oxygen is available
Maximum pressure 30 msw (98 fsw)
Run time 4 hours 12 minutes
=== French Navy Recompression Treatment Table 2 (GERS 1962) ===
Use: Treatment of mild to moderate decompression sickness.
Oxygen is available
Maximum pressure 50 msw (164 fsw)
Run time 6 hours 44 minutes
=== French Navy Recompression Treatment Table 3 (GERS 1962) ===
Use: Treatment of moderate to severe decompression sickness.
Oxygen is available
Maximum pressure 50 msw (164 fsw)
Run time 12 hours 44 minutes
=== French Navy Recompression Treatment Table 4 (GERS 1962) ===
Use: Treatment of severe decompression sickness.
Oxygen is available
Maximum pressure 50 msw (164 fsw)
Run time 36 hours 14 minutes or 37 hours 44 minutes
=== French Navy Recompression Treatment Table 4A (GERS 1962) ===
Use: Treatment of severe decompression sickness.
Oxygen is not available
Maximum pressure 50 msw (164 fsw)
Run time 38 hours 14 minutes or 39 hours 39 minutes
=== French Navy Air Recompression Treatment Table (GERS 1964) ===
Use: Treatment of decompression sickness.
Oxygen is not available or the patient cannot tolerate high partial pressures of oxygen
Maximum pressure 50 msw (164 fsw)
Run time 73 hours 10 minutes
=== French Navy Air Recompression Treatment Table (GERS 1964) ===
Use: Treatment of decompression sickness.
Oxygen is not available or the patient cannot tolerate high partial pressures of oxygen
Maximum pressure 50 msw (164 fsw)
Run time 76 hours 40 minutes
=== French Navy High-Oxygen Recompression Treatment Table (GERS 1964) ===
Use: Treatment of moderately severe decompression sickness.
Oxygen is available
Maximum pressure 30 msw (98 fsw)
Run time between 20 hours 33 minutes and 36 hours 3 minutes
=== French Navy Recompression Treatment Table A (GERS 1968) ===
Use: Treatment of mild decompression sickness after dives to less than 40 m depth.
Oxygen is available
Maximum pressure 30 msw (98 fsw)
Run time 5 hours 33 minutes
=== French Navy Recompression Treatment Table B (GERS 1968) ===
Use: Treatment of mild decompression sickness after dives to more than 40 m depth.
Oxygen is available
Maximum pressure 30 msw (98 fsw)
Run time 8 hours 3 minutes
=== French Navy Recompression Treatment Table C (GERS 1968) ===
Use: Treatment of moderately severe decompression sickness after dives to more than 40m depth or severe decompression sickness after dives shallower than 40m.
Oxygen is available
Maximum pressure 30 msw (98 fsw)
Run time 14 hours 29 minutes to 36 hours 57 minutes
=== French Navy Recompression Treatment Table D (GERS 1968) ===
Use: Treatment of moderately severe and severe decompression sickness.
Oxygen is not available or cannot be tolerated by the patient
Maximum pressure 50 msw (164 fsw)
Run time 69 hours 45 minutes or 77 hours 45 minutes
=== French Navy Recompression Treatment Table 1A (GERS 1968) ===
Use: Treatment of mild decompression sickness after dives to less than 40 m.
Oxygen is not available or cannot be tolerated by the patient
Maximum pressure 30 msw (98 fsw)
Run time 7 hours 18 minutes
=== French Navy Recompression Treatment Table 2A (GERS 1968) ===
Use: Treatment of mild decompression sickness after dives to more than 40 m.
Oxygen is not available or cannot be tolerated by the patient
Maximum pressure 50 msw (164 fsw)
Run time 12 hours 45 minutes
=== French Navy Recompression Treatment Table 3A (GERS 1968) ===
Use: Treatment of moderate or severe decompression sickness.
Oxygen is not available or cannot be tolerated by the patient
Maximum pressure 50 msw (164 fsw)
Run time 20 hours 45 minutes
=== Comex Therapeutic Table CX 12 ===
Use: Treatment of musculoskeletal decompression sickness following normal decompression if symptoms are relieved within 4 minutes or at less than 8 msw.
Oxygen is available
Maximum pressure 12 msw (40 fsw)
Run time 2 hours 10 minutes
=== Comex Therapeutic Table 18C ===
Use: Treatment of musculoskeletal decompression sickness following normal or shortened decompression if symptoms are not relieved within 4 minutes at 8 msw, but are relieved within 15 minutes at or less than 18 msw.
Oxygen is available
Maximum pressure 18 msw (60 fsw)
Run time 2 hours 54 minutes
=== Comex Therapeutic Table 18L ===
Use: Treatment of musculoskeletal decompression sickness following normal or shortened decompression if symptoms are not relieved within 15 minutes at 18 msw.
Oxygen is available
Maximum pressure 18 msw (60 fsw)
Run time 4 hours 59 minutes
=== Comex Therapeutic Table CX 30 ===
Use: Treatment of vestibular and general neurological decompression sickness following normal or shortened decompression.
Oxygen and Heliox 50 or Nitrox 50 is available
Maximum pressure 30 msw (100 fsw)
Run time 7 hours 2 minutes
=== Comex Therapeutic Table CX 30A ===
Use: Treatment of musculoskeletal decompression sickness when signs of oxygen toxicity are present.
Oxygen is available
Maximum pressure 30 msw
Run time 8 hours 44 minutes
=== Comex Therapeutic Table CX 30AL ===
Use: Treatment of vestibular and general neurological decompression sickness when signs of oxygen toxicity are present.
Oxygen is available
Maximum pressure 30 sw
Run time 11 hours 8 minutes
=== Russian Therapeutic Recompression Regimen I ===
Use: Treatment of light forms of decompression sickness when the symptoms are completely resolved when reaching a pressure of 29 msw (96 fsw).
Oxygen is not used
Maximum pressure 49 msw (160 fsw)
Run time 13 hours 9 minutes
=== Russian Therapeutic Recompression Regimen II ===
Use: Treatment of light forms of decompression sickness when the symptoms are completely resolved when reaching a pressure of 49 msw (160 fsw), or if there is a relapse after use of Regimen I.
Oxygen is not used
Maximum pressure 49 msw (160 fsw)
Run time 26 hours 11 minutes
=== Russian Therapeutic Recompression Regimen III ===
Use: Treatment of moderately severe decompression sickness, or if there is a relapse after use of Regimen II.
Oxygen is not used
Maximum pressure 68 msw (224 fsw)
Run time 31 hours 26 minutes
=== Russian Therapeutic Recompression Regimen IV ===
Use: Treatment of severe decompression sickness, or if there is a relapse after use of Regimen III.
Oxygen is not used
Maximum pressure 97 msw (320 fsw)
Run time 39 hours 2 minutes
=== Russian Therapeutic Recompression Regimen V ===
Use: Treatment of very severe decompression sickness, or if there is a relapse after use of Regimen IV.
Oxygen is not used. Helium may optionally be used for compression below 224 fsw in addition to the air used for initial compression.
Maximum pressure 97 msw (320 fsw)
Run time 87 hours 7 minutes (3 days 15 hours 7 minutes)
=== German Short Air Recompression Treatment Table used during the Rendsburg pedestrian tunnel project ===
Use: Treatment of mild decompression sickness where relief occurs within 30 minutes at 30 msw (98 fsw)
Oxygen not used
Maximum pressure 30 msw (98 fsw)
Run time 2 hours 18 minutes
=== German Recompression Treatment Table used during the Rendsburg pedestrian tunnel project ===
Use: Treatment of mild decompression sickness where relief does not occur within 30 minutes at 30 msw (98 fsw)
Oxygen is used
Maximum pressure 30 msw (98 fsw)
Run time 5 hours 24 minutes
=== German Recompression Treatment Table used during the Rendsburg pedestrian tunnel project ===
Use: Treatment of severe decompression sickness where relief does not occur within 30 minutes at 30 msw (98 fsw)
Oxygen is used
Maximum pressure 30 msw (98 fsw)
Run time 36 hours 55 minutes or 38 hours 25 minutes
== Oxygen tables designed for monoplace chambers ==
(specifically for chambers without facility for air breaks)
=== Hart monoplace table ===
100% oxygen for 30 minutes at 3.0 ATA followed by 60 minutes at 2.5 ATA.
=== Kindwall's monoplace table ===
Indication:
Pain only or skin bends for symptoms that resolve within 10 minutes of reaching treatment depth:
30 minutes at 2.8 bar (60 fsw)
Continuous decompression to 1.9 bar over 15 minutes
60 minutes at 1.9 bar (30 fsw)
Continuous decompression to surface over 15 minutes
Neurological decompression sickness, arterial gas embolism or unresolved symptoms after 10 minutes at treatment pressure:
30 minutes at 2.8 bar (60 fsw)
Continuous decompression to 1.9 bar over 30 minutes
60 minutes at 1.9 bar (30 fsw)
Continuous decompression to surface over 30 minutes
Repeat after 30 minutes on air at surface pressure if symptoms have not resolved.
== In-water recompression schedules ==
In-water recompression (IWR) or underwater oxygen treatment is the emergency treatment of decompression sickness (DCS) by sending the diver back underwater to allow the gas bubbles in the tissues, which are causing the symptoms, to resolve. It is a risky procedure that should only ever be used when the time to travel to the nearest recompression chamber is too long to save the victim's life.
Carrying out in-water recompression when there is a nearby recompression chamber or without special equipment and training is never a favoured option. The risk of the procedure comes from the fact that a diver with DCS is seriously ill and may become paralysed, unconscious or stop breathing whilst under water. Any one of these events is likely to result in the diver drowning or further injury to the diver during a subsequent rescue to the surface.
Six IWR treatment tables have been published in the scientific literature. Each of these methods have several commonalities including the use of a full face mask, a tender to supervise the diver during treatment, a weighted recompression line and a means of communication. The history of the three older methods for providing oxygen at 9 m (30 fsw) was described in great detail by Drs. Richard Pyle and Youngblood. The fourth method for providing oxygen at 7.5 m (25 fsw) was described by Pyle at the 48th Annual UHMS Workshop on In-water Recompression in 1999. The Clipperton method involves recompression to 9 m (30 fsw) while the Clipperton(a) rebreather method involves a recompression to 30 m (98 fsw).
Recommended equipment common to these tables includes:
a means of securely holding the casualty at a measured depth, such as a harness and 20 metre lazy shot line with a 20 kg lead weight at the bottom and a buoy at the top of at least 40 litres buoyancy
a means of allowing the casualty to ascend slowly, such as loops in the line to which the harness could be clipped
full face diving masks for the casualty and for an in-water attendant diver with two-way communication to the surface and an umbilical gas supply system
surface supplied breathing gases including pure oxygen and air delivered to the casualty by umbilical
=== Australian In-water Recompression Table ===
The Australian IWR Tables were developed by the Royal Australian Navy in the 1960s in response to their need for treatment in remote locations far away from recompression chambers. It was the shallow portion of the table developed for recompression chamber use.
Oxygen is breathed the entire portion of the treatment without any air breaks and is followed by alternating periods (12 hours) of oxygen and air breathing on the surface.
=== Clipperton In-water Recompression Tables ===
The Clipperton and Clipperton(a) methods were developed for use on a scientific mission to the atoll of Clipperton, 1,300 km from the Mexican coast. The two versions are based on the equipment available for treatment with the Clipperton(a) table being designed for use with rebreathers.
Both methods begin with 10 minutes of surface oxygen. For the Clipperton IWR table, oxygen is then breathed the entire portion of the treatment without any air breaks. For the Clipperton(a) IWR table, descent is made to the initial treatment depth maintaining a partial pressure of 1.4 ATA. Oxygen breathing on the surface for 6 hours post treatment and intravenous fluids are also administered following both treatment tables.
=== Hawaiian In-water Recompression Table ===
The Hawaiian IWR table was first described by Farm et al. while studying the diving habits of Hawaii's diving fishermen.
The initial portion of the treatment involves descent on air to the depth of relief plus 30 fsw or a maximum of 165 fsw for ten minutes. Ascent from initial treatment depth to 30 fsw occurs over 10 minutes. The diver then completes the treatment breathing oxygen and is followed by oxygen breathing on the surface for 30 minutes post treatment.
The Hawaiian IWR Table with Pyle modifications can be found in the proceedings of the DAN 2008 Technical Diving Conference (In Press) or through download from DAN here.
=== Pyle In-water Recompression Table ===
The Pyle IWR table was developed by Dr. Richard Pyle as a method for treating DCS in the field following scientific dives.
This method begins with a 10-minute surface oxygen evaluation period. Compression to 25 fsw on oxygen for another 10-minute evaluation period. The table is best described by the treatment algorithm (Pyle IWR algorithm). This table does include alternating air breathing periods or "air breaks".
=== US Navy In-water Recompression Tables ===
The US Navy developed two IWR treatment tables. The table used depends on the symptoms diagnosed by the medical officer.: 20‑4.4.2.2
Oxygen is breathed the entire duration of the treatment without any air breaks and is followed by 3 hours of oxygen breathing on the surface.
Diver descends to 30 feet accompanied by a standby diver, and remains there for 60 minutes for Type I symptoms and 90 minutes for Type II symptoms, after this ascends to 20 feet even if symptoms have not resolved, and decompresses for 60 minutes at 20 feet and 60 minutes at 10 feet. Oxygen is breathed for another 3 hours after surfacing.: 20‑4.4.2.2
=== Royal Navy Table 81 – Emergency therapy in the water ===
Use: Emergency in-water recompression when no chamber is available.
Oxygen is not used
Maximum depth 30 m (98 ft) for 5 minutes
Continuous ascent to 20 m at 4.5 minutes per metre
Continuous ascent to 10 m at 8 minutes per metre
Continuous ascent to surface at 15 metres per minute
Run time 4 hours 41 minutes
== "Informal" in-water recompression ==
Although in-water recompression is regarded as risky, and to be avoided, there is increasing evidence that technical divers who surface and demonstrate mild DCS symptoms may often get back into the water and breathe pure oxygen at a depth 20 feet (6.1 meters) for a period of time to seek to alleviate the symptoms. This trend is noted in paragraph 3.6.5 of DAN's 2008 accident report. The report also notes that whilst the reported incidents showed very little success, "[w]e must recognize that these calls were mostly because the attempted IWR failed. In case the IWR were successful, [the] diver would not have called to report the event. Thus we do not know how often IWR may have been used successfully."
== Other tables to be fitted in later ==
=== Lambertsen/Solus Ocean Systems Table 7A ===
Used in commercial diving for:
symptoms that develop at pressure.
recompression deeper than 165 fsw (50 msw)' or
where extended decompression is necessary.
Protocol:
Depth unlimited on heliox, limit 200 fsw for air.
Compress to Depth of relief +10 msw but no deeper than max depth of dive
Hold for 30 min, then decompress to 50 msw at 4.4 msw per hour.
From 50 msw per USN T7
Run time more than 36 hours depending on depth
=== IANTD in-water recompression schedules ===
Used for emergency recompression of technical divers in remote areas.
IANTD in water recompression protocol
The certification agency International Association of Nitrox and Technical Divers (IANTD) have developed a training program for technical divers to run in water therapeutic recompression for suitably competent technical divers in remote locations, when conditions and equipment are suitable and the condition of the diver is assessed to require emergency treatment and the diver is likely to benefit sufficiently to justify the risk.
Most of the time on hyperbaric oxygen is at 25 fsw (7.5 msw) Oxygen is breathed, with air breaks.
== References ==
== Further reading ==
Walker, Morton (1 January 1998). Hyperbaric Oxygen Therapy. Penguin. ISBN 9780895297594.
Antonelli, C; Franchi, F; Della Marta, M.E.; Carinci, A.; Sbrana, G.; Tanasi, P.; de Fina, L.; Brauzzi, M. (2009). "Guiding principles in choosing a therapeutic table for DCI hyperbaric therapy" (PDF). Minerva Anestesiologica. 75 (3). Minerva Medica: 151–161. PMID 19221544. Retrieved 26 February 2016.
Risberg, Jan; Møllerløkken, Andreas; Eftedal, Olav Sande (12 August 2019). Norwegian Diving- and Treatment Tables. Tables and guidelines for surface orientated diving on air and nitrox. Tables and guidelines for treatment of decompression illness (PDF) (Report). ISBN 978-82-690699-7-6. | Wikipedia/Hyperbaric_treatment_schedules |
The Varying Permeability Model, Variable Permeability Model or VPM is an algorithm that is used to calculate the decompression needed for ambient pressure dive profiles using specified breathing gases. It was developed by D.E. Yount and others for use in professional and recreational diving. It was developed to model laboratory observations of bubble formation and growth in both inanimate and in vivo systems exposed to pressure. In 1986, this model was applied by researchers at the University of Hawaiʻi to calculate diving decompression tables.
Several variations of the algorithm have been used in mobile and desktop dive planning software and om dive computers.
== Theoretical basis ==
The VPM presumes that microscopic bubble nuclei always exist in water and tissues that contain water. Any nuclei larger than a specific "critical" size, which is related to the maximum dive depth (exposure pressure), will grow during decompression when the diver ascends. The VPM aims to minimize the total volume of these growing bubbles by keeping the external pressure sufficiently large and the inspired inert gas partial pressures relatively low during decompression. The model depends on the assumptions that different sizes of bubbles exist within the body, that the larger bubbles require less reduction in pressure to begin to grow than smaller ones, and that fewer large bubbles exist than smaller ones. These assumptions can be used to construct an algorithm that provides decompression schedules, designed to eliminate the larger, growing bubbles before they cause problems.
Varying permeability refers to the layer of molecules surrounding the bubbles, which may vary in permeability to gas molecules in the bubble and the surrounding medium, and which affect the diffusion of gases between the surroundings and the bubble, and the variation of compressibility of the bubble under changes of pressure.
== Bibliography ==
This bibliography list was compiled by E.B. Maiken and E.C. Baker as reference material for the V-Planner web site in 2002.
=== Primary Modeling Sources ===
Yount, D.E.; Hoffman, D.C. (1984). Bachrach, Arthur J.; Matzen, M.M. (eds.). Decompression theory: A dynamic critical-volume hypothesis. Underwater physiology VIII: Proceedings of the eighth symposium on underwater physiology. Bethesda: Undersea and Hyperbaric Medical Society. pp. 131–146.</ref>
Yount, D.E.; Hoffman, D.C. (1986). "On the use of a bubble formation model to calculate diving tables". Aviat Space Environ Med. 57 (2): 149–156. ISSN 0095-6562. PMID 3954703.
Yount, D.E.; Hoffman, D.C. (1989). "On the use of a bubble formation model to calculate nitrogen and helium diving tables". In Paganelli, C.V.; Farhi, L.E. (eds.). Physiological functions in special environments. New York: Springer-Verlag. pp. 95–108.
Yount, D.E.; Maiken, E.B.; Baker, E.C. (2000). Lang, M.A.; Lehner, C.E. (eds.). Implications of the Varying Permeability Model for Reverse Dive Profiles. Proceedings of the Reverse Dive Profiles Workshop. Washington, D.C.: Smithsonian Institution. pp. 29–61.
=== VPM Research and Development Sources ===
D'Arrigo, J.S. (1978). "Improved method for studying the surface chemistry of bubble formation". Aviat Space Environ Med. 49 (2): 358–361. ISSN 0095-6562. PMID 637789.
Kunkle, T.D. 1979. Bubble nucleation in supersaturated fluids. Univ. of Hawaii Sea Grant Technical Report UNIHI-SEAGRANT-TR-80-01. Pp. 108.
Paganelli, C.V.; Strauss, R.H.; Yount, D.E. (1978). "Bubble formation within decompressed hen's eggs". Aviat Space Environ Med. 48 (1): 48–49. ISSN 0095-6562. PMID 831713.
Strauss, R.H. (1974). "Bubble formation in gelatin: Implications for prevention of decompression sickness". Undersea Biomed. Res. 1 (2): 169–174. ISSN 0093-5387. OCLC 2068005. PMID 4469188. Archived from the original on April 15, 2013. Retrieved 2008-04-16.
Strauss, R.H.; Kunkle, T.D. (1974). "Isobaric bubble growth: A consequence of altering atmospheric gas". Science. 186 (4162): 443–444. Bibcode:1974Sci...186..443S. doi:10.1126/science.186.4162.443. ISSN 0193-4511. OCLC 5206521. PMID 4413996. S2CID 32874911.
Yount, D.E.; Kunkle, T.D. (1975). "Gas nucleation in the vicinity of solid hydrophobic spheres". Journal of Applied Physics. 46 (10): 4484–4486. Bibcode:1975JAP....46.4484Y. doi:10.1063/1.321381. ISSN 0021-8979. Archived from the original on 2013-02-24. Retrieved 2008-04-16.
Yount, D.E.; Strauss, R.H. (1976). "Bubble formation in gelatin: A model for decompression sickness". Journal of Applied Physics. 47 (11): 5081–5089. Bibcode:1976JAP....47.5081Y. doi:10.1063/1.322469. ISSN 0021-8979. Archived from the original on 2013-02-23. Retrieved 2008-04-16.
Yount, D.E.; Kunkle, T.D.; D'Arrigo, J.S.; Ingle, F.W.; Yeung, C.M.; Beckman, E.L. (1977). "Stabilization of gas cavitation nuclei by surface-active compounds". Aviat Space Environ Med. 48 (3): 185–191. ISSN 0095-6562. PMID 856151.
Yount, D.E. (1979). "Skins of varying permeability: a stabilization mechanism for gas cavitation nuclei". J. Acoust. Soc. Am. 65 (6): 1429–1439. Bibcode:1979ASAJ...65.1429Y. doi:10.1121/1.382930. ISSN 1520-8524. S2CID 53315872.
Yount, D.E.; Yeung, C.M.; Ingle, F.W. (1979). "Determination of the radii of gas cavitation nuclei by filtering gelatin". J. Acoust. Soc. Am. 65 (6): 1440–1450. Bibcode:1979ASAJ...65.1440Y. doi:10.1121/1.382905. ISSN 1520-8524.
Yount, D.E. (1979). "Application of a bubble formation model to decompression sickness in rats and humans". Aviat Space Environ Med. 50 (1): 44–50. ISSN 0095-6562. PMID 217330.
Yount, D.E. 1979. Multiple inert-gas bubble disease: a review of the theory. In: Lambertsen, C.J. and Bornmann, R.C. eds. Isobaric Inert Gas Counterdiffusion Workshop. Undersea Medical Society, Bethesda, 90-125.
Yount, D.E.; Lally, D.A. (1980). "On the use of oxygen to facilitate decompression". Aviat Space Environ Med. 51 (6): 544–550. ISSN 0095-6562. PMID 6774706.
Yount, D.E. (1981). "Application of a bubble formation model to decompression sickness in fingerling salmon". Undersea Biomed. Res. 8 (4): 199–208. ISSN 0093-5387. OCLC 2068005. PMID 7324253. Archived from the original on 2018-05-04. Retrieved 2008-04-16.
Yount, D.E.; Yeung, C.M. (1981). "Bubble formation in supersaturated gelatin: a further investigation of gas cavitation nuclei". J. Acoust. Soc. Am. 69 (3): 702–708. Bibcode:1981ASAJ...69..702Y. doi:10.1121/1.385567. ISSN 1520-8524. S2CID 54050598.
Yount, D.E. (1982). "On the evolution, generation, and regeneration of gas cavitation nuclei". J. Acoust. Soc. Am. 71 (6): 1473–1481. Bibcode:1982ASAJ...71.1473Y. doi:10.1121/1.387845. ISSN 1520-8524. S2CID 53411356.
Yount, D.E.; Hoffman, D.C. (1983). Hoyt, J.W. (ed.). "On the use of a cavitation model to calculate diving tables". Cavitation and Multiphase Flow Forum 1983. New York: American Society of Mechanical Engineers: 65–68. OCLC 232584820.
Yount, D.E. (1983). "A model for microbubble fission in surfactant solutions". Journal of Colloid and Interface Science. 91 (2): 349–360. Bibcode:1983JCIS...91..349Y. doi:10.1016/0021-9797(83)90347-8. ISSN 0021-9797.
Yount, D.E.; Gillary, E.W.; Hoffman, D.C. (1984). "A microscopic investigation of bubble formation nuclei". J. Acoust. Soc. Am. 76 (5): 1511–1521. Bibcode:1984ASAJ...76.1511Y. doi:10.1121/1.391434. ISSN 1520-8524. S2CID 46764818.
Yount, D.E. (1997). "On the elastic properties of the interfaces that stabilize gas cavitation nuclei". Journal of Colloid and Interface Science. 193 (1): 50–59. Bibcode:1997JCIS..193...50Y. doi:10.1006/jcis.1997.5048. ISSN 0021-9797. PMID 9299088.
== VPM Dive Planning Software ==
V-Planner: VPM-B & VPM-B/E, VPM-B/FBO.
MultiDeco: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-B, ZHL-C, GF, and GFS.
Ultimate Planner: VPM-B, VPM-B/U, VPM-B (Dec-12), VPM-B/U (Dec-12), ZHL-B, ZHL-C, ZHL-D, GF and GF/U.
DecoPlanner: VPM-B.
HLPlanner: VPM-B.
JDeco: VPM-B.
PalmVPM: VPM.
DivePlan: VPM.
Baltic Deco Planner: VPM-B.
Subsurface: VPM-B.
== VPM Dive computers ==
V-Planner Live: VPM-B & VPM-B/E.
MultiDeco-X1: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.
MultiDeco-DR5: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.
Shearwater Research Predator, Petrel, Perdix and NERD models: GF, VPM-B plus GFS.
RATIO Computers: iX3M series and iDive (Tech and Reb) series VPM-B and ZHL16-B.
TDC-3 with MultiDeco-TDC: VPM-B & VPM-B/E, VPM-B/FBO, ZHL-C, GF, and GFS.
HeinrichsWeikamp OSTC4: VPM-B
== See also ==
Decompression (diving) – Pressure reduction and its effects during ascent from depth
Decompression sickness – Disorder caused by dissolved gases forming bubbles in tissues
Decompression theory – Theoretical modelling of decompression physiology
Dive computer – Instrument to calculate decompression status in real time
Physiology of decompression – The physiological basis for decompression theory and practice
Reduced gradient bubble model – Decompression algorithm
Bühlmann decompression algorithm – Mathematical model of tissue inert gas uptake and release with pressure change
Thalmann algorithm – Mathematical model for diver decompression
== References ==
== External links ==
VPM web site
VPM development time line | Wikipedia/Varying_Permeability_Model |
A remotely operated underwater vehicle (ROUV) or remotely operated vehicle (ROV) is a free-swimming submersible craft used to perform underwater observation, inspection and physical tasks such as valve operations, hydraulic functions and other general tasks within the subsea oil and gas industry, military, scientific and other applications. ROVs can also carry tooling packages for undertaking specific tasks such as pull-in and connection of flexible flowlines and umbilicals, and component replacement. They are often used to do research and commercial work at great depths beyond the capacities of most submersibles and divers.
== Description ==
This meaning is different from remote control vehicles operating on land or in the air because ROVs are designed specifically to function in underwater environments, where conditions such as high pressure, limited visibility, and the effects of buoyancy and water currents pose unique challenges. While land and aerial vehicles use wireless communication for control, ROVs typically rely on a physical connection, such as a tether or umbilical cable, to transmit power, video, and data signals, ensuring reliable operation even at great depths. The tether also provides a stable means of communication, which is crucial in underwater conditions where radio waves are absorbed quickly by water, making wireless signals ineffective for long-range underwater use.
ROVs are unoccupied, usually highly maneuverable, and operated by a crew either aboard a vessel/floating platform or on proximate land. They are common in deepwater industries such as offshore hydrocarbon extraction. They are generally, but not necessarily, linked to a host ship by a neutrally buoyant tether or, often when working in rough conditions or in deeper water, a load-carrying umbilical cable is used along with a tether management system (TMS). The TMS is either a garage-like device which contains the ROV during lowering through the splash zone or, on larger work-class ROVs, a separate assembly mounted on top of the ROV. The purpose of the TMS is to lengthen and shorten the tether so the effect of cable drag where there are underwater currents is minimized. The umbilical cable is an armored cable that contains a group of electrical conductors and fiber optics that carry electric power, video, and data signals between the operator and the TMS. Where used, the TMS then relays the signals and power for the ROV down the tether cable. Once at the ROV, the electric power is distributed between the components of the ROV. However, in high-power applications, most of the electric power drives a high-power electric motor which drives a hydraulic pump. The pump is then used for propulsion and to power equipment such as torque tools and manipulator arms where electric motors would be too difficult to implement subsea. Most ROVs are equipped with at least a video camera and lights. Additional equipment is commonly added to expand the vehicle's capabilities. These may include sonars, magnetometers, a still camera, a manipulator or cutting arm, water samplers, and instruments that measure water clarity, water temperature, water density, sound velocity, light penetration, and temperature.
=== Terminology ===
In the professional diving and marine contracting industry, the term remotely operated vehicle (ROV) is used.
== Classification ==
Submersible ROVs are normally classified into categories based on their size, weight, ability or power. Some common ratings are:
Micro - typically Micro-class ROVs are very small in size and weight. Today's Micro-Class ROVs can weigh less than 3 kg. These ROVs are used as an alternative to a diver, specifically in places where a diver might not be able to physically enter such as a sewer, pipeline or small cavity.
Mini - typically Mini-Class ROVs weigh in around 15 kg. Mini-Class ROVs are also used as a diver alternative. One person may be able to transport the complete ROV system out with them on a small boat, deploy it and complete the job without outside help. Some Micro and Mini classes are referred to as "eyeball"-class to differentiate them from ROVs that may be able to perform intervention tasks.
General - typically less than 5 HP (propulsion); occasionally small three finger manipulators grippers have been installed, such as on the very early RCV 225. These ROVs may be able to carry a sonar unit and are usually used on light survey applications. Typically the maximum working depth is less than 1,000 metres though one has been developed to go as deep as 7,000 m.
Inspection Class - these are typically rugged commercial or industrial use observation and data gathering ROVs - typically equipped with live-feed video, still photography, sonar, and other data collection sensors. Inspection Class ROVs can also have manipulator arms for light work and object manipulation.
Light Workclass - typically less than 50 hp (propulsion). These ROVs may be able to carry some manipulators. Their chassis may be made from polymers such as polyethylene rather than the conventional stainless steel or aluminium alloys. They typically have a maximum working depth less than 2000 m.
Heavy Workclass - typically less than 220 hp (propulsion) with an ability to carry at least two manipulators. They have a working depth up to 3500 m.
Trenching & Burial - typically more than 200 hp (propulsion) and not usually greater than 500 hp (while some do exceed that) with an ability to carry a cable laying sled and work at depths up to 6000 m in some cases.
Submersible ROVs may be "free swimming" where they operate neutrally buoyant on a tether directly from the launch ship or platform, or they may be "garaged" where they operate from a heavy submersible "garage" or "tophat" on a tether deployed from the garage which is lowered from the ship or platform. Both techniques have their pros and cons; however very deep work is normally done with a garage.
== History ==
In the 1970s and '80s the Royal Navy used "Cutlet", a remotely operated submersible, to recover practice torpedoes and mines. RCA (Noise) maintained the "Cutlet 02" System based at BUTEC ranges, whilst the "03" system was based at the submarine base on the Clyde and was operated and maintained by RN personnel.
The U.S. Navy funded most of the early ROV technology development in the 1960s into what was then named a "Cable-Controlled Underwater Recovery Vehicle" (CURV). This created the capability to perform deep-sea rescue operation and recover objects from the ocean floor, such as a nuclear bomb lost in the Mediterranean Sea after the 1966 Palomares B-52 crash. Building on this technology base; the offshore oil and gas industry created the work-class ROVs to assist in the development of offshore oil fields. More than a decade after they were first introduced, ROVs became essential in the 1980s when much of the new offshore development exceeded the reach of human divers. During the mid-1980s the marine ROV industry suffered from serious stagnation in technological development caused in part by a drop in the price of oil and a global economic recession. Since then, technological development in the ROV industry has accelerated and today ROVs perform numerous tasks in many fields. Their tasks range from simple inspection of subsea structures, pipelines, and platforms, to connecting pipelines and placing underwater manifolds. They are used extensively both in the initial construction of a sub-sea development and the subsequent repair and maintenance. The oil and gas industry has expanded beyond the use of work class ROVs to mini ROVs, which can be more useful in shallower environments. They are smaller in size, oftentimes allowing for lower costs and faster deployment times.
Submersible ROVs have been used to identify many historic shipwrecks, including the RMS Titanic, the Bismarck, USS Yorktown, the SM U-111, and SS Central America. In some cases, such as the Titanic and the SS Central America, ROVs have been used to recover material from the sea floor and bring it to the surface, the most recent being in July 2024 during a Titanic expedition in recovering artefacts for the first time through a magnetometer.
While the oil and gas industry uses the majority of ROVs, other applications include science, military, and salvage. The military uses ROV for tasks such as mine clearing and inspection. Science usage is discussed below.
== Construction ==
Work-class ROVs are built with a large flotation pack on top of an aluminium chassis to provide the necessary buoyancy to perform a variety of tasks. The sophistication of construction of the aluminum frame varies depending on the manufacturer's design. Syntactic foam is often used for the flotation material. A tooling skid may be fitted at the bottom of the system to accommodate a variety of sensors or tooling packages. By placing the light components on the top and the heavy components on the bottom, the overall system has a large separation between the center of buoyancy and the center of gravity: this provides stability and the stiffness to do work underwater. Thrusters are placed between center of buoyancy and center of gravity to maintain the attitude stability of the robot in maneuvers. Various thruster configurations and control algorithms can be used to give appropriate positional and attitude control during the operations, particularly in high current waters. Thrusters are usually in a balanced vector configuration to provide the most precise control possible.
Electrical components can be in oil-filled water tight compartments or one-atmosphere compartments to protect them from corrosion in seawater and being crushed by the extreme pressure exerted on the ROV while working deep. The ROV will be fitted with thrusters, cameras, lights, tether, a frame, and pilot controls to perform basic work. Additional sensors, such as manipulators and sonar, can be fitted as needed for specific tasks. It is common to find ROVs with two robotic arms; each manipulator may have a different gripping jaw. The cameras may also be guarded for protection against collisions.
The majority of the work-class ROVs are built as described above; however, this is not the only style in ROV building method. Smaller ROVs can have very different designs, each appropriate to its intended task. Larger ROVs are commonly deployed and operated from vessels, so the ROV may have landing skids for retrieval to the deck.
== Configurations ==
Remotely operated vehicles have three basic configurations. Each of these brings specific limitations.
Open or box frame ROVs - this is the most familiar of the ROV configurations - consisting of an open frame where all the operational sensors, thrusters, and mechanical components are enclosed. These are useful for free-swimming in light currents (less than 4 knots based upon manufacturer specifications). These are not suitable for towed applications due to their very poor hydrodynamic design. Most Work-Class and Heavy Work-Class ROVs are based upon this configuration.
Torpedo shaped ROVs - this is a common configuration for data gathering or inspection class ROVs. The torpedo shape offers low hydrodynamic resistance, but comes with significant control limitations. The torpedo shape requires high speed (which is why this shape is used for military munitions) to remain positionally and attitudinally stable, but this type is highly vulnerable at high speed. At slow speeds (0–4 knots) suffers from numerous instabilities, such as tether induced roll and pitch, current induced roll, pitch, and yaw. It has limited control surfaces at the tail or stern, which easily cause over compensation instabilities. These are frequently referred to as "Tow Fish", since they are more often used as a towed ROV.
== Tether management ==
ROVs require a tether, or an umbilical, (unlike an AUV) in order to transmit power and data between the vehicle and the surface. The size and weight of the tether should be considered: too large of a tether will adversely affect the drag of the vehicle, and too small may not be robust enough for lifting requirements during launch and recovery.
The tether is typically spooled onto a tether management system (TMS) which helps manage the tether so that it does not become tangled or knotted. In some situations it can be used as a winch to lower or recover the vehicle.
== Applications ==
=== Survey ===
Survey or inspection ROVs are generally smaller than work class ROVs and are often sub-classified as either Class I: Observation Only or Class II Observation with payload. They are used to assist with hydrographic survey, i.e. the location and positioning of subsea structures, and also for inspection work for example pipeline surveys, jacket inspections and marine hull inspection of vessels. Survey ROVs (also known as "eyeballs"), although smaller than workclass, often have comparable performance with regard to the ability to hold position in currents, and often carry similar tools and equipment - lighting, cameras, sonar, ultra-short baseline (USBL) beacon, Raman spectrometer, and strobe flasher depending on the payload capability of the vehicle and the needs of the user.
=== Support of diving operations ===
ROV operations in conjunction with simultaneous diving operations are under the overall supervision of the diving supervisor for safety reasons.
The International Marine Contractors Association (IMCA) published guidelines for the offshore operation of ROVs in combined operations with divers in the document Remotely Operated Vehicle Intervention During Diving Operations (IMCA D 054, IMCA R 020), intended for use by both contractors and clients.
Remotely operated vehicles might be used during Submarine rescue operations.
=== Military ===
ROVs have been used by several navies for decades, primarily for minehunting and minebreaking.
In October 2008 the U.S. Navy began to improve its locally piloted rescue systems, based on the Mystic DSRV and support craft, with a modular system, the SRDRS, based on a tethered, occupied ROV called a pressurized rescue module (PRM). This followed years of tests and exercises with submarines from the fleets of several nations. It also uses the uncrewed Sibitzky ROV for disabled submarine surveying and preparation of the submarine for the PRM.
The US Navy also uses an ROV called AN/SLQ-48 Mine Neutralization Vehicle (MNV) for mine warfare. It can go 1,000 yards (910 m) away from the ship due to a connecting cable, and can reach 2,000 feet (610 m) deep. The mission packages available for the MNV are known as MP1, MP2, and MP3.
The MP1 is a cable cutter to surface the moored mine for recovery exploitation or explosive ordnance disposal (EOD).
The MP2 is a bomblet of 75 lb (34 kg) polymer-bonded explosive PBXN-103 high explosive for neutralizing bottom/ground mines.
The MP3 is a moored mine cable gripper and a float with the MP2 bomblet combination to neutralize moored mines underwater.
The charges are detonated by acoustic signal from the ship.
The AN/BLQ-11 autonomous uncrewed undersea vehicle (UUV) is designed for covert mine countermeasure capability and can be launched from certain submarines.
The U.S.Navy's ROVs are only on Avenger-class mine countermeasures ships. After the grounding of USS Guardian (MCM-5) and decommissioning of USS Avenger (MCM-1), and USS Defender (MCM-2), only 11 US Minesweepers remain operating in the coastal waters of Bahrain (USS Sentry (MCM-3), USS Devastator (MCM-6), USS Gladiator (MCM-11) and USS Dextrous (MCM-13)), Japan (USS Patriot (MCM-7), USS Pioneer (MCM-9), USS Warrior (MCM-10) and USS Chief (MCM-14)), and California (USS Champion (MCM-4), USS Scout (MCM-8), and USS Ardent (MCM-12) ).
During August 19, 2011, a Boeing-made robotic submarine dubbed Echo Ranger was being tested for possible use by the U.S. military to stalk enemy waters, patrol local harbors for national security threats and scour ocean floors to detect environmental hazards. The Norwegian Navy inspected the ship Helge Ingstad by the Norwegian Blueye Pioneer underwater drone.
As their abilities grow, smaller ROVs are also increasingly being adopted by navies, coast guards, and port authorities around the globe, including the U.S. Coast Guard and U.S. Navy, Royal Netherlands Navy, the Norwegian Navy, the Royal Navy and the Saudi Border Guard. They have also been widely adopted by police departments and search and recovery teams. Useful for a variety of underwater inspection tasks such as explosive ordnance disposal (EOD), meteorology, port security, mine countermeasures (MCM), and maritime intelligence, surveillance, reconnaissance (ISR).
=== Science ===
ROVs are also used extensively by the scientific community to study the ocean. A number of deep sea animals and plants have been discovered or studied in their natural environment through the use of ROVs; examples include the jellyfish Stellamedusa ventana and the eel-like halosaurs. In the US, cutting-edge work is done at several public and private oceanographic institutions, including the Monterey Bay Aquarium Research Institute (MBARI), the Woods Hole Oceanographic Institution (WHOI) (with Nereus), and the University of Rhode Island / Institute for Exploration (URI/IFE). In Europe, Alfred Wegener Institute use ROVs for Arctic and Antarctic surveys of sea ice, including measuring ice draft, light transmittance, sediments, oxygen, nitrate, seawater temperature, and salinity. For these purposes, it is equipped with a single- and multibeam sonar, spectroradiometer, manipulator, fluorometer, conductivity/ temperature/depth (salinity measurement) (CTD), optode, and UV-spectrometer.
Science ROVs take many shapes and sizes. Since good video footage is a core component of most deep-sea scientific research, research ROVs tend to be outfitted with high-output lighting systems and broadcast quality cameras. Depending on the research being conducted, a science ROV will be equipped with various sampling devices and sensors. Many of these devices are one-of-a-kind, state-of-the-art experimental components that have been configured to work in the extreme environment of the deep ocean. Science ROVs also incorporate a good deal of technology that has been developed for the commercial ROV sector, such as hydraulic manipulators and highly accurate subsea navigation systems. They are also used for underwater archaeology projects such as the Mardi Gras Shipwreck Project in the Gulf of Mexico and the CoMAS project in the Mediterranean Sea.
There are several larger high-end systems that are notable for their capabilities and applications. MBARI's Tiburon vehicle cost over $6 million US dollars to develop and is used primarily for midwater and hydrothermal research on the West Coast of the US. WHOI's Jason system has made many significant contributions to deep-sea oceanographic research and continues to work all over the globe. URI/IFE's Hercules ROV is one of the first science ROVs to fully incorporate a hydraulic propulsion system and is uniquely outfitted to survey and excavate ancient and modern shipwrecks. The Canadian Scientific Submersible Facility ROPOS system is continually used by several leading ocean sciences institutions and universities for challenging tasks such as deep-sea vents recovery and exploration to the maintenance and deployment of ocean observatories.
==== Educational outreach ====
The SeaPerch Remotely Operated Underwater Vehicle (ROV) educational program is an educational tool and kit that allows elementary, middle, and high-school students to construct a simple, remotely operated underwater vehicle, from polyvinyl chloride (PVC) pipe and other readily made materials. The SeaPerch program teaches students basic skills in ship and submarine design and encourages students to explore naval architecture and marine and ocean engineering concepts. SeaPerch is sponsored by the Office of Naval Research, as part of the National Naval Responsibility for Naval Engineering (NNRNE), and the program is managed by the Society of Naval Architects and Marine Engineers.
Another innovative use of ROV technology was during the Mardi Gras Shipwreck Project. The "Mardi Gras Shipwreck" sank some 200 years ago about 35 miles off the coast of Louisiana in the Gulf of Mexico in 4,000 feet (1,200 meters) of water. The shipwreck, whose real identity remains a mystery, lay forgotten at the bottom of the sea until it was discovered in 2002 by an oilfield inspection crew working for the Okeanos Gas Gathering Company (OGGC). In May 2007, an expedition, led by Texas A&M University and funded by OGGC under an agreement with the Minerals Management Service (now BOEM), was launched to undertake the deepest scientific archaeological excavation ever attempted at that time to study the site on the seafloor and recover artifacts for eventual public display in the Louisiana State Museum. As part of the educational outreach Nautilus Productions in partnership with BOEM, Texas A&M University, the Florida Public Archaeology Network and Veolia Environmental produced a one-hour HD documentary about the project, short videos for public viewing and provided video updates during the expedition. Video footage from the ROV was an integral part of this outreach and used extensively in the Mystery Mardi Gras Shipwreck documentary.
The Marine Advanced Technology Education (MATE) Center uses ROVs to teach middle school, high school, community college, and university students about ocean-related careers and help them improve their science, technology, engineering, and math skills. MATE's annual student ROV competition challenges student teams from all over the world to compete with ROVs that they design and build. The competition uses realistic ROV-based missions that simulate a high-performance workplace environment, focusing on a different theme that exposes students to many different aspects of marine-related technical skills and occupations. The ROV competition is organized by MATE and the Marine Technology Society's ROV Committee and funded by organizations such as the National Aeronautics and Space Administration (NASA), National Oceanic and Atmospheric Administration (NOAA), and Oceaneering, and many other organizations that recognize the value of highly trained students with technology skills such as ROV designing, engineering, and piloting. MATE was established with funding from the National Science Foundation and is headquartered at Monterey Peninsula College in Monterey, California.
==== List of scientific ROVs ====
=== Media ===
As cameras and sensors have evolved and vehicles have become more agile and simple to pilot, ROVs have become popular particularly with documentary filmmakers due to their ability to access deep, dangerous, and confined areas unattainable by divers. There is no limit to how long an ROV can be submerged and capturing footage, which allows for previously unseen perspectives to be gained. ROVs have been used in the filming of several documentaries, including Nat Geo's Shark Men and The Dark Secrets of the Lusitania and the BBC Wildlife Special Spy in the Huddle.
Due to their extensive use by military, law enforcement, and coastguard services, ROVs have also featured in crime dramas such as the popular CBS series CSI.
=== Hobby ===
With an increased interest in the ocean by many people, both young and old, and the increased availability of once expensive and non-commercially available equipment, ROVs have become a popular hobby amongst many. This hobby involves the construction of small ROVs that generally are made out of PVC piping and often can dive to depths between 50 and 100 feet but some have managed to get to 300 feet.
=== STEM education ===
This new interest in ROVs has led to the formation of many competitions, including MATE (Marine Advanced Technology Education), NURC (National Underwater Robotics Challenge), and RoboSub. These are competitions in which competitors, most commonly schools and other organizations, compete against each other in a series of tasks using ROVs that they have built. Most hobby ROVs are tested in swimming pools and lakes where the water is calm, however some have tested their own personal ROVs in the sea. Doing so, however, creates many difficulties due to waves and currents that can cause the ROV to stray off course or struggle to push through the surf due to the small size of engines that are fitted to most hobby ROVs.
== See also ==
Remotely Operated Vehicle - a submersible robot designed to explore and perform underwater tasks in marine environments.
Autonomous underwater vehicle – Uncrewed underwater vehicle with autonomous guidance system
Echo Ranger – Marine autonomous underwater vehicle built by Boeing
Eelume – An autonomous underwater vehicle for inspection, maintenance, and repair
Global Explorer ROV – Deep water science and survey remotely operated vehicle
Helix Energy Solutions Group – Provider of offshore services and ROV operations
Nereus (underwater vehicle) – Hybrid remotely operated or autonomous underwater vehicle
PantheROV – Remotely operated vehicle built by undergraduate students at the University of Wisconsin–Milwaukee
Scorpio ROV – Work class remotely operated underwater vehicle
Subsea technology – Technology of submerged operations in the sea
Underwater acoustic positioning system – System for tracking and navigation of underwater vehicles or divers using acoustic signals
UNESCO Convention on the Protection of the Underwater Cultural Heritage – Treaty adopted on 2 November 2001
VideoRay UROVs – Series of inspection class remotely operated underwater vehicles
Robotic non-destructive testing – Method of inspection using remotely operated tools
Radio-controlled submarine – Scale model of a submarine that can be steered via radio control.
Unmanned underwater vehicle – Submersible vehicles that can operate underwater without a human occupant
== References ==
== External links ==
What are Underwater ROVs and What are they used for?
Remotely Operated Vehicles (ROV), Ocean Explorer, NOAA
What are Remotely Operated Vehicles (ROVs)?
ROVs at the Smithsonian Ocean Portal
Mystery Mardi Gras Shipwreck on YouTube | Wikipedia/Remotely_operated_underwater_vehicle |
The reduced gradient bubble model (RGBM) is an algorithm developed by Bruce Wienke for calculating decompression stops needed for a particular dive profile. It is related to the Varying Permeability Model. but is conceptually different in that it rejects the gel-bubble model of the varying permeability model.
It is used in several dive computers, particularly those made by Suunto, Aqwary, Mares, HydroSpace Engineering, and Underwater Technologies Center. It is characterised by the following assumptions: blood flow (perfusion) provides a limit for tissue gas penetration by diffusion; an exponential distribution of sizes of bubble seeds is always present, with many more small seeds than large ones; bubbles are permeable to gas transfer across surface boundaries under all pressures; the haldanean tissue compartments range in half time from 1 to 720 minutes, depending on gas mixture.
Some manufacturers such as Suunto have devised approximations of Wienke's model. Suunto uses a modified haldanean nine-compartment model with the assumption of reduced off-gassing caused by bubbles. This implementation offers both a depth ceiling and a depth floor for the decompression stops. The former maximises tissue off-gassing and the latter minimises bubble growth. The model has been correlated and validated in a number of published articles using collected dive profile data.
== Description ==
The model is based on the assumption that phase separation during decompression is random, yet highly probable, in body tissue, and that a bubble will continue to grow by acquiring gas from adjacent saturated tissue, at a rate depending on the local free/dissolved concentration gradient. Gas exchange mechanisms are fairly well understood in comparison with nucleation and stabilization mechanisms, which are computationally uncertainly defined. Nevertheless there is an opinion among some decompression researchers that the existing practices and studies on bubbles and nuclei provide useful information on bubble growth and elimination processes and the time scales involved. Wienke considers that the consistency between these practices and the underlying physical principles suggest directions for decompression modelling for algorithms beyond parameter fitting and extrapolation. He considers that the RGBM implements the theoretical model in these aspects and also supports the efficacy of recently developed safe diving practice due to its dual phase mechanics. These include:
reduced no-stop time limits;
safety stops in the 10-20 fsw depth zone;
ascent rates not exceeding 30 fsw per minute;
restricted repetitive exposures, particularly beyond 100 fsw,
restricted reverse profile and deep spike diving;
restricted multi day activity;
smooth coalescence of bounce and saturation limit points;
consistent diving protocols for altitude;
deep stops for decompression, extended range, and mixed gas diving with overall shorter decompression times, particularly in the shallow zone;
use of helium rich mixtures for technical diving, with shallower isobaric switches to nitrox than suggested by Haldanian strategies;
use of pure oxygen in the shallow zone to efficiently eliminate both dissolved and bubble phase inert gases.
== References == | Wikipedia/Reduced_gradient_bubble_model |
The Thalmann Algorithm (VVAL 18) is a deterministic decompression model originally designed in 1980 to produce a decompression schedule for divers using the US Navy Mk15 rebreather. It was developed by Capt. Edward D. Thalmann, MD, USN, who did research into decompression theory at the Naval Medical Research Institute, Navy Experimental Diving Unit, State University of New York at Buffalo, and Duke University. The algorithm forms the basis for the current US Navy mixed gas and standard air dive tables (from US Navy Diving Manual Revision 6). The decompression model is also referred to as the Linear–Exponential model or the Exponential–Linear model.
== History ==
The Mk15 rebreather supplies a constant partial pressure of oxygen of 0.7 bar (70 kPa) with nitrogen as the inert gas. Prior to 1980 it was operated using schedules from printed tables. It was determined that an algorithm suitable for programming into an underwater decompression monitor (an early dive computer) would offer advantages. This algorithm was initially designated "MK15 (VVAL 18) RTA", a real-time algorithm for use with the Mk15 rebreather.
== Description ==
VVAL 18 is a deterministic model that utilizes the Naval Medical Research Institute Linear Exponential (NMRI LE1 PDA) data set for calculation of decompression schedules. Phase two testing of the US Navy Diving Computer produced an acceptable algorithm with an expected maximum incidence of decompression sickness (DCS) less than 3.5% assuming that occurrence followed the binomial distribution at the 95% confidence level.
The use of simple symmetrical exponential gas kinetics models has shown up the need for a model that would give slower tissue washout. In the early 1980s the US Navy Experimental Diving Unit developed an algorithm using a decompression model with exponential gas absorption as in the usual Haldanian model, but a slower linear release during ascent. The effect of adding linear kinetics to the exponential model is to lengthen the duration of risk accumulation for a given compartment time constant.
The model was originally developed for programming decompression computers for constant oxygen partial pressure closed circuit rebreathers. Initial experimental diving using an exponential-exponential algorithm resulted in an unacceptable incidence of DCS, so a change was made to a model using the linear release model, with a reduction in DCS incidence. The same principles were applied to developing an algorithm and tables for a constant oxygen partial pressure model for Heliox diving
The linear component is active when the tissue pressure exceeds ambient pressure by a given amount specific to the tissue compartment. When the tissue pressure drops below this cross-over criterion the tissue is modelled by exponential kinetics. During gas uptake tissue pressure never exceeds ambient, so it is always modelled by exponential kinetics. This results in a model with the desired asymmetrical characteristics of slower washout than uptake. The linear/exponential transition is smooth. Choice of cross-over pressure determines the slope of the linear region as equal to the slope of the exponential region at the cross-over point.
During the development of these algorithms and tables, it was recognized that a successful algorithm could be used to replace the existing collection of incompatible tables for various air and Nitrox diving modes currently in the US Navy Diving Manual with a set of mutually compatible decompression tables based on a single model, which was proposed by Gerth and Doolette in 2007. This has been done in Revision 6 of the US Navy Diving Manual published in 2008, though some changes were made.
=== Implementation in dive computers ===
An independent implementation of the EL-Real Time Algorithm was developed by Cochran Consulting, Inc. for the diver-carried Navy Dive Computer under the guidance of E. D. Thalmann.
Since the discontinuation of Cochran Undersea Technology after the death of the owner, the algorithm has been implemented on some models of Shearwater Research's dive computers for use by the US Navy.
=== Physiological interpretation ===
Computer testing of a theoretical bubble growth model reported by Ball, Himm, Homer and Thalmann produced results which led to the interpretation of the three compartments used in the probabilistic LE model, with fast (1.5min), intermediate (51 min) and slow (488min) time constants, of which only the intermediate compartment uses the linear kinetics modification during decompression, as possibly not representing distinct anatomically identifiable tissues, but three different kinetic processes which relate to different elements of DCS risk.
They conclude that bubble evolution may not be sufficient to explain all aspects of DCS risk, and the relationship between gas phase dynamics and tissue injury requires further investigation.
== References ==
=== Sources ===
== External links ==
"The U.S. Navy Decompression Computer" - F. Butler | Wikipedia/Thalmann_algorithm |
The Bühlmann decompression model is a neo-Haldanian model which uses Haldane's or Schreiner's formula for inert gas uptake, a linear expression for tolerated inert gas pressure coupled with a simple parameterised expression for alveolar inert gas pressure and expressions for combining Nitrogen and Helium parameters to model the way inert gases enter and leave the human body as the ambient pressure and inspired gas changes. Different parameter sets are used to create decompression tables and in personal dive computers to compute no-decompression limits and decompression schedules for dives in real-time, allowing divers to plan the depth and duration for dives and the required decompression stops.
The model (Haldane, 1908) assumes perfusion limited gas exchange and multiple parallel tissue compartments and uses an exponential formula for in-gassing and out-gassing, both of which are assumed to occur in the dissolved phase.
Bühlmann, however, assumes that safe dissolved inert gas levels are defined by a critical difference instead of a critical ratio.
Multiple sets of parameters were developed by Swiss physician Dr. Albert A. Bühlmann, who did research into decompression theory at the Laboratory of Hyperbaric Physiology at the University Hospital in Zürich, Switzerland.
The results of Bühlmann's research that began in 1959 were published in a 1983 German book whose English translation was entitled Decompression-Decompression Sickness. The book was regarded as the most complete public reference on decompression calculations and was used soon after in dive computer algorithms.
== Principles ==
Building on the previous work of John Scott Haldane (The Haldane model, Royal Navy, 1908) and Robert Workman (M-Values, US-Navy, 1965) and working off funding from Shell Oil Company, Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues. These studies were confirmed by the Capshell experiments in the Mediterranean Sea in 1966.
=== Alveolar inert gas pressure ===
The Bühlmann model uses a simplified version of the alveolar gas equation to calculate alveolar inert gas pressure
P
a
l
v
=
[
P
a
m
b
−
P
H
2
0
+
1
−
R
Q
R
Q
P
C
O
2
]
⋅
Q
{\displaystyle P_{alv}=[P_{amb}-P_{H_{2}0}+{\frac {1-RQ}{RQ}}P_{CO_{2}}]\cdot Q}
Where
P
H
2
0
{\displaystyle P_{H_{2}0}}
is the water vapour pressure at 37°C (conventionally defined as 0.0627 bar),
P
C
O
2
{\displaystyle P_{CO_{2}}}
the carbon dioxide pressure (conventionally defined as 0.0534 bar),
Q
{\displaystyle Q}
the inspired inert gas fraction, and
R
Q
{\displaystyle RQ}
the respiratory coefficient: the ratio of carbon dioxide production to oxygen consumption. The Buhlmann model sets
R
Q
{\displaystyle RQ}
to 1, simplifying the equation to
P
a
l
v
=
[
P
a
m
b
−
P
H
2
0
]
⋅
Q
{\displaystyle P_{alv}=[P_{amb}-P_{H_{2}0}]\cdot Q}
=== Tissue inert gas exchange ===
Inert gas exchange in haldanian models is assumed to be perfusion limited and is governed by the ordinary differential equation
d
P
t
d
t
=
k
(
P
a
l
v
−
P
t
)
{\displaystyle {\dfrac {\mathrm {d} P_{t}}{\mathrm {d} t}}=k(P_{alv}-P_{t})}
This equation can be solved for constant
P
a
l
v
{\displaystyle P_{alv}}
to give the Haldane equation:
P
t
(
t
)
=
P
a
l
v
+
(
P
t
(
0
)
−
P
a
l
v
)
⋅
e
−
k
t
{\displaystyle P_{t}(t)=P_{alv}+(P_{t}(0)-P_{alv})\cdot e^{-kt}}
and for constant rate of change of alveolar gas pressure
R
{\displaystyle R}
to give the Schreiner equation:
P
t
(
t
)
=
P
a
l
v
(
0
)
+
R
(
t
−
1
k
)
−
(
P
a
l
v
(
0
)
−
P
t
(
0
)
−
R
k
)
e
−
k
t
{\displaystyle P_{t}(t)=P_{alv}(0)+R(t-{\dfrac {1}{k}})-(P_{alv}(0)-P_{t}(0)-{\dfrac {R}{k}})e^{-kt}}
=== Tissue inert gas limits ===
Similarly to Workman, the Bühlmann model specifies an affine relationship between ambient pressure and inert gas saturation limits. However, the Buhlmann model expresses this relationship in terms of absolute pressure
P
i
g
t
o
l
=
a
+
P
a
m
b
b
{\displaystyle P_{igtol}=a+{\frac {P_{amb}}{b}}}
Where
P
i
g
t
o
l
{\displaystyle P_{igtol}}
is the inert gas saturation limit for a given tissue and
a
{\displaystyle a}
and
b
{\displaystyle b}
constants for that tissue and inert gas.
The constants
a
{\displaystyle a}
and
b
{\displaystyle b}
, were originally derived from the saturation half-time using the following expressions:
a
=
2
bar
t
1
/
2
3
{\displaystyle a={\frac {2\,{\text{bar}}}{\sqrt[{3}]{t_{1/2}}}}}
b
=
1.005
−
1
t
1
/
2
2
{\displaystyle b=1.005-{\frac {1}{\sqrt[{2}]{t_{1/2}}}}}
The
b
{\displaystyle b}
values calculated do not precisely correspond to those used by Bühlmann for tissue compartments 4 (0.7825 instead of 0.7725) and 5 (0.8126 instead of 0.8125).
Versions B and C have manually modified the coefficient
a
{\displaystyle a}
.
In addition to this formulation, the Bühlmann model also specifies how the constants for multiple inert gas saturation combine when both Nitrogen and Helium are present in a given tissue.
a
=
a
N
2
(
1
−
R
)
+
a
H
e
R
{\displaystyle a=a_{N_{2}}(1-R)+a_{He}R}
b
=
b
N
2
(
1
−
R
)
+
b
H
e
R
{\displaystyle b=b_{N_{2}}(1-R)+b_{He}R}
where
a
N
2
{\displaystyle a_{N_{2}}}
and
a
H
e
{\displaystyle a_{He}}
are the tissue's
a
{\displaystyle a}
Nitrogen and Helium coefficients and
R
{\displaystyle R}
the ratio of dissolved Helium to total dissolved inert gas.
=== Ascent rates ===
Ascent rate is intrinsically a variable, and may be selected by the programmer or user for table generation or simulations, and measured as real-time input in dive computer applications.
The rate of ascent to the first stop is limited to 3 bar per minute for compartments 1 to 5, 2 bar per minute for compartments 6 and 7, and 1 bar per minute for compartments 8 to 16. Chamber decompression may be continuous, or if stops are preferred they may be done at intervals of 1 or 3 m.
== Applications ==
The Buhlmann model has been used within dive computers and to create tables.
=== Tables ===
Since precomputed tables cannot take into account the actual diving conditions, Buhlmann specifies a number of initial values and recommendations.
Atmospheric pressure
Water density
Initial tissue loadings
Descent rate
Breathing gas
Ascent rate
In addition, Buhlmann recommended that the calculations be based on a slightly deeper bottom depth.
=== Dive computers ===
Buhlmann assumes no initial values and makes no other recommendations for the application of the model within dive computers, hence all pressures and depths and gas fractions are either read from the computer sensors or specified by the diver and grouped dives do not require any special treatment.
== Versions ==
Several versions and extensions of the Bühlmann model have been developed, both by Bühlmann and by later workers. The naming convention used to identify the set of parameters is a code starting ZH-L, from Zürich (ZH), Linear (L) followed by the number of different (a,b) couples (ZH-L 12 and ZH-L 16)) or the number of tissue compartments (ZH-L 6, ZH-L 8), and other unique identifiers.
ZH-L 12 (1983)
ZH-L 12: The set of parameters published in 1983 with "Twelve Pairs of Coefficients for Sixteen Half-Value Times"
ZH-L 16 (1986)
ZH-L 16 or ZH-L 16 A (air, nitrox): The experimental set of parameters published in 1986.
ZH-L 16 B (air, nitrox): The set of parameters modified for printed dive table production, using slightly more conservative “a” values for tissue compartments #6, 7, 8 and 13.
ZH-L 16 C (air, nitrox): The set of parameters with more conservative “a” values for tissue compartments #5 to 15. For use in dive computers.
ZH-L 16 (helium): The set of parameters for use with helium.
ZH-L 16 ADT MB: set of parameters and specific algorithm used by Uwatec for their trimix-enabled computers. Modified in the middle compartments from the original ZHL-C, is adaptive to diver workload and includes Profile-Determined Intermediate Stops. Profile modification is by means of "MB Levels", personal option conservatism settings, which are not defined in the manual.
ZH-L 6 (1988)
ZH-L 6 is an adaptation (Albert Bühlmann, Ernst B.Völlm and Markus Mock) of the ZH-L16 set of parameters, implemented in Aladin Pro computers (Uwatec, Beuchat), with 6 tissue compartments (half-time : 6 mn / 14 mn / 34 mn / 64 mn / 124 mn / 320 mn).
ZH-L 8 ADT (1992)
ZH-L 8 ADT: A new approach with variable half-times and supersaturation tolerance depending on risk factors. The set of parameters and the algorithm are not public (Uwatec property, implemented in Aladin Air-X in 1992 and presented at BOOT in 1994). This algorithm may reduce the no-stop limit or require the diver to complete a compensatory decompression stop after an ascent rate violation, high work level during the dive, or low water temperature. This algorithm may also take into account the specific nature of repetitive dives.
ZH-L 8 ADT MB: A version of the ZHL-8 ADT claimed to suppress MicroBubble formation.
ZH-L 8 ADT MB PDIS: Profile-Determined Intermediate Stops.
ZH-L 8 ADT MB PMG: Predictive Multi-Gas.
== References ==
== Further reading ==
== External links ==
Many articles on the Bühlmann tables are available on the web.
Chapman, Paul (November 1999). "An Explanation of Professor A.A. Buehlmann's ZH-L16 Algorithm". New Jersey Scuba Diver. Archived from the original on 2010-02-15. Retrieved 20 January 2010. – Detailed background and worked examples
Decompression Theory: Robert Workman and Prof A Bühlmann. An overview of the history of Bühlmann tables
Stuart Morrison: DIY Decompression (2000). Works through the steps involved in using Bühlmann's ZH-L16 algorithm to write a decompression program. | Wikipedia/Bühlmann_decompression_algorithm |
Harald Ulrik Sverdrup (15 November 1888 – 21 August 1957) was a Norwegian oceanographer and meteorologist. He served as director of the Scripps Institution of Oceanography and the Norwegian Polar Institute.
== Background ==
He was born at Sogndal in Sogn og Fjordane, Norway.
He was the son of Lutheran theologian Edvard Sverdrup (1861–1923) and Maria Vollan (1865–1891). His sister Mimi Sverdrup Lunden (1894–1955) was an educator and author. His brother Leif Sverdrup (1898–1976) was a General with the U.S. Army Corps of Engineers. His brother
Einar Sverdrup (1895–1942) was CEO of Store Norske Spitsbergen Kulkompani.
Sverdrup was a student at Bergen Cathedral School in 1901 before graduating in 1906 at Kongsgård School in Stavanger. He graduated cand. real. in 1914 from University of Oslo. He studied under Vilhelm Bjerknes and earned his Dr. Philos. at the University of Leipzig in 1917.
== Career ==
He was the scientific director of the North Polar expedition of Roald Amundsen aboard the Maud from 1918 to 1925. His measurements of bottom depths, tidal currents, and tidal elevations on the vast shelf areas off the East Siberian Sea correctly described the propagation of tides as Poincare waves. Upon his return from this long expedition exploring the shelf seas to the north of Siberia, he became the chair in meteorology at the University of Bergen.
He was made director of California's Scripps Institution of Oceanography in 1936, initially for three years but the intervention of World War II meant he held the post until 1948. During 33 expeditions with the research vessel E. W. Scripps between 1938 and 1941, he produced a detailed oceanographic dataset off the coast of California. He also developed a simple theory of the general ocean circulation postulating a dynamical vorticity balance between the wind-stress curl and the meridional gradient of the Coriolis parameter, the Sverdrup balance. This balance describes wind-driven ocean gyres away from continental margins at western boundaries.
After leaving Scripps, he became director of the Norwegian Polar Institute in Oslo and continued to contribute to oceanography, ocean biology, and polar research. In biological oceanography, his critical depth hypothesis (published in 1953) was a significant milestone in the explanation of spring blooms of phytoplankton.
Sverdrup was a member of both the United States National Academy of Sciences, the Norwegian Academies of Science, the American Academy of Arts and Sciences, and the American Philosophical Society. He served as President of the International Association of Physical Oceanography and of the International Council for the Exploration of the Sea (ICES). His many publications include his magnum opus The Oceans: Their Physics, Chemistry and General Biology by Sverdrup, Martin W. Johnson and Richard H. Fleming (1942, new edition 1970) which formed the basic curriculum of oceanography for the next 40 years around the world.
== Personal life ==
In 1928, he married Gudrun (Vaumund) Bronn (1893–1983) and adopted her daughter Anna Margrethe.
== Honors ==
He was awarded the William Bowie Medal by the American Geophysical Union, the Alexander Agassiz Medal of the National Academy of Sciences, the Patron's Medal of the Royal Geographical Society, the Vega Medal by the Swedish Society for Anthropology and Geography and the Swedish Order of the Polar Star.
== Legacy ==
The Sverdrup, a unit describing the volume of water transport in ocean currents, is named after Harald Sverdrup. 1 Sverdrup is a volume flux of one million cubic meters per second (1 Sv = 106 m3 per second).
The Sverdrup Gold Medal Award was named in his honor by the American Meteorological Society.
The Norwegian research vessel MS H.U. Sverdrup II is named in his honor.
In 1977, the UK-APC named a series of peaks in Palmer Land, Antarctica the Sverdrup Nunataks after him.
== References ==
== Sources ==
Wordie, J. M. (November 1957). "Prof. H. U. Sverdrup". Nature. 180 (4594): 1023. Bibcode:1957Natur.180.1023W. doi:10.1038/1801023a0. S2CID 4153268.
Spjeldnaes, Nils (1976). "Harald Ulrik Sverdrup". Dictionary of Scientific Biography. Vol. 13. New York: Scribner's. pp. 166–167.
Sager, Gunther (September 1957). "In Memoriam Prof. Dr. Harald Ulrik Sverdrup". Zeitschrift für Meteorologie. 11 (9): 257–259.
Revelle, Roger; Munk, Walter (1948). "Harald Ulrik Sverdrup – An Appreciation" (PDF). Journal of Marine Research. 7 (3): 127–131. Archived (PDF) from the original on 2021-05-17.
Nierenberg, William A. (1996). "Harald Ulrik Sverdrup, 1888–1957" (PDF). Biographical Memoirs. Vol. 69. National Academy of Sciences. pp. 337–375. ISBN 978-0-309-05346-4.
Oreskes, Naomi; Rainger, Ronald (September 2000). "Science and Security before the Atomic Bomb: The Loyalty Case of Harald U. Sverdrup". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 31 (3): 309–369. Bibcode:2000SHPMP..31..309O. doi:10.1016/S1355-2198(00)00019-8.
== External links ==
Scripps Institution of Oceanography website
Harald Sverdrup Manuscripts SMC 121. Special Collections & Archives, UC San Diego Library.
H U Sverdrup II Research/Survey Vessel
Haral Ulrik Sverdrop Writings at Dartmouth College Library
Family genealogy | Wikipedia/Harald_Sverdrup_(oceanographer) |
An uncontrolled decompression is an undesired drop in the pressure of a sealed system, such as a pressurised aircraft cabin or hyperbaric chamber, that typically results from human error, structural failure, or impact, causing the pressurised vessel to vent into its surroundings or fail to pressurize at all.
Such decompression may be classed as explosive, rapid, or slow:
Explosive decompression (ED) is violent and too fast for air to escape safely from the lungs and other air-filled cavities in the body such as the sinuses and eustachian tubes, typically resulting in severe to fatal barotrauma.
Rapid decompression may be slow enough to allow cavities to vent but may still cause serious barotrauma or discomfort.
Slow or gradual decompression occurs so slowly that it may not be sensed before hypoxia sets in.
== Description ==
The term uncontrolled decompression here refers to the unplanned depressurisation of vessels that are occupied by people; for example, a pressurised aircraft cabin at high altitude, a spacecraft, or a hyperbaric chamber. For the catastrophic failure of other pressure vessels used to contain gas, liquids, or reactants under pressure, the term explosion is more commonly used, or other specialised terms such as BLEVE may apply to particular situations.
Decompression can occur due to structural failure of the pressure vessel, or failure of the compression system itself. The speed and violence of the decompression is affected by the size of the pressure vessel, the differential pressure between the inside and outside of the vessel, and the size of the leak hole.
The US Federal Aviation Administration recognizes three distinct types of decompression events in aircraft: explosive, rapid, and gradual decompression.
=== Explosive decompression ===
Explosive decompression occurs typically in less than 0.1 to 0.5 seconds, a change in cabin pressure faster than the lungs can decompress. Normally, the time required to release air from the lungs without restrictions, such as masks, is 0.2 seconds. The risk of lung trauma is very high, as is the danger from any unsecured objects that can become projectiles because of the explosive force, which may be likened to a bomb detonation.
Immediately after an explosive decompression, a heavy fog may fill the aircraft cabin as the air cools, raising the relative humidity and causing sudden condensation. Military pilots with oxygen masks must pressure-breathe, whereby the lungs fill with air when relaxed, and effort has to be exerted to expel the air again.
=== Rapid decompression ===
Rapid decompression typically takes more than 0.1 to 0.5 seconds, allowing the lungs to decompress more quickly than the cabin. The risk of lung damage is still present, but significantly reduced compared with explosive decompression.
=== Gradual decompression ===
Slow, or gradual, decompression occurs slowly enough to go unnoticed and might only be detected by instruments. This type of decompression may also come about from a failure to pressurize the cabin as an aircraft climbs to altitude. An example of this is the 2005 Helios Airways Flight 522 crash, in which the maintenance service left the pressurization system in manual mode and the pilots did not check the pressurization system. As a result, they suffered a loss of consciousness (as well as most of the passengers and crew) due to hypoxia (lack of oxygen). The plane continued to fly due to the autopilot system and eventually crashed due to fuel exhaustion after leaving its flight path.
== Decompression injuries ==
The following physical injuries may be associated with decompression incidents:
Hypoxia is the most serious risk associated with decompression, especially as it may go undetected or incapacitate the aircrew.
Barotrauma: an inability to equalize pressure in internal air spaces such as the middle ear or gastrointestinal tract, or more serious injury such as a burst lung.
Decompression sickness.
Altitude sickness.
Frostbite or hypothermia from exposure to freezing cold air at high altitude.
Physical trauma caused by the violence of explosive decompression, which can turn people and loose objects into projectiles.
At least two confirmed cases have been documented of a person being blown through an airplane passenger window. The first occurred in 1973 when debris from an engine failure struck a window roughly midway in the fuselage. Despite efforts to pull the passenger back into the airplane, the occupant was forced entirely through the cabin window. The passenger's skeletal remains were eventually found by a construction crew, and were positively identified two years later. The second incident occurred on April 17, 2018, when a woman on Southwest Airlines Flight 1380 was partially blown through an airplane passenger window that had broken from a similar engine failure. Although the other passengers were able to pull her back inside, she later died from her injuries. In both incidents, the plane landed safely with the sole fatality being the person seated next to the window involved.
According to NASA scientist Geoffrey A. Landis, the effect depends on the size of the hole, which can be expanded by debris that is blown through it; "it would take about 100 seconds for pressure to equalise through a roughly 30.0 cm (11.8 in) hole in the fuselage of a Boeing 747." Anyone blocking the hole would have half a ton of force pushing them towards it, but this force reduces rapidly with distance from the hole.
== Implications for aircraft design ==
Modern aircraft are specifically designed with longitudinal and circumferential reinforcing ribs in order to prevent localised damage from tearing the whole fuselage open during a decompression incident. However, decompression events have nevertheless proved fatal for aircraft in other ways. In 1974, explosive decompression onboard Turkish Airlines Flight 981 caused the floor to collapse, severing vital flight control cables in the process. The FAA issued an Airworthiness Directive the following year requiring manufacturers of wide-body aircraft to strengthen floors so that they could withstand the effects of in-flight decompression caused by an opening of up to 20 square feet (1.9 m2) in the lower deck cargo compartment. Manufacturers were able to comply with the Directive either by strengthening the floors and/or installing relief vents called "dado panels" between the passenger cabin and the cargo compartment.
Cabin doors are designed to prevent losing cabin pressure through them by making it nearly impossible to open them in flight, whether accidentally or intentionally. The plug door design ensures that when the pressure inside the cabin exceeds the pressure outside, the doors are forced shut and will not open until the pressure is equalized. Cabin doors, including the emergency exits, but not all cargo doors, open inwards, or must first be pulled inwards and then rotated before they can be pushed out through the door frame because at least one dimension of the door is larger than the door frame. Pressurization prevented the doors of Saudia Flight 163 from being opened on the ground after the aircraft made a successful emergency landing, resulting in the deaths of all 287 passengers and 14 crew members from fire and smoke.
Prior to 1996, approximately 6,000 large commercial transport airplanes were type certified to fly up to 45,000 feet (14,000 m), without being required to meet special conditions related to flight at high altitude. In 1996, the FAA adopted Amendment 25–87, which imposed additional high-altitude cabin-pressure specifications, for new designs of aircraft types. For aircraft certified to operate above 25,000 feet (FL 250; 7,600 m), it "must be designed so that occupants will not be exposed to cabin pressure altitudes in excess of 15,000 feet (4,600 m) after any probable failure condition in the pressurization system." In the event of a decompression which results from "any failure condition not shown to be extremely improbable," the aircraft must be designed so that occupants will not be exposed to a cabin altitude exceeding 25,000 feet (7,600 m) for more than 2 minutes, nor exceeding an altitude of 40,000 feet (12,000 m) at any time. In practice, that new FAR amendment imposes an operational ceiling of 40,000 feet on the majority of newly designed commercial aircraft.
In 2004, Airbus successfully petitioned the FAA to allow cabin pressure of the A380 to reach 43,000 feet (13,000 m) in the event of a decompression incident and to exceed 40,000 feet (12,000 m) for one minute. This special exemption allows the A380 to operate at a higher altitude than other newly designed civilian aircraft, which have not yet been granted a similar exemption.
== International standards ==
The Depressurization Exposure Integral (DEI) is a quantitative model that is used by the FAA to enforce compliance with decompression-related design directives. The model relies on the fact that the pressure that the subject is exposed to and the duration of that exposure are the two most important variables at play in a decompression event.
Other national and international standards for explosive decompression testing include:
MIL-STD-810, 202
RTCA/DO-160
NORSOK M710
API 17K and 17J
NACE TM0192 and TM0297
TOTALELFFINA SP TCS 142 Appendix H
== Notable decompression accidents and incidents ==
Decompression incidents are not uncommon on military and civilian aircraft, with approximately 40–50 rapid decompression events occurring worldwide annually. However, in most cases the problem is manageable, injuries or structural damage rare and the incident not considered notable. One notable, recent case was Southwest Airlines Flight 1380 in 2018, where an uncontained engine failure ruptured a window, causing a passenger to be partially blown out.
Decompression incidents do not occur solely in aircraft; the Byford Dolphin accident is an example of violent explosive decompression of a saturation diving system on an oil rig. A decompression event is often the result of a failure caused by another problem (such as an explosion or mid-air collision), but the decompression event may worsen the initial issue.
== Myths ==
=== A bullet through a window may cause explosive decompression ===
In 2004, the TV show MythBusters examined whether explosive decompression occurs when a bullet is fired through the fuselage of an airplane informally by way of several tests using a decommissioned pressurised DC-9. A single shot through the side or the window did not have any effect – it took actual explosives to cause explosive decompression – suggesting that the fuselage is designed to prevent people from being blown out. Professional pilot David Lombardo states that a bullet hole would have no perceived effect on cabin pressure as the hole would be smaller than the opening of the aircraft's outflow valve.
However, NASA scientist Geoffrey A. Landis points out that the impact depends on the size of the hole, which can be expanded by debris that is blown through it. Landis went on to say that "it would take about 100 seconds for pressure to equalise through a roughly 30.0 cm (11.8 in) hole in the fuselage of a Boeing 747." He then stated that anyone sitting next to the hole would have about half a ton of force pulling them towards it. At least two confirmed cases have been documented of a person being blown through an airplane passenger window. The first occurred in 1973 when debris from an engine failure struck a window roughly midway in the fuselage. Despite efforts to pull the passenger back into the airplane, the occupant was forced entirely through the cabin window. The passenger's skeletal remains were eventually found by a construction crew, and were positively identified two years later. The second incident occurred on April 17, 2018, when a woman on Southwest Airlines Flight 1380 was partially blown through an airplane passenger window that had broken from a similar engine failure. Although the other passengers were able to pull her back inside, she later died from her injuries. In both incidents, the plane landed safely with the sole fatality being the person seated next to the window involved. Fictional accounts of this include a scene in Goldfinger, when James Bond kills the eponymous villain by blowing him out a passenger window and Die Another Day, when an errant gunshot shatters a window on a cargo plane and rapidly expands, causing multiple enemy officials, henchmen and the main villain to be sucked out to their deaths.
=== Exposure to a vacuum causes the body to explode ===
This persistent myth is based on a failure to distinguish between two types of decompression and their exaggerated portrayal in some fictional works. The first type of decompression deals with changing from normal atmospheric pressure (one atmosphere) to a vacuum (zero atmosphere) which is usually centered around space exploration. The second type of decompression changes from exceptionally high pressure (many atmospheres) to normal atmospheric pressure (one atmosphere) as may occur in deep-sea diving.
The first type is more common as pressure reduction from normal atmospheric pressure to a vacuum can be found in both space exploration and high-altitude aviation. Research and experience have shown that while exposure to a vacuum causes swelling, human skin is tough enough to withstand the drop of one atmosphere. The most serious risk from vacuum exposure is hypoxia, in which the body is starved of oxygen, leading to unconsciousness within a few seconds. Rapid uncontrolled decompression can be much more dangerous than vacuum exposure itself. Even if the victim does not hold their breath, venting through the windpipe may be too slow to prevent the fatal rupture of the delicate alveoli of the lungs. Eardrums and sinuses may also be ruptured by rapid decompression, and soft tissues may be affected by bruises seeping blood. If the victim somehow survived, the stress and shock would accelerate oxygen consumption, leading to hypoxia at a rapid rate. At the extremely low pressures encountered at altitudes above about 63,000 feet (19,000 m), the boiling point of water becomes less than normal body temperature. This measure of altitude is known as the Armstrong limit, which is the practical limit to survivable altitude without pressurization. Fictional accounts of bodies exploding due to exposure from a vacuum include, among others, several incidents in the movie Outland, while in the movie Total Recall, characters appear to suffer effects of ebullism and blood boiling when exposed to the atmosphere of Mars.
The second type is rare since it involves a pressure drop over several atmospheres, which would require the person to have been placed in a pressure vessel. The only likely situation in which this might occur is during decompression after deep-sea diving. A pressure drop as small as 100 Torr (13 kPa), which produces no symptoms if it is gradual, may be fatal if it occurs suddenly. One such incident occurred in 1983 in the North Sea, where violent explosive decompression from nine atmospheres to one caused four divers to die instantly from massive and lethal barotrauma. Dramatized fictional accounts of this include a scene from the film Licence to Kill, when a character's head explodes after his hyperbaric chamber is rapidly depressurized, and another in the film DeepStar Six, wherein rapid depressurization causes a character to hemorrhage profusely before exploding in a similar fashion.
== See also ==
Decompression (altitude) – Reduction in ambient pressure due to ascent above sea level
Decompression (diving) – Pressure reduction and its effects during ascent from depth
Decompression (physics) – Reduction of pressure or compression
Time of useful consciousness – Duration of effective performance in a hypoxic environment
== Notes ==
== References ==
== External links ==
Human Exposure to Vacuum
Will an astronaut explode if he takes off his helmet? | Wikipedia/Uncontrolled_decompression |
Demand Valve Oxygen Therapy (DVOT) is a way of delivering high flow oxygen therapy using a device that only delivers oxygen when the patient breathes in and shuts off when they breathe out. DVOT is commonly used to treat conditions such as cluster headache, which affects up to four in 1000 people (0.4%), and is a recommended first aid procedure for several diving disorders. It is also a recommended prophylactic for decompression sickness in the event of minor omitted decompression without symptoms.
== Medical uses ==
=== Cluster headache ===
High flow oxygen therapy, delivered at a rate of between 7 and 15 litres per minute, has been recognized as an effective treatment for cluster headache since 1981. Since then, several double-blind, randomized, placebo-controlled, crossover trials have provided further clinical evidence for its efficacy.
When inhaled at 100% at the outset of a cluster headache attack, high flow oxygen therapy has been proven to abort episodes in up to 78% of patients. Inhaling 100% oxygen is recommended by the European Federation of Neurological Societies as the first choice for the treatment of cluster headache attacks. The British Thoracic Society and National Institute of Health and Care Excellence, among other organisations, endorse the therapy.
=== Diving disorders ===
Decompression sickness, as first aid during transport to recompression facility.
Omitted decompression, with or without symptoms of DCS. As prophylaxis where recompression is not practicable.
== Equipment ==
A portable administration set will comprise a portable high-pressure oxygen cylinder containing sufficient gas for the expected treatment, with an oxygen service cylinder valve, an oxygen compatible first stage regulator with pressure gauge, intermediate pressure hose, and demand valve with mouthpiece.
=== Equipment for cluster headache treatment ===
Demand valves have been proven to be particularly effective at delivering high flow oxygen therapy. Unlike conventional breathing systems, oxygen demand valves only deliver gas when the patient inhales and shut off the flow when they exhale. Exhaled gas is directed to the atmosphere through side vents. This means that almost 100 percent of the oxygen is inhaled, while the amount of exhaled carbon dioxide that the patient rebreathes is minimized.
Compared to other mask types, demand valves have been better at achieving pain relief at 15 minutes in the first cluster headache attack.
=== Equipment for diving first aid ===
For diving first aid an oxygen compatible diving regulator may be used if a special purpose oxygen treatment demand valve is not available. Technical divers routinely use such equipment for in-water decompression.
When used in diving recompression chambers and multi-place medical hyperbaric chambers, a built-in breathing system venting to the exterior is generally used to avoid buildup of oxygen partial pressure in the chamber to dangerous levels which would otherwise require more frequent venting.
== Procedure ==
== Contraindications ==
== Hazards and precautions ==
High oxygen concentrations in the surroundings constitute a fire hazard. Oxygen therapy should be accompanied by good ventilation and avoidance of ignition sources, and where reasonably practicable, removal of combustible materials. Oxygen firebreaks are a requirement in some countries for patients using oxygen therapy.
== See also ==
Oxygen therapy – Use of oxygen as a medical treatment
Hyperbaric medicine – Medical treatment at raised pressure
In-water recompression – In-water treatment for decompression sickness
Built-in breathing system – System for supply of breathing gas on demand within a confined space
Oxygen for cluster headaches - Information for cluster headache patients, carers, and clinicians
== References == | Wikipedia/Demand_valve_oxygen_therapy |
Divers Alert Network (DAN) is a group of not-for-profit organizations dedicated to improving diving safety for all divers. It was founded in Durham, North Carolina, United States, in 1980 at Duke University providing 24/7 telephonic hot-line diving medical assistance. Since then the organization has expanded globally and now has independent regional organizations in North America, Europe, Japan, Asia-Pacific and Southern Africa.
The DAN group of organizations provide similar services, some only to members, and others to any person on request. Member services usually include a diving accident hot-line, and diving accident and travel insurance. Services to the general public usually include diving medical advice and training in first aid for diving accidents. DAN America and DAN Europe maintain databases on diving accidents, treatment and fatalities, and crowd-sourced databases on dive profiles uploaded by volunteers which are used for ongoing research programmes. They publish research results and collaborate with other organizations on projects of common interest.
== Function ==
DAN has an international network of emergency call centers which operate 24 hours a day to provide members with specialized assistance for diving emergencies from a group of experts in Diving and Hyperbaric Medicine
== History ==
In 1977, Undersea Medical Society (later the Undersea and Hyperbaric Medical Society) introduced the concept of a national organization (to replace LEO-FAST at Brooks Air Force Base, directed by Colonel Jefferson Davis, M.D.) where a diving medicine specialist could be contacted by telephone 24 hours a day. Peter B. Bennett received a two-year grant from National Oceanic and Atmospheric Administration and National Institute for Occupational Safety and Health in September 1980 to form the "National Diving Accident Network" at the Frank G. Hall Hyperbaric Center at Duke University Medical Center in Durham, North Carolina.
In 1981, DAN published its "Underwater Diving Accident Manual". The Hyperbaric Center received 305 calls for information and assistance. DAN implemented a medical/safety advisory telephone line to handle questions from recreational divers with non-emergency questions in 1982. This change was followed by a name change from "Diving Accident Network" to "Divers Alert Network" and hosted the first annual Diving Accident and Hyperbaric Treatment continuing medical education course at the Duke University Medical Center.
In 1983 International Diving Assistance, later to become DAN Europe, was founded by Alessandro Marroni as a 24-hour per day diving emergency assistance service, set up as a membership organization, with specific insurance benefits since the start.
In 1984, federal grant monies were decreased (50 percent in 1982 and then by 25 percent in 1983) and support now comes exclusively from divers and the diving industry.
In 1985 DAN started a 'sponsor program' for clubs, stores and corporations,
In 1987 the Civil Alert Network (CAN) began assisting diving emergencies in Japan, under the guidance of prof. Yoshihiro Mano of the University of Tokyo Medical School. This would become DAN Japan. Also in 1987, DAN started the first dive accident insurance program for members. After the introduction of this program the membership numbers doubled to 32,000 in 1988.
The IRS granted DAN its 501(c)(3) non-profit status in 1990. The organization continues to be associated with Duke University Medical Center, but moved its offices from the Frank G. Hall Labs to off campus office space. In 1991 DAN introduced its first training course 'Oxygen First aid Training Program' and DAN Travel Assist. In the same year the 'Flying After Diving' research trials began.
The need for an international organisation that would be available to all divers, wherever they dived around the world, became increasingly apparent and, during a meeting at DAN Headquarters in Durham, N.C., US, in February 1991, the process to form an International DAN was started. The four existing organisations decided to adopt the common name of DAN. and International DAN – also known as IDAN – was established to support the regional IDAN members - DAN America, DAN Europe, DAN Japan, and DAN Asia-Pacific.
In 1992 Emergency medical evacuation, was added as a member benefit, and DAN was awarded the Undersea and Hyperbaric Medical Society's Craig Hoffman Diving Safety Award in June of that year for its significant contributions to the health and safety of recreational divers. In September the first DAN Instructor Training Workshop was held, and the Oxygen First Aid Training program was introduced to Europe.
1993 saw DAN open an insurance company 'Accident General Insurance'.
Dan Asia Pacific was founded in 1994 under the name DAN Australia by Australian diver, John Lippmann OAM, after dual approaches from DAN America and John Williamson of the Australian Diver Emergency Service to "establish a DAN entity in the Asia-Pacific."
DAN Southern Africa joined the IDAN in 1996 with Frans Cronjé, M.D. as CEO By 1996 Oxygen First Aid Training was being taught in seven continents.
DAN introduced other diving related first aid training courses – 'Oxygen first aid for aquatic emergencies' (1998), 'Remote Oxygen (REMO2) (1999), Hazardous Marine Life Injuries (2000), Automatic External Difibrillation (2001) and Advanced Oxygen Provider (2002). DAN moved to its new, permanent headquarters, the Peter B. Bennett Center.
Bennett received the 2002 Diving Equipment and Marketing Association Reaching Out Award for his contribution to the dive industry and the Carolinas' Ernst and Young Entrepreneur of the Year 2002 award for contributions to business in the life sciences. He announced his retirement as DAN President effective June 30, 2003 After Bennett resigned as DAN President and CEO, DAN Executive Vice President and Chief Operating Officer Dan Orr, MS was named acting president and CEO. DAN established the Peter B. Bennett Research Fund, within the Endowment Fund to support research initiatives, enhancing dive safety into the future.
In 2004, Michael D. Curley, Ph.D. was named DAN America President and CEO. In 2006, Curley stepped down and Mr. Orr was named as the DAN President and CEO. In February 2009, DAN launched a web site for their bi-monthly magazine "Alert Diver Online".
DAN reported membership numbers worldwide for 2019 as: DAN US/Canada, 274,708; DAN Europe, 123,680; DAN Japan, 18,137; DAN World Asia Pacific, 12,163; DAN World Latin America/Brazil, 8,008; DAN Southern Africa, 5,894.
== IDAN ==
International DAN (IDAN) comprises independently administered nonprofit DAN organizations based around the world that provide expert emergency medical and referral services to regional diving communities. Each DAN depends on the support of the divers of its region to provide its safety and educational services, and may provide locally appropriate insurance options. They operate under protocol standards set by the IDAN Headquarters.
DAN (America) serves as the headquarters for IDAN.
== DAN America ==
Divers Alert Network America, DAN America, or just DAN is a non-profit 501(c)(3) organization devoted to assisting divers in need. It is supported by donations, grants, and membership dues. Its research department conducts medical research on recreational scuba diving safety while its medical department helps divers to find answers to their diving medical questions.
Regions of coverage include the United States and Canada.
== DAN Asia-Pacific ==
Divers Alert Network Asia Pacific Limited (DAN Asia Pacific) is a diving safety organization founded in 1994 and has not-for-profit incorporation in Australia as a public company limited by guarantee. The address for legal, operational and administrative purposes is 49A Karnak Road, Ashburton, Victoria, 3147, Australia. It previously traded under the following names - Divers Alert Network (DAN) S.E. Asia-Pacific Limited and DAN Australasia Limited.
It is funded by membership subscriptions, insurance commissions, training courses, product sales and other undisclosed sources.
Membership as of June 2014 totalled 10,561.
Its region of operation includes Australia, China, India, Korea, New Zealand, the South Pacific, Southeast Asia and Taiwan.
=== Services ===
==== Medical hotlines ====
DAN Asia Pacific promotes the use of 24-hour emergency hotline services in Australia, New Zealand and Korea. It fully funds the operation of the Australian hotline, the Diving Emergency Service, which is based in the Hyperbaric Medical Unit at the Royal Adelaide Hospital in South Australia and which provides medical consultancy service for diving-related emergencies on a 24-hour basis within and outside of Australia.
==== Medical advice ====
==== Insurance cover ====
As of 2016, DAN Asia Pacific provides insurance cover for its members in Australia underwritten by Honan Insurance Group Pty Ltd and cover for its members residing outside of Australia underwritten by Accident & General Insurance Company, Ltd.
==== Training ====
DAN Asia Pacific provides training and certification for divers, professional rescuers and the general public in respect to diving and general first aid. It also trains and qualifies instructors to provide this training. It has status in Australia as a registered provider of vocational education under the Australian government's Australian Qualifications Framework.
As of 2016, it offers the following training courses including some which have national recognition in Australia:
Oxygen for dive accidents
Basic oxygen administration
First aid programs
Automated external defibrillators
Cardiopulmonary resuscitation
Anaphylaxis
Advanced oxygen provision
First aid for hazardous marine life injuries
On-site neurological assessment
Instructor training
=== Membership ===
DAN Asia Pacific offers the following membership classes:
individuals
family
=== Research ===
Examples of DAN Asia Pacific research projects:
Reports on Australian diving deaths for the years 1972 to 2002
== DAN Brasil ==
Region of coverage is Brazil.
== DAN Europe ==
Divers Alert Network Europe (DAN Europe) is an international non-profit medical and research organization founded in 1983. The legal address is 26, Triq Fidiel Zarb, Gharghur NXR07, Malta, but the operational and administrative address is C. da Padune 11, 64026 Roseto Italy
The Foundation is primarily funded through the membership fees paid annually by individual supporters, and also through contributions by public or private individuals or organisations, through the sale of goods and services related to its statutory activities, and fund raising schemes, subsidies or sponsorships in order to finance specific projects such as medical and scientific research. Membership (Feb. 2016) exceeds 100,000.
Region of coverage includes geographical Europe, other countries bordering the Mediterranean Sea, the countries on the shores of the Red Sea, the Middle East including the Persian Gulf, the countries on the shores of the Indian Ocean north of the equator and west of (not including) India and Sri Lanka, and their overseas territories, districts and protectorates.
=== Services ===
DAN Europe provides expert information and advice for the benefit of its members and the diving public, including:
emergency medical advice and assistance for underwater diving injuries.
promoting diving safety
underwater diving research and education
providing information on issues of common concern to the diving public
==== Medical hotline ====
DAN Europe provides its members with medical assistance in case of a diving emergency, 24/7 and from anywhere in the world. There is an international line for use when the member is abroad, and each country has a national emergency number.
When the emergency is in the diver's country of residence, the national hotline is used and the case is managed locally from the national center, according to Standard DAN Europe protocol.
When the emergency occurs outside of the diver's country of residence. the central DAN Europe hotline is used. A diver who calls from abroad is normally put into contact with a DAN specialist of the same language as the victim, so that the case may be evaluated without language difficulties.
If the accident occurred in an area where a national DAN centre exists, the local centre will manage the emergency in coordination with the Rome centre and the specialist from the victim's home country.
If the accident occurred in a country without a national DAN centre, the intervention will be managed directly by the central DAN Europe hotline.
==== Medical advice ====
For non-urgent diving medical information DAN Europe has a number of articles on the website, an FAQ page, and if the information needed was not available from those resources, there is an email form to request information. Specialised medical advice is reserved to active DAN Members.
==== Insurance cover ====
DAN Europe provides insurance cover for members underwritten by International Diving Assurance.
==== Technical ====
Since 1997 the Recompression Chamber Assistance and Partnership Program has been available to provide recompression chambers operators with equipment, training and emergency assistance, to help ensure that they are available, in good condition and safe when needed.
==== Training ====
DAN Europe provides training and certification for divers professional rescuers and the general public and in aspects of first aid, and trains instructors to provide this training.
Courses available include:
=== Membership ===
Membership classes of DAN Europe include:
ordinary members
supporting members
promoting members
honorary members
=== Research ===
Examples of DAN Europe research projects:
== DAN Japan ==
Region of coverage includes Japan, Japanese islands and related territories, with regional IDAN responsibility for Northeast Asia-Pacific.
== DAN Southern Africa ==
Divers Alert Network Southern Africa is a Public Benefit Organization with the primary purpose to provide emergency medical advice and assistance for underwater diving injuries, to work to prevent injuries and to promote dive safety.
DAN SA also promotes and supports research and education relating to the improvement of dive safety, medical treatment and first aid, and provides information on dive safety, diving physiology and diving medical issues of common concern to the diving public. Legal advice relating to diving matters is also available. The organisation is funded by membership fees, training fees, donations and the sale of branded first aid, safety and promotional products.
Regions of coverage include South Africa, Angola, Botswana, Comoros, Kenya, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, Seychelles, Swaziland, Tanzania, Zaire, Zambia, and Zimbabwe.
=== Timeline ===
1996: DAN SA was founded and recognized as a valid membership organisation by International Divers Alert Network.
1997: DAN SA was registered as a Section 21 not for profit organisation.
=== Services ===
==== Medical hotline ====
DAN South Africa provides emergency hotline for diving and evacuation emergencies. Response staff and diving medicine specialists are on call 24 hours a day, 365 days a year, to provide information and assist with care coordination and evacuation assistance. A toll-free 0800 number is available for calls from within South Africa, and an international number for calls from outside South Africa which is not toll-free.
==== Medical advice ====
DAN SA also provides a diving medical information service. During business hours this can be accessed by telephone or e-mail. Other related information is available from a FAQ and articles on the website. They are linked to the South African Underwater and Hyperbaric Medical Association (SAUHMA) diving medical practitioner database, and maintain an international list of diving medical practitioners for referral.
==== Legal advice ====
DAN has access to legal professionals with an interest in diving and who are experienced in local, regional and international law. Members who are in need of legal assistance can contact DAN via email. DAN staff will consider requests and, if appropriate, refer the member to an appropriate legal expert within the network, who will make appropriate suggestions to the member on how best to represent or defend their interests.
==== Insurance cover ====
DAN SA is not an insurance company. It has a group insurance policy from AIG South Africa which allows it to extend emergency cover to members for specific diving, travel and medical emergencies. Cover is limited according to membership level.
Cover includes:
Medical expenses for treatment of injuries which occur in the water and are a direct consequence of diving or snorkelling activities.
Emergency medical expenses while travelling outside country of residence.
Evacuation costs to nearest appropriate medical treatment facilities for incidents in categories above.
==== Technical ====
A joint project of DAN SA and Subaquatic Safety Services (SSS) Network established the Zanzibar Hyperbaric Chamber, which is the only publicly available hyperbaric facility in East Africa.
==== Training ====
DAN SA provides training and certification for divers in aspects of diving first aid, and trains instructors to provide this training.
Courses available include:
=== Membership ===
Several options for membership of DAN SA are available:
Annual membership for individual divers and immediate family members
Temporary membership for short duration trips
Student membership for entry-level students
Commercial membership for commercial divers and diving contractors
Industry partner for dive businesses
Diving safety partners for dive businesses
=== Research ===
DAN SA cooperates with DAN Europe and the University of Stellenbosch in gathering crowdsourced data for decompression and other diving physiology and medicine, and diving accident research projects. Most of these are long term projects, but annual statistical reports are published, and contributing divers can get immediate feedback on relative risk of their uploaded dive profiles.
=== Alert diver (SA edition) ===
The Alert Diver is a magazine containing information on dive medicine, the latest DAN statistics, and research, safety and training advice by DAN staff. It is published twice-yearly in paper and digital versions. Non-members can download the digital version of the Alert Diver for a nominal fee.
== DAN World ==
Regions of coverage include the Bahamas, British and U.S. Virgin Islands, Caribbean, Central and South America, Guam, Micronesia and Melanesia (except Fiji), Puerto Rico, and any other places not covered by the regional organisations.
== Research ==
=== Completed programs ===
Flying After Recompression Treatment Study. Online survey of divers in 2003 who were recompressed for decompression illness within the previous five years and then flew in an airplane. The study was published in the Management of Mild or Marginal Decompression Illness in Remote Locations Workshop Proceedings.
Diabetes & Diving. Two studies were made on recreational diving by persons with diabetes who showed good general blood glucose control prior to entry to the study. The first followed adults with diabetes who were previously certified to dive and the second studied teenagers with diabetes immediately following their certification training.
US Navy Survey. DAN conducted a survey of recreational divers to obtain information about diver demographics, dive experience and diving habits on behalf of the US Navy in early 1998.
Live-aboard Doppler. Researchers assessed the effects of age, gender and dive profiles on post-dive vascular bubble presence in volunteer participants during 1988/9 using Doppler monitoring devices.
Aging Diver Study. Preliminary evaluation of the effects of age and associated medical conditions on dive style and dive outcome using PDE methodology.
Breath-Hold Study. The effects of hyperventilation, work, breathing mixture and dive depth on immersed breath-hold duration were investigated to allow an increase in breath-hold time to a maximum safe level without excessive risk of loss of consciousness or functional incapacity due to hypocapnia, hypoxia or hypercapnia.
Flying After Diving. DAN conducted human trials from 1993 to 1999 to investigate how long to wait after diving before flying for recreational divers with support from the US Navy.
First Aid Oxygen Rebreather. Performance studies made on first- and second-generation closed-circuit oxygen rebreathing circuits developed for remote duty first aid applications confirmed effective performance in the second-generation device.
Cialis™/Viagra™ and the Risk of Oxygen Toxicity. A rat model produced positive results of increased risk of oxygen toxicity risk using these drugs.
=== Ongoing programs ===
Flying After Diving Calibration Study. To find out how exercise affects the minimum safe waiting period before flying after diving.
Risk/Benefit of PFO Closure. To find out if divers with PFO who underwent the closure procedure are better off than divers with PFO who continue diving without the closure.
Sudafed and Risk of Oxygen Toxicity. This study uses an animal model to find out whether Sudafed increases the risk of oxygen toxicity.
Extreme Diving Field Study. To analyse aspects of safety including decompression safety, physical fitness requirements and cardiovascular effects of extreme diving.
Incidents and Accidents in Compressed Air Diving. DAN compiles case reports of diving incidents, injuries and fatalities in air, nitrox and mixed-gas diving and includes data from these reports in the DAN Annual Diving Report.
Incidents and Accidents in Breath-Hold Diving. Both fatal and nonfatal cases are collected to identify risks and aid in public education. Data from case reports is included in the DAN Annual Diving Report.
Project Dive Exploration (PDE). Dive profiles, diver characteristics and diver behaviour are uploaded by volunteers using the dive computer's dive log software and recorded for statistically accurate analysis. This is a prospective observational study of the demographics, medical history, depth-time exposure and medical outcome of a sample of the recreational diving population, with the intention of finding the incidence of decompression sickness in population subgroups and the relationship of DCS probability to depth-time profile and dive and diver characteristics. The data also provides an injury-free control population for comparison with DAN's injury and fatality data to identify possible risk factors associated with injury and death. The results of this study are likely to be useful in the development of future decompression models. Divers using one of many compatible dive computers may contribute their electronic dive log data to PDE.
DAN Membership Health Survey. To establish the prevalence of cardiovascular risk factors, diabetes and asthma, access to primary health care and the diving practices of DAN Members to help the diving community decide on preventive measures for injuries and fatalities.
Database of Dive Exposure and Dive Outcomes. Data from the US Navy, Duke University, PDE, DAN Europe's Dive Safety Lab and the Institute of Nautical Archaeology are converted to a format which can be used as a reference database for calibration and evaluation of decompression algorithms.
Diver Physical Fitness Study. Physical fitness of divers and the physical fitness required for typical diving activities will be assessed.
Fatality Database. DAN collects data on diving fatalities of recreational divers in the US, Canada and diving destinations frequented by US and Canadian divers, compiles case reports, and includes the data in the DAN Annual Diving Report.
=== Publications ===
DAN publishes research results on a wide range of matters relating to diving safety and medicine and diving accident analysis, including annual reports on decompression illness and diving fatalities. Many are freely available on the internet.
The magazine "Alert Diver" is published by some of the regional branches, including the US, Europe, and Southern Africa, in paper and electronic formats. Although the different publications may occasionally reprint material from each other, they generally contain different content. Article topics generally include diving physiology, medicine, safety, and diving destinations.
== Conferences ==
=== Rebreather Forum 3 ===
In May 2012, DAN along with the American Academy of Underwater Sciences and the Professional Association of Diving Instructors hosted the Rebreather Forum 3 (RF3) which was organised by Rosemary E Lunn. This three-day safety symposium was convened to address major issues surrounding rebreather technology, and its application in commercial, media, military, scientific, recreational and technical diving. Experts, manufactures, instructor trainers, training agencies and divers from all over the world discussed this technology and shared information. Associate Professor Simon J Mitchell chaired the final session at RF3 and, as a result, 16 key consensus statements were agreed and ratified by the global rebreather community.
== In media ==
"The Mystery of the Bends," a 1992 episode of the PBS television series Return to the Sea, includes a profile of the Divers Alert Network.
== See also ==
Diving Diseases Research Centre – British hyperbaric medical organisation
Diving Medical Advisory Council – Independent organisation of diving medical specialists from Northern Europe
European Underwater and Baromedical Society – Source of information for diving and hyperbaric medicine
Rubicon Foundation – Non-profit organization for promoting research and information access for underwater diving
Southern African Underwater and Hyperbaric Medical Association – Special interest group of the Council of the South African Medical Association
South Pacific Underwater Medicine Society – Publisher for diving and hyperbaric medicine and physiology
== References ==
== External links ==
Divers Alert Network
DAN on Facebook
Undersea and Hyperbaric Medical Society
Rubicon Research Repository
DAN Asia-Pacific Office
DAN Europe Office
DAN Southern African Office
South African Undersea and Hyperbaric Medical Society
International DAN Website
Return to the Sea Episode 203 "The Mystery of the Bends" at OceanArchives (Fair use policy for video at OceanArchives) | Wikipedia/Divers_Alert_Network |
Earth's energy budget (or Earth's energy balance) is the balance between the energy that Earth receives from the Sun and the energy the Earth loses back into outer space. Smaller energy sources, such as Earth's internal heat, are taken into consideration, but make a tiny contribution compared to solar energy. The energy budget also takes into account how energy moves through the climate system.: 2227 The Sun heats the equatorial tropics more than the polar regions. Therefore, the amount of solar irradiance received by a certain region is unevenly distributed. As the energy seeks equilibrium across the planet, it drives interactions in Earth's climate system, i.e., Earth's water, ice, atmosphere, rocky crust, and all living things.: 2224 The result is Earth's climate.
Earth's energy budget depends on many factors, such as atmospheric aerosols, greenhouse gases, surface albedo, clouds, and land use patterns. When the incoming and outgoing energy fluxes are in balance, Earth is in radiative equilibrium and the climate system will be relatively stable. Global warming occurs when earth receives more energy than it gives back to space, and global cooling takes place when the outgoing energy is greater.
Multiple types of measurements and observations show a warming imbalance since at least year 1970. The rate of heating from this human-caused event is without precedent.: 54 The main origin of changes in the Earth's energy is from human-induced changes in the composition of the atmosphere. During 2005 to 2019 the Earth's energy imbalance (EEI) averaged about 460 TW or globally 0.90±0.15 W/m2.
It takes time for any changes in the energy budget to result in any significant changes in the global surface temperature. This is due to the thermal inertia of the oceans, land and cryosphere. Most climate models make accurate calculations of this inertia, energy flows and storage amounts.
== Definition ==
Earth's energy budget includes the "major energy flows of relevance for the climate system". These are "the top-of-atmosphere energy budget; the surface energy budget; changes in the global energy inventory and internal flows of energy within the climate system".: 2227
== Earth's energy flows ==
In spite of the enormous transfers of energy into and from the Earth, it maintains a relatively constant temperature because, as a whole, there is little net gain or loss: Earth emits via atmospheric and terrestrial radiation (shifted to longer electromagnetic wavelengths) to space about the same amount of energy as it receives via solar insolation (all forms of electromagnetic radiation).
The main origin of changes in the Earth's energy is from human-induced changes in the composition of the atmosphere, amounting to about 460 TW or globally 0.90±0.15 W/m2.
=== Incoming solar energy (shortwave radiation) ===
The total amount of energy received per second at the top of Earth's atmosphere (TOA) is measured in watts and is given by the solar constant times the cross-sectional area of the Earth corresponded to the radiation. Because the surface area of a sphere is four times the cross-sectional area of a sphere (i.e. the area of a circle), the globally and yearly averaged TOA flux is one quarter of the solar constant and so is approximately 340 watts per square meter (W/m2). Since the absorption varies with location as well as with diurnal, seasonal and annual variations, the numbers quoted are multi-year averages obtained from multiple satellite measurements.
Of the ~340 W/m2 of solar radiation received by the Earth, an average of ~77 W/m2 is reflected back to space by clouds and the atmosphere and ~23 W/m2 is reflected by the surface albedo, leaving ~240 W/m2 of solar energy input to the Earth's energy budget. This amount is called the absorbed solar radiation (ASR). It implies a value of about 0.3 for the mean net albedo of Earth, also called its Bond albedo (A):
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{\displaystyle ASR=(1-A)\times 340~\mathrm {W} ~\mathrm {m} ^{-2}\simeq 240~\mathrm {W} ~\mathrm {m} ^{-2}.}
=== Outgoing longwave radiation ===
Thermal energy leaves the planet in the form of outgoing longwave radiation (OLR). Longwave radiation is electromagnetic thermal radiation emitted by Earth's surface and atmosphere. Longwave radiation is in the infrared band. But, the terms are not synonymous, as infrared radiation can be either shortwave or longwave. Sunlight contains significant amounts of shortwave infrared radiation. A threshold wavelength of 4 microns is sometimes used to distinguish longwave and shortwave radiation.
Generally, absorbed solar energy is converted to different forms of heat energy. Some of the solar energy absorbed by the surface is converted to thermal radiation at wavelengths in the "atmospheric window"; this radiation is able to pass through the atmosphere unimpeded and directly escape to space, contributing to OLR. The remainder of absorbed solar energy is transported upwards through the atmosphere through a variety of heat transfer mechanisms, until the atmosphere emits that energy as thermal energy which is able to escape to space, again contributing to OLR. For example, heat is transported into the atmosphere via evapotranspiration and latent heat fluxes or conduction/convection processes, as well as via radiative heat transport. Ultimately, all outgoing energy is radiated into space in the form of longwave radiation.
The transport of longwave radiation from Earth's surface through its multi-layered atmosphere is governed by radiative transfer equations such as Schwarzschild's equation for radiative transfer (or more complex equations if scattering is present) and obeys Kirchhoff's law of thermal radiation.
A one-layer model produces an approximate description of OLR which yields temperatures at the surface (Ts=288 Kelvin) and at the middle of the troposphere (Ta=242 K) that are close to observed average values:
O
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{\displaystyle OLR\simeq \epsilon \sigma T_{\text{a}}^{4}+(1-\epsilon )\sigma T_{\text{s}}^{4}.}
In this expression σ is the Stefan–Boltzmann constant and ε represents the emissivity of the atmosphere, which is less than 1 because the atmosphere does not emit within the wavelength range known as the atmospheric window.
Aerosols, clouds, water vapor, and trace greenhouse gases contribute to an effective value of about ε = 0.78. The strong (fourth-power) temperature sensitivity maintains a near-balance of the outgoing energy flow to the incoming flow via small changes in the planet's absolute temperatures.
As viewed from Earth's surrounding space, greenhouse gases influence the planet's atmospheric emissivity (ε). Changes in atmospheric composition can thus shift the overall radiation balance. For example, an increase in heat trapping by a growing concentration of greenhouse gases (i.e. an enhanced greenhouse effect) forces a decrease in OLR and a warming (restorative) energy imbalance. Ultimately when the amount of greenhouse gases increases or decreases, in-situ surface temperatures rise or fall until the absorbed solar radiation equals the outgoing longwave radiation, or ASR equals OLR.
=== Earth's internal heat sources and other minor effects ===
The geothermal heat flow from the Earth's interior is estimated to be 47 terawatts (TW) and split approximately equally between radiogenic heat and heat left over from the Earth's formation. This corresponds to an average flux of 0.087 W/m2 and represents only 0.027% of Earth's total energy budget at the surface, being dwarfed by the 173000 TW of incoming solar radiation.
Human production of energy is even lower at an average 18 TW, corresponding to an estimated 160,000 TW-hr, for all of year 2019. However, consumption is growing rapidly and energy production with fossil fuels also produces an increase in atmospheric greenhouse gases, leading to a more than 20 times larger imbalance in the incoming/outgoing flows that originate from solar radiation.
Photosynthesis also has a significant effect: An estimated 140 TW (or around 0.08%) of incident energy gets captured by photosynthesis, giving energy to plants to produce biomass. A similar flow of thermal energy is released over the course of a year when plants are used as food or fuel.
Other minor sources of energy are usually ignored in the calculations, including accretion of interplanetary dust and solar wind, light from stars other than the Sun and the thermal radiation from space. Earlier, Joseph Fourier had claimed that deep space radiation was significant in a paper often cited as the first on the greenhouse effect.
== Budget analysis ==
In simplest terms, Earth's energy budget is balanced when the incoming flow equals the outgoing flow. Since a portion of incoming energy is directly reflected, the balance can also be stated as absorbed incoming solar (shortwave) radiation equal to outgoing longwave radiation:
A
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{\displaystyle ASR=OLR.}
=== Internal flow analysis ===
To describe some of the internal flows within the budget, let the insolation received at the top of the atmosphere be 100 units (= 340 W/m2), as shown in the accompanying Sankey diagram. Called the albedo of Earth, around 35 units in this example are directly reflected back to space: 27 from the top of clouds, 2 from snow and ice-covered areas, and 6 by other parts of the atmosphere. The 65 remaining units (ASR = 220 W/m2) are absorbed: 14 within the atmosphere and 51 by the Earth's surface.
The 51 units reaching and absorbed by the surface are emitted back to space through various forms of terrestrial energy: 17 directly radiated to space and 34 absorbed by the atmosphere (19 through latent heat of vaporisation, 9 via convection and turbulence, and 6 as absorbed infrared by greenhouse gases). The 48 units absorbed by the atmosphere (34 units from terrestrial energy and 14 from insolation) are then finally radiated back to space. This simplified example neglects some details of mechanisms that recirculate, store, and thus lead to further buildup of heat near the surface.
Ultimately the 65 units (17 from the ground and 48 from the atmosphere) are emitted as OLR. They approximately balance the 65 units (ASR) absorbed from the sun in order to maintain a net-zero gain of energy by Earth.
=== Heat storage reservoirs ===
Land, ice, and oceans are active material constituents of Earth's climate system along with the atmosphere. They have far greater mass and heat capacity, and thus much more thermal inertia. When radiation is directly absorbed or the surface temperature changes, thermal energy will flow as sensible heat either into or out of the bulk mass of these components via conduction/convection heat transfer processes. The transformation of water between its solid/liquid/vapor states also acts as a source or sink of potential energy in the form of latent heat. These processes buffer the surface conditions against some of the rapid radiative changes in the atmosphere. As a result, the daytime versus nighttime difference in surface temperatures is relatively small. Likewise, Earth's climate system as a whole shows a slow response to shifts in the atmospheric radiation balance.
The top few meters of Earth's oceans harbor more thermal energy than its entire atmosphere. Like atmospheric gases, fluidic ocean waters transport vast amounts of such energy over the planet's surface. Sensible heat also moves into and out of great depths under conditions that favor downwelling or upwelling.
Over 90 percent of the extra energy that has accumulated on Earth from ongoing global warming since 1970 has been stored in the ocean. About one-third has propagated to depths below 700 meters. The overall rate of growth has also risen during recent decades, reaching close to 500 TW (1 W/m2) as of 2020. That led to about 14 zettajoules (ZJ) of heat gain for the year, exceeding the 570 exajoules (=160,000 TW-hr) of total primary energy consumed by humans by a factor of at least 20.
=== Heating/cooling rate analysis ===
Generally speaking, changes to Earth's energy flux balance can be thought of as being the result of external forcings (both natural and anthropogenic, radiative and non-radiative), system feedbacks, and internal system variability. Such changes are primarily expressed as observable shifts in temperature (T), clouds (C), water vapor (W), aerosols (A), trace greenhouse gases (G), land/ocean/ice surface reflectance (S), and as minor shifts in insolaton (I) among other possible factors. Earth's heating/cooling rate can then be analyzed over selected timeframes (Δt) as the net change in energy (ΔE) associated with these attributes:
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{\displaystyle {\begin{aligned}\Delta E/\Delta t&=(\ \Delta E_{T}+\Delta E_{C}+\Delta E_{W}+\Delta E_{A}+\Delta E_{G}+\Delta E_{S}+\Delta E_{I}+...\ )/\Delta t\\\\&=ASR-OLR.\end{aligned}}}
Here the term ΔET, corresponding to the Planck response, is negative-valued when temperature rises due to its strong direct influence on OLR.
The recent increase in trace greenhouse gases produces an enhanced greenhouse effect, and thus a positive ΔEG forcing term. By contrast, a large volcanic eruption (e.g. Mount Pinatubo 1991, El Chichón 1982) can inject sulfur-containing compounds into the upper atmosphere. High concentrations of stratospheric sulfur aerosols may persist for up to a few years, yielding a negative forcing contribution to ΔEA. Various other types of anthropogenic aerosol emissions make both positive and negative contributions to ΔEA. Solar cycles produce ΔEI smaller in magnitude than those of recent ΔEG trends from human activity.
Climate forcings are complex since they can produce direct and indirect feedbacks that intensify (positive feedback) or weaken (negative feedback) the original forcing. These often follow the temperature response. Water vapor trends as a positive feedback with respect to temperature changes due to evaporation shifts and the Clausius-Clapeyron relation. An increase in water vapor results in positive ΔEW due to further enhancement of the greenhouse effect. A slower positive feedback is the ice-albedo feedback. For example, the loss of Arctic ice due to rising temperatures makes the region less reflective, leading to greater absorption of energy and even faster ice melt rates, thus positive influence on ΔES. Collectively, feedbacks tend to amplify global warming or cooling.: 94
Clouds are responsible for about half of Earth's albedo and are powerful expressions of internal variability of the climate system. They may also act as feedbacks to forcings, and could be forcings themselves if for example a result of cloud seeding activity. Contributions to ΔEC vary regionally and depending upon cloud type. Measurements from satellites are gathered in concert with simulations from models in an effort to improve understanding and reduce uncertainty.
== Earth's energy imbalance (EEI) ==
The Earth's energy imbalance (EEI) is defined as "the persistent and positive (downward) net top of atmosphere energy flux associated with greenhouse gas forcing of the climate system".: 2227
If Earth's incoming energy flux (ASR) is larger or smaller than the outgoing energy flux (OLR), then the planet will gain (warm) or lose (cool) net heat energy in accordance with the law of energy conservation:
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{\displaystyle EEI\equiv ASR-OLR}
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Positive EEI thus defines the overall rate of planetary heating and is typically expressed as watts per square meter (W/m2). During 2005 to 2019 the Earth's energy imbalance averaged about 460 TW or globally 0.90 ± 0.15 W per m2.
When Earth's energy imbalance (EEI) shifts by a sufficiently large amount, the shift is measurable by orbiting satellite-based instruments. Imbalances that fail to reverse over time will also drive long-term temperature changes in the atmospheric, oceanic, land, and ice components of the climate system. Temperature, sea level, ice mass and related shifts thus also provide measures of EEI.
The biggest changes in EEI arise from changes in the composition of the atmosphere through human activities, thereby interfering with the natural flow of energy through the climate system. The main changes are from increases in carbon dioxide and other greenhouse gases, that produce heating (positive EEI), and pollution. The latter refers to atmospheric aerosols of various kinds, some of which absorb energy while others reflect energy and produce cooling (or lower EEI).
It is not (yet) possible to measure the absolute magnitude of EEI directly at top of atmosphere, although changes over time as observed by satellite-based instruments are thought to be accurate. The only practical way to estimate the absolute magnitude of EEI is through an inventory of the changes in energy in the climate system. The biggest of these energy reservoirs is the ocean.
=== Energy inventory assessments ===
The planetary heat content that resides in the climate system can be compiled given the heat capacity, density and temperature distributions of each of its components. Most regions are now reasonably well sampled and monitored, with the most significant exception being the deep ocean.
Estimates of the absolute magnitude of EEI have likewise been calculated using the measured temperature changes during recent multi-decadal time intervals. For the 2006 to 2020 period EEI was about +0.76±0.2 W/m2 and showed a significant increase above the mean of +0.48±0.1 W/m2 for the 1971 to 2020 period.
EEI has been positive because temperatures have increased almost everywhere for over 50 years. Global surface temperature (GST) is calculated by averaging temperatures measured at the surface of the sea along with air temperatures measured over land. Reliable data extending to at least 1880 shows that GST has undergone a steady increase of about 0.18 °C per decade since about year 1970.
Ocean waters are especially effective absorbents of solar energy and have a far greater total heat capacity than the atmosphere. Research vessels and stations have sampled sea temperatures at depth and around the globe since before 1960. Additionally, after the year 2000, an expanding network of nearly 4000 Argo robotic floats has measured the temperature anomaly, or equivalently the ocean heat content change (ΔOHC). Since at least 1990, OHC has increased at a steady or accelerating rate. ΔOHC represents the largest portion of EEI since oceans have thus far taken up over 90% of the net excess energy entering the system over time (Δt):
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{\displaystyle EEI\gtrsim \Delta OHC/\Delta t}
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Earth's outer crust and thick ice-covered regions have taken up relatively little of the excess energy. This is because excess heat at their surfaces flows inward only by means of thermal conduction, and thus penetrates only several tens of centimeters on the daily cycle and only several tens of meters on the annual cycle. Much of the heat uptake goes either into melting ice and permafrost or into evaporating more water from soils.
=== Measurements at top of atmosphere (TOA) ===
Several satellites measure the energy absorbed and radiated by Earth, and thus by inference the energy imbalance. These are located top of atmosphere (TOA) and provide data covering the globe. The NASA Earth Radiation Budget Experiment (ERBE) project involved three such satellites: the Earth Radiation Budget Satellite (ERBS), launched October 1984; NOAA-9, launched December 1984; and NOAA-10, launched September 1986.
NASA's Clouds and the Earth's Radiant Energy System (CERES) instruments are part of its Earth Observing System (EOS) since March 2000. CERES is designed to measure both solar-reflected (short wavelength) and Earth-emitted (long wavelength) radiation. The CERES data showed increases in EEI from +0.42±0.48 W/m2 in 2005 to +1.12±0.48 W/m2 in 2019. Contributing factors included more water vapor, less clouds, increasing greenhouse gases, and declining ice that were partially offset by rising temperatures. Subsequent investigation of the behavior using the GFDL CM4/AM4 climate model concluded there was a less than 1% chance that internal climate variability alone caused the trend.
Other researchers have used data from CERES, AIRS, CloudSat, and other EOS instruments to look for trends of radiative forcing embedded within the EEI data. Their analysis showed a forcing rise of +0.53±0.11 W/m2 from years 2003 to 2018. About 80% of the increase was associated with the rising concentration of greenhouse gases which reduced the outgoing longwave radiation.
Further satellite measurements including TRMM and CALIPSO data have indicated additional precipitation, which is sustained by increased energy leaving the surface through evaporation (the latent heat flux), offsetting some of the increase in the longwave greenhouse flux to the surface.
It is noteworthy that radiometric calibration uncertainties limit the capability of the current generation of satellite-based instruments, which are otherwise stable and precise. As a result, relative changes in EEI are quantifiable with an accuracy which is not also achievable for any single measurement of the absolute imbalance.
=== Geodetic and hydrographic surveys ===
Observations since 1994 show that ice has retreated from every part of Earth at an accelerating rate. Mean global sea level has likewise risen as a consequence of the ice melt in combination with the overall rise in ocean temperatures.
These shifts have contributed measurable changes to the geometric shape and gravity of the planet.
Changes to the mass distribution of water within the hydrosphere and cryosphere have been deduced using gravimetric observations by the GRACE satellite instruments. These data have been compared against ocean surface topography and further hydrographic observations using computational models that account for thermal expansion, salinity changes, and other factors. Estimates thereby obtained for ΔOHC and EEI have agreed with the other (mostly) independent assessments within uncertainties.
=== Importance as a climate change metric ===
Climate scientists Kevin Trenberth, James Hansen, and colleagues have identified the monitoring of Earth's energy imbalance as an important metric to help policymakers guide the pace for mitigation and adaptation measures. Because of climate system inertia, longer-term EEI (Earth's energy imbalance) trends can forecast further changes that are "in the pipeline".
Scientists found that the EEI is the most important metric related to climate change. It is the net result of all the processes and feedbacks in play in the climate system. Knowing how much extra energy affects weather systems and rainfall is vital to understand the increasing weather extremes.
In 2012, NASA scientists reported that to stop global warming atmospheric CO2 concentration would have to be reduced to 350 ppm or less, assuming all other climate forcings were fixed. As of 2020, atmospheric CO2 reached 415 ppm and all long-lived greenhouse gases exceeded a 500 ppm CO2-equivalent concentration due to continued growth in human emissions.
== See also ==
Lorenz energy cycle
Planetary equilibrium temperature
Climate sensitivity
Tipping points in the climate system
Climate change portal
== References ==
== External links ==
NASA: The Atmosphere's Energy Budget
Clouds and Earth's Radiant Energy System (CERES)
NASA/GEWEX Surface Radiation Budget (SRB) Project | Wikipedia/Earth's_energy_balance |
Human factors in diving equipment design are the influences of the interactions between the user and equipment in the design of diving equipment and diving support equipment. The underwater diver relies on various items of diving and support equipment to stay alive, healthy and reasonably comfortable and to perform planned tasks during a dive.
Divers vary considerably in anthropometric dimensions, physical strength, joint flexibility, and other factors. Diving equipment should be versatile and chosen to fit the diver, the environment, and the task. How well the overall design achieves a fit between equipment and diver can strongly influence its functionality. Diving support equipment is usually shared by a wide range of divers and must work for them all. When correct operation of equipment is critical to diver safety, it is desirable that different makes and models should work similarly to facilitate rapid familiarisation with new equipment. When this is not possible, additional training for the required skills may be necessary.
The most difficult stages for recreational divers are out of water activities and transitions between the water and the surface site, such as carrying equipment on shore, exiting from water to boat and shore, swimming on the surface, and putting on equipment. Safety and reliability, adjustability to fit the individual, performance, and simplicity were rated the most important features for diving equipment by recreational divers.
The professional diver is supported by a surface team, who are available to assist with the out-of-water activities to the extent necessary, to reduce the risk associated with them to a level acceptable in terms of the governing occupational safety and health regulations and codes of practice. This tends to make professional diving more expensive, and the cost tends to be passed on to the client.
Human factors engineering (HFE), also known as human factors and ergonomics, is the application of psychological and physiological principles to the engineering and design of equipment, procedures, processes, and systems. Primary goals of human factors engineering are to reduce human error, increase productivity and system availability, and enhance safety, health and comfort with a specific focus on the interaction between the human and equipment.
== General principles ==
Diving equipment is used to facilitate underwater activity by the diver. The primary requirements are to keep the diver alive and healthy, while secondary requirements include providing comfort and the capacity to perform required tasks. Safe operation requires correct equipment function as well as diver competence.
Fault tolerance is the property that enables a system to continue operating properly in the event of the failure of some of its components. If its operating quality decreases at all, the decrease is proportional to the severity of the failure. Diving equipment, especially those pieces which are high availability or safety-critical systems, must have a high fault tolerance. The ability to maintain functionality when portions of a system break down is referred to as 'graceful degradation', as opposed to a small failure causing total breakdown. The diver must also be fault tolerant, a state that is achieved by competence, situational awareness and fitness to dive, .
=== Physiological variables ===
Task loading, nitrogen narcosis, fatigue, and cold can lead to loss of concentration and focus, reducing situation awareness. Reduced situation awareness can increase the risk of a situation that should be manageable developing into an incident where damage, injury or death may occur.
A diver must be able to survive any reasonably foreseeable single equipment failure long enough to reach a place where longer-term correction can be made. The solo diver can not rely on team redundancy, and must provide all the necessary emergency equipment indicated as necessary by the risk assessment. On the other hand, a team can reduce risk to an acceptable level in most cases by distributing redundancy among its members. However, the effectiveness of this strategy is tied to team cohesion and good communication.
No gender-specific traits have been identified which require design of tasks and tools exclusively for female divers. Fit of diving suits must be tailored to suit the range of human shapes and sizes, and most other equipment fits all sizes, is adjustable to suit all sizes, or is available in several sizes. A few items are designed specifically for female use, but this is often more a fine tuning for comfort or cosmetic styling than an ergonomically functional difference. Female divers are reported, on average, to experience greater difficulty in performing five tasks of recreational diving: carrying heavy equipment on shore, putting on the scuba set, underwater orientation, underwater balance, and trim and descent. The first two are related to lifting large, heavy and bulky equipment. Balance and trim could be related to buoyancy and weight distribution, but insufficient data is available to specify a remedy.
There is a relative growth in the older sector of recreational diver demographics. Some are newcomers to the activity and others are veterans continuing a long career of diving activity. They include older female divers. More research is needed to establish the implications of age and sex-related variations on human factors and safety issues.
== Breathing apparatus ==
The breathing apparatus must allow the diver to breathe with minimal added work of breathing, and minimum additional dead space. It should be comfortable to wear, and not cause stress injury or allergic reactions to its materials. It must be reliable and not require constant attention or adjustment during a dive, and performance should degrade gradually in the event of malfunctions, allowing time for corrective action to be taken with minimum risk. When more than one breathing gas mixture is available, the risk of selecting a gas unsuitable for the current depth must be minimised.
=== Demand valves ===
Holding the scuba mouthpiece between the teeth can cause jaw fatigue on a long dive. The loads that cause this fatigue can be reduced by using smaller second stages, different hose lengths and routing, angled swivels, and improved mouthpiece design, which may include customised bite grips. Allergic reactions to mouthpiece materials are less common with silicone rubber and other [[Hypoallergenic]] materials than with natural rubber, which was commonly used in older equipment. Some divers experience a gag reflex with mouthpieces that contact the roof of the mouth, but this can be corrected by fitting a different style of mouthpiece.
Purging the second stage is a useful function to clear water from the interior. The purge button should function only when pressed, and should be powerful enough to sufficiently clear the chamber while not blowing its contents down the diver's throat. Cracking pressure is the pressure difference over the diaphragm needed to open the second stage valve. This should be low but not excessively sensitive to water movement or orientation. Once open with gas flowing, the gas flow often produces a slight increase in the pressure drop in the demand valve. This helps hold the demand valve open during inhalation, effectively reducing the work of breathing, but making the regulator more susceptible to free-flow. In high performance models, the user can adjust these sensitivity settings.
The exhaust valve should offer the minimum resistance to exhalation, including a minimum opening pressure difference, and low resistance to flow through the opening. It should not easily block or leak due to foreign matter such as vomit. Exhaust gas flow should not be too distracting or annoying to the diver in a normal diving posture. Flow should be directed away from the faceplate of the mask and bubbles should not flow directly over the ears.
=== Work of breathing ===
Breathing effort should be reasonable in all diver attitudes. The diver can rotate in three axes, and may need to do so for a significant period including several breaths from any arbitrary orientation. The DV should continue to function correctly throughout the maneuvers, though some variation in breathing effort is inevitable. Breathing performance testing for compliance to standards is generally done facing forward and facing down. Manual adjustment of the inhalation valve spring may be available, and can help if an unusual orientation must be maintained for a long period.
=== Hose routing ===
Scuba divers must be able to easily provide emergency gas to other scuba divers who are diving as part of the same group, which can be made easier or more difficult by the handedness of the regulator, the hose length, and the hose routing. Different configurations are used for specific circumstances. For example, the 5 to 7 feet (1.5 to 2.1 m) "long hose" arrangement is used to facilitate gas sharing when swimming in single file through a restriction. There are hose routings that have been standardised to a reliable system.
=== Rebreathers ===
Rebreather equipment removes carbon dioxide from exhaled gas and replaces it with oxygen, allowing the diver to breathe the gas again. This can be done in a self-contained system carried by the diver, in a system where the scrubber is carried by the diver and gas is supplied from the surface, or where the gas is returned to the surface for recycling. The power to circulate gas in the loop can be the lung power of the diver, energy from the supply gas pressure, or externally powered booster pumps. Scuba rebreathers tend to circulate by lung power, and the work of breathing can make up a significant part of diver effort at depth; in extreme circumstances it may exceed the capacity of the diver without additional workload. The position of the counterlungs and the orientation of the diver in the water, can have a significant effect on work of breathing, as can the restriction of flow between the diver's teeth.
Using two scrubber canisters in series can provide a level of redundancy in that a fault in one that allows carbon dioxide breakthrough will not necessarily directly affect the other. It is also possible to repack just the first scrubber after a short dive, and may be possible to also change the order so that the freshest scrubber is last in the circuit. Mounting the counterlung across the diver between the scrubbers can eliminate transverse shifts in the centre of buoyancy during the breathing cycle, and also mounting it longitudinally in line with the lungs eliminates longitudinal buoyancy shifts during the breathing cycle. The counterlung could be mounted across the back or across the chest.
A wide variety of rebreather types are used in diving because of the highly variable requirements in different situations. A diving rebreather is safety-critical life-support equipment – some modes of failure can kill the diver without warning, some others require immediate appropriate response for survival.
Some rebreathers have control systems which will lock out if they do not complete a satisfactory pre-dive test, but others which may be used for cave diving, where the inability to start a dive may prevent the diver from exiting from a cave in which they have surfaced in a space isolated from the exit by a water-filled passage, will not prevent the diver from starting a return dive, but will warn them of the problems detected, as it may be possible to escape by operating the rebreather manually.
=== Mouthpiece retaining straps ===
Rebreather diving incidents commonly involve an inappropriate breathing gas, which can result in loss of consciousness, water aspiration and drowning. Water aspiration may be delayed by use of a full-face mask or a mouthpeice retaining strap. According to a study of military rebreather accidents, the number of fatalities was low where mouthpiece retaining straps were used. The availability of a tethered dive buddy also helped ensure timely rescue.
=== Snorkels ===
A separate snorkel, or tube snorkel, used for freediving and swimming at the surface on scuba, typically comprises a curved tube for breathing and a means of attaching the tube to the head of the wearer. The tube has an opening at the top and a mouthpiece at the bottom. Snorkels are classified by their dimensions and by their orientation and shape. The length and the inner diameter (or inner volume) of the tube are important ergonomic considerations when matching a snorkel to the requirements of its user. The orientation and shape of the tube must also be taken into account when matching a snorkel to its use while seeking to optimise ergonomic factors such as low drag through the water, airflow, water retention, interrupting the field of vision, work of breathing, and dead space. The collapsible snorkel is intended for scuba divers who do not need a snorkel on every dive, but may find it occasionally useful. It can be folded up and stored in a pocket until it is needed.
Some snorkels have a sump and drain valve at the lowest point to help clear the snorkel and drain the remnant volume of water in the snorkel out of the direct air passage. The effectiveness of these has not been clearly established. These valves have a tendency to fail if infrequently used, stored for long periods, through environmental fouling, or owing to lack of maintenance. Many also slightly increase the flow resistance of the snorkel, retain a small amount of water in the tube after clearing, or both.
=== Dead space ===
Mechanical dead space of diving breathing apparatus is the volume in which the exhaled breathing gas is immediately inhaled on the next breath, increasing the necessary tidal volume and respiratory effort to get the same amount of usable breathing gas, increasing the accumulation of carbon dioxide from shallow breaths, and limiting the maximum volume of fresh or recycled gas in a breath. It is in effect an external extension of the physiological dead space.
The importance of minimising dead space volume is greater when the work of breathing is large, as work of breathing can also be a limiting factor in gas exchange. This becomes critical at high ambient pressures when the density of the breathing gas is high. Lower density breathing gas diluents help mitigate this problem.
== Masks and helmets ==
Diving masks and helmets provide air space between the eyes and a transparent window to allow the diver a clear view underwater.
=== Internal volume ===
The internal volume of masks and helmets affects buoyancy and trim, and dead space, which affects gas exchange and work of breathing.
The volume of dead space is important for full-face masks and helmets, but not relevant to half masks as they are not part of the breathing passage. For breathhold diving, the mask internal volume must be equalised from the single breath in the diver's lungs, so a small volume is highly desirable, but scuba divers have sufficient air available that this is not a problem.
Large internal volume half-masks tend to float up against the nose, which is uncomfortable and becomes painful over time. The trend is towards low volumes and wide fields of vision, which requires the viewport to be close to the face. This makes it difficult to design a frame and nose pocket that will accommodate the full range of face shapes and sizes. Wide and high-bridged noses and very narrow faces are a particular problem. The clearance between the viewport and eyes should account for the eyelashes when blinking.
Full-face masks have larger internal volumes, but they are strapped on more securely and the load is carried by the neck. This load is small enough to be easily accommodated by most divers, though it may take some time to get used to it, and a lower volume is more comfortable. A large volume may adversely affect diver trim and necessitate moving or adding ballast weight to compensate.
=== Helmet buoyancy ===
The weight of a lightweight demand helmet in air is about 15 kg. Underwater it is nearly neutrally buoyant so it is not an excessive static load on the neck. The helmet is a close fit to the head and moves with the head, allowing the diver to aim the viewport using head movement to compensate for the restricted field of vision.
Free-flow helmets compensate for a potentially large dead space by a high gas flow rate, so that exhaled gas is flushed away before it can be rebreathed.: Ch.3 They tend to have a large internal volume, and be heavier than demand helmets, and usually rest on the shoulders, so do not move with the head. As there is no need for an oro-nasal inner mask, they usually have a large viewport or several viewports to compensate for the fixed position. The diver can move the head inside the helmet to a limited extent, but to look around further, the diver must rotate the torso. The view downwards is particularly restricted, and requires the diver to bend over to see the area near the feet. Buoyancy may be compensated by direct weighting of the helmet and corselet, or by a jocking harness and indirect weighting.
=== Seal ===
The mask must form a watertight seal around the edges to keep water out, regardless of the attitude of the diver in the water. This seal is between the elastomer skirt of the mask and the skin of the face. The fit of a mask affects the seal and comfort and must account for the variability of face shapes and sizes. For half masks, this is achieved by the very wide range of models available, but in spite of this some faces are too narrow or noses too large to fit comfortably. This is less of a problem with full-face masks and less again with helmets. However, these are affected by other factors like overall head size and neck length and circumference, so there is still a need for adjustment and different size options.
Face and neck seals may be compromised by hair passing under the seal between the rubber and skin, and the amount of leakage will depend on the amount of hair and the position of the compromised part of the seal. Divers with large amounts of facial hair can usually compensate adequately on open circuit by occasional exhalation through the nose to clear the mask, but with a rebreather the gas used for mask clearing is lost from the circuit.
=== Equalising ===
Two aspects of equalising the pressure in gas spaces are influenced by mask and helmet design. These are equalising the internal space of the mask or helmet itself, and equalising the ears. Equalising the internal space of a half mask is normally achieved through the nose, and equalising the ears requires a method to block the nostrils. This is relatively easy to do with half-masks, where the diver can usually pinch the nostrils closed through the rubber of the mask skirt.
Helmets and most full-face masks do not allow the diver finger access to the nose, and various mechanical aids have been tried with varying levels of comfort and convenience.
=== Vision ===
The field of vision of the diver is reduced by opaque parts of the helmet or mask. Peripheral vision is more reduced in the lower areas due to the size of the demand valve. Helmet design is a compromise between low mass and inertia (with a smaller interior volume and restricted field of vision), and large viewports that lead to a larger interior volume. A viewport close to the eyes provides a better view for the same area, but this is complicated because of the varying nose sizes of divers and the need for clearance for the oro-nasal mask. Curved viewports can introduce visual distortions that reduce the ability to judge distance, and almost all viewports are made flat. Even a flat viewport causes some distortion, but it takes relatively little time to get used to this, as it is constant. Spherical port surfaces are generally used in newer atmospheric suits for structural reasons, and work well when the interior volume is large enough. They can be made wide enough for adequate peripheral vision. Field of vision in helmets is affected by the mobility of the helmet. A helmet directly supported by the head can rotate with the head, allowing the diver to aim the viewport at the target. In this case, however, peripheral vision is constrained by the dimensions of the viewport, the weight in air and unbalanced buoyancy forces when immersed must be carried by the neck, and inertial and hydrodynamic loads must also be carried by the neck. A helmet fixed to a breastplate is supported by the torso, which can safely support much greater loads, but it cannot rotate with the head. The entire upper body must rotate to direct the field of vision. This makes it necessary to use larger viewports so the diver has an acceptable field of vision at times when rotating the body is impractical. The need to rotate the head inside the non-rotatable helmet requires internal clearance, therefore a larger volume, and consequently a greater mass of ballast.
Optical correction is another factor that is considered in mask and helmet design. Contact lenses can be worn under all types of masks and helmets. Regular spectacles can be worn in most helmets, but cannot be adjusted during the dive. Corrective lenses can be glued to the inside of half-masks and some full-face masks, but the distance from the eyes to the lenses may not be optimal, and some correction may be needed to compensate for the increased distance from the cornea to the lens. Bifocal arrangements are available, mostly for far-sightedness, and may be necessary with older divers to allow them to read their instruments. Defogging of bonded lenses is the same as for plain glass. Some dive computers have relatively large font displays, and adjustable brightness to suit the ambient lighting.
An open circuit breathing apparatus produces exhalation gas bubbles at the exhaust ports. Free-flow systems produce the largest volumes, but the outlet can be behind the viewports so it does not obscure the diver's vision. Demand systems must have the second stage diaphragm and exhaust ports at approximately the same depth as the mouth and lungs to minimise work of breathing. To get consistent breathing effort for the range of postures the diver may need to assume, this is most practicable when the exhaust ports and valves are close to the mouth, so some form of ducting is required to direct the bubbles away from the viewports of helmet or mask. This generally diverts exhaust gases around the sides of the head, where they tend to be rather noisy as the bubbles rise past the ears. Closed circuit systems vent far less gas, which can be released behind the diver, and are significantly quieter. Diffuser systems have been tried, but have not been successful for open circuit equipment, though they have been used on rebreathers, where they improve stealth characteristics.
The inside surface of the viewport of a mask or helmet tends to be prone to fogging, where tiny droplets of condensed water disperse light passing through the transparent material, blurring the view. Treating the inside surface with a defogging surfactant before the dive can reduce fogging. Fogging may occur anyway, and it must be possible to actively defog, either by rinsing with water or by blowing dry air over it until it is clear. There is no supply of dry air to a half-mask, but rinsing is easy and only momentarily interrupts breathing. A spitcock may be provided on standard helmets for rinsing. Demand helmets generally have a free-flow supply valve that directs dry air over the inside of the faceplate. Full-face masks may use either rinsing or free-flow, depending on whether they are intended primarily for scuba or surface-supply diving.
=== Security ===
Masks held in place by adjustable straps can be knocked off or moved from the correct position, allowing water to flood in. Half masks are more susceptible to this, but because the diver can still breathe with a flooded half mask this is not considered a major issue unless the mask is lost. Full-face masks are part of the breathing passage, and need to be more securely supported, usually by four or five adjustable straps connected at the back of the head. It is still possible for these to be dislodged, so it must be possible for the diver to refit them sufficiently to continue breathing with their hands in cold-water gloves. On the other hand, the regulator is fixed to the mask so the mask is not easily lost and can be retrieved in the same way as a regulator second stage. Helmets are much more securely attached, and it is considered an emergency if they come off the head, as it is difficult for the diver to rectify the problem underwater, though it is usually still possible to breathe carefully if the free-flow valve is opened and the helmet held over the head with the bottom opening level.
== Cylinders ==
When using multiple gas sources and mixtures it is important to avoid confusing the gas mix in use and the pressure remaining in the various cylinders. The cylinder arrangement must allow access to cylinder valves when in the water. Use of the wrong gas for the depth can have fatal consequences with no warning. High task loading for technical divers can distract from checking the mix when switching gas. It is important to check that each cylinder is the correct gas and is mounted in the right place, to positively identify the new gas at each gas switch, and to adjust the decompression computer to allow for each change in gas for correct decompression. Some computers automatically change based on data from integrated pressure transducers, but still require correct pre-dive setting of gas mixes.
A back-mounted single cylinder configuration is stable on the diver in and out of the water, and is compact and acceptably balanced. However, some divers have difficulty reaching the valve knob, which is behind the back, particularly when the cylinder is mounted relatively low on the harness, or the suit is thick or tight. Back-mounted twin cylinders with an isolation manifold are also stable in and out of the water. They are compact, heavy, and acceptably balanced for most divers. Some divers have difficulty reaching the valve knobs behind the back. This can be a problem in a free-flow or leak emergency, where a large volume of gas can be lost due to inability to access knobs quickly to shut down the cylinder. The weight and buoyancy distribution may be top heavy for some divers. In back-mounted independent doubles, gas is not available if a cylinder valve must be shut down. The side-mount emergency options of feather breathing and regulator swap-out are also not available. Flexible valve knob extensions on back mount sets are not very satisfactory and not very reliable, and are an additional snag risk. Pony cylinders for bailout or decompression gas clamped to the main gas supply put the valve where it cannot be seen, and may be difficult to reach. They are reasonably compact and manageable out of the water. Sling mount bailout and decompression cylinders allow easy access to the valve and allow the visual checking of labels during gas switching. Up to four sling cylinders are reasonably manageable with some practice.
Alternative configurations include an inverted single or manifolded twin cylinders. These have valves at the bottom which are more reachable, but are more vulnerable to impact damage. Custom hose lengths are needed, and hose routing will be different. This arrangement is used by firefighters, and has also been used by military divers. Weight and buoyancy distribution may be bottom heavy for some divers, and may adversely affect trim. This arrangement is also used for the gas cylinders on some rebreather models. Side mounts provide much easier valve access, and it is possible to see the top of each cylinder to check the label when switching gas, which allows confirmation of correct gas. It is possible to hand off a cylinder when donating gas to another diver, so a long hose is not needed.
=== Cylinder buoyancy ===
The material and pressure rating of cylinders affects convenience, ergonomics, and safety. Aluminum alloy and steel are the two commonly available materials that are most often used for scuba cylinders. Their strength to weight ratio allows the manufacture of scuba cylinders that are near neutral buoyancy when empty. Cylinders that require a buoyancy compensator for support when they are empty can be unsafe, since it could be necessary to ditch breathing gas to regain buoyancy in the event of a buoyancy compensator failure. Cylinders that are buoyant when full require ballasting to make them manageable underwater. This kind of cylinder is usually a fibre wound composite cylinder, which are expensive, relatively easy to damage, and usually have a shorter service life. They tend to be used for cave diving when they must be carried through a difficult route to get to the water. Buoyancy control is easier, more stable, and safer when the gas volume needed to achieve neutral buoyancy is minimised, particularly at the end of a dive during ascent and decompression. The need for a large volume of gas in the buoyancy compensator during ascent increases risk of an uncontrolled buoyant ascent during decompression.
For stage drops, sidemount diving where the cylinders will be pushed ahead of the diver for long distances, and where a cylinder may be handed off to another diver, it is particularly convenient if the cylinder has nearly neutral buoyancy during these maneuvers, as this has the least immediate impact on the buoyancy and trim of the diver. This convenience reduces task loading and improves safety.
== Diving suits ==
Diving suits are worn for protection from the environment. In most cases this is to keep the diver warm, as heat loss to water is rapid. There is a trade-off between insulation, comfort, and mobility. When diving in the presence of hazardous materials, the diving suit also serves as personal protective equipment to limit exposure to those materials.
=== Wetsuits ===
Wetsuits rely on a good fit to work effectively. They rely on the low heat conductivity of the gas bubbles in the neoprene foam of the suit, which slows heat loss. If the water inside the suit can be flushed out and replaced by cold water, this insulating function is bypassed. Movement of the diver tends to move the water in the suit around mostly where it is present in thick layers, and if this water is forced out it will be replaced by cold water from outside. A close fit reduces the thickness of the layer of water and makes it more resistant to flushing. A suit that is too tight can also cause problems. It could restrict movement and increase the diver's work of breathing. The gas bubbles in the neoprene foam will compress at depth, reducing insulation as the diver gets deeper. Semi-dry suits attempt to address this issue by making it more difficult for water to enter and leave the suit, but are still most effective when they are close-fitting.
=== Dry suits ===
Dry suits rely on staying dry inside and maintaining a limited volume of gas distributed through the thermal undergarments. The volume of gas needed is fairly constant, but it expands and contracts due to pressure variations as the diver changes depth. Suit squeeze is caused by insufficient gas in the suit, and will reduce flexibility of the suit and restrict the diver's freedom of motion. This could prevent the diver from reaching critical equipment in an emergency. Gas is added manually by pressing a button to open the inflation valve, which is normally in the central chest area where it can easily be reached by both hands and is clear of the harness and buoyancy compensator. High flow rates are neither necessary nor desirable, as they could lead to over-inflation, particularly if the valve sticks open due to freezing. Over-inflation causes an uncontrollable rapid ascent if not corrected. Dumping of suit gas is only possible when the dump valve is above the gas to be dumped. During ascent, the diver has several things to monitor, so an adjustable automatic exhaust valve which provides hands-free operation helps reduce this task loading.
If the dry suit is flooded, thermal insulation is lost which may make it necessary to abort the dive. Buoyancy can also be lost, a problem that can countered by ditching ballast, inflating the buoyancy compensator if it is large enough, or deploying a DSMB or small lifting bag. The extra weight of the water can make it difficult to exit the water, but this can be mitigated by having ankle dumps or cutting the suit to allow water drainage.
The ability of the diver to reach the cylinder valve can be constrained by the suit and personal joint flexibility of the diver. Back-mount configurations with valves up are particularly difficult to reach. This can cause delays in reacting effectively to some emergencies. This is partly a suit issue and partly a cylinder configuration issue.
The combination of suit and helmet can further constrain movement. Considerable effort may be necessary to overcome the encumbrance of the suit so it can take longer to complete complex tasks, in an environment that is already non-conducive to dexterity or heavy labour. This was particularly noticeable on the standard diving suit. Wrist and neck seals are commonly available in latex rubber, silicone rubber, and expanded neoprene. Some divers are allergic to latex, and should avoid latex seals.
Dry suits can be effective for protection against exposure to a wide range of hazardous materials, and the choice of suit material should take into account its resistance to the known contaminants. Hazmat diving often requires complete isolation of the diver from the environment, necessitating the use of dry glove systems and helmets sealed directly to the suit.
The suit should allow sufficient freedom of movement to swim, work, and reach all necessary accessories and controls when worn over undergarments suitable for the water temperature, without having excess internal volume, particularly in the legs. Excess leg length and loose fit can cause the boots to float off the feet, followed by a loss of ability to swim, and orientate correctly, which can be dangerous. The seals should be tight enough to be reliable without restricting blood flow, particularly at the neck.
The operation and skill requirements for the safe use of dry suits has become fairly standardised, so although initial training is considered essential, switching between makes and models does not usually require retraining.
=== Hot water suits ===
Hot water suits are often used for deep dives when breathing mixes containing helium are used. Helium has a higher heat conductivity than air, but has a lower specific heat. The expansion of gas in the diving regulator causes intense cooling, and the chilled gas is heated to body temperature and humidified in the alveoli, which causes rapid heat loss from the body by conduction and evaporation. The amount of heat loss is proportional to the mass of gas breathed, which is proportional to ambient pressure at depth. This compounds the risk of hypothermia already present in the cold temperatures found at these depths.
Hot water suits are usually one piece suits made of foamed neoprene with a zipper on the front of the torso and on the lower part of each leg. They are similar to wetsuits in construction and appearance, but do not fit as closely by design; they are not as thick because they only need to temporarily retain and guide the flow of the heating water. The wrists and ankles of the suit must allow water to flush out of the suit as it is replenished with fresh hot water from the surface. Gloves and boots are worn which receive hot water from the ends of the arm and leg hoses. If a full-face mask is worn, the hood may be supplied by a tube at the neck of the suit. Helmets do not require heating.: ch18 Breathing gas can be heated at the helmet by using a hot water shroud over the helmet inlet piping between the valve block and the regulator, which reduces heat loss to the breathing gas.
Heated water in the suit forms an active insulation barrier to heat loss, but the temperature must be regulated within fairly close limits. If the temperature falls below about 32 °C, hypothermia can result, and temperatures above 45 °C can cause burn injury to the diver. The diver may not notice a gradual change in temperature, and could enter the early stages of hypo- or hyperthermia without noticing. The suit must be loose fitting to allow unimpeded water flow, but this causes a large transient volume of water (13 to 22 litres) to be held in the suit, which can impede swimming due to the added inertia in the legs.
Hot water suits are an active heating system; they are very effective while they are working correctly, but if they fail, they are very ineffective. Loss of heated water supply for hot water suits can be a life-threatening emergency with a high risk of debilitating hypothermia. Just as an emergency backup source of breathing gas is required, a backup water heater is also an essential precaution whenever dive conditions warrant a hot water suit. If the heater fails and a backup unit cannot be immediately brought online, a diver in the coldest conditions can die within minutes. Depending on decompression obligations, bringing the diver directly to the surface could be equally deadly.
The diver will usually wear something under a hot water suit for protection against scalding, chafe and for personal hygiene, as hot water suits may be shared by divers on different shifts, and the interior of the suit may transmit fungal infections if not sufficiently cleaned. Wetsuits can prevent scalding of the parts of the body they cover, and thermal underwear can protect against chafe and keep the standby diver warm at the surface before the dive.
The hot water supply hose of the umbilical is connected to a supply manifold at the right hip of the suit, which has a set of valves to allow the diver to control flow to the front and back of the torso and the arms and legs, and to dump the supply to the environment if the water is too hot or too cold. The manifold distributes the water through the suit via perforated tubes.: ch18
Some initial training in the safe and effective use of hot water suits is considered necessary, but the skills are quickly learned and easily transferable between makes and the arrangement is fairly standard.
=== Atmospheric suits ===
The physiological problems of ambient pressure diving are largely eliminated by isolating the diver from the water and hydrostatic pressure in an atmospheric suit. However, dexterity problems with manipulators on atmospheric diving suits reduce their effectiveness for many tasks. The joints of atmospheric suits allow walking but are not suitable for swimming.
The suit must maintain constant volume during articulation, as a variable volume would require additional effort to move from a lower volume geometry to higher volume due to the large pressure difference. A range of user sizes can be accommodated by adding spacers between components, but the extra joints increase the likelihood of leaks. Alternative parts with different lengths that require moving high-pressure seals to be split and reconnected may need to be pressure tested before each use.
The work required to overcome friction in the pressure-resistant joint seals, inertia of the limb armour, and drag of the bulky limbs moving through the water are major constraints on agility and limit the ways the diver can move. However, buoyancy control is relatively simple, as the suit is mostly incompressible and the life support system is closed so there is no weight change due to gas consumption.
Although the pressure hull of the suit is often made from metals with high heat conductivity, insulating the diver is largely a matter of wearing clothing suitable for the internal air temperature, and insulating the shell away from the moving parts of joints is fairly straightforward. The air is recycled through the scrubber, which will heat it slightly through the exothermic chemical reaction that removes carbon dioxide.
The helmet is rigidly connected to the torso of the suit, which limits the field of vision. This can be partly compensated by using a nearly hemispherical dome viewport.
Atmospheric diving suits are still an emerging technology, and differ considerably, so specialist training is required for each model.
== Harness ==
The surface-supplied diver's harness is an item of strong webbing, and sometimes cloth, which is fastened around a diver over the exposure suit. It must allow the diver to be lifted without risk of falling out of the harness.: ch6 It also provides support for the bailout gas cylinder, and may carry the ballast weights, a buoyancy compensator, the cutting tool, and other equipment. Several types are in use. Recreational scuba harnesses are mainly used to support the gas cylinders, buoyancy compensator and often the weights and small accessories, but are not normally required to function as a lifting harness. In professional diving, when the harness may also be used to lift the diver, it must be strong enough to support the diver and equipment without causing injury. Some discomfort is considered acceptable when lifting out of the water, as this is an emergency procedure.
Improper distribution of weight carried by the harness can cause discomfort and nerve pressure injury out of the water, and the weight of the harness including cylinders can be problematic for putting the set on for some divers.
== Buoyancy control equipment ==
Because pressure varies rapidly with depth, buoyancy is inherently unstable and controlling it requires continuous monitoring and input from the diver. The instability is proportional to the volume of the gas required for neutral buoyancy, so the volume of gas required for neutral buoyancy should be kept as low as possible over the course of the dive.
Most of the weight change in a dive is due to gas use. Unless equipment is lost or abandoned, the maximum weight change is the consumption of all the gas in all the cylinders carried. The diver needs enough buoyancy volume to remain comfortably afloat before the dive starts. At the end of the dive there will be more buoyancy in reserve as a result of the gas consumption. However, too much reserve volume in the buoyancy compensator has the potential for contributing to an uncontrolled buoyant ascent.
In dry suits, gas is primarily intended for thermal insulation, and the additional buoyancy it creates is undesirable. Removing excess gas is only possible when there is an upward path from the gas to the venting point.
Automatic dump valve position is conventionally on the upper left sleeve, clear of the harness, but in easy reach of the diver at all times and at a natural high point for the most useful and likely trim positions for swimming, work, and particularly ascents. The gas will expand as a diver ascends, increasing the need to vent it. However, a body orientation that allows for sufficient venting during an ascent is inefficient for horizontal propulsion. On the other hand, maintaining an orientation with the feet kept higher means the diver loses the ability to vent and risks losing control of buoyancy. Ankle venting points can mitigate this, but they are not fitted as standard equipment as they have proven to be a common leak point. Diving suits should not be excessively baggy, to reduce the amount of trapped gas, but must be loose enough to allow freedom of movement and access for the feet to the boots. The problem can be exacerbated if the legs are baggy at the ankles and the boots are loose, as if they slip off the feet, all control of the fins, and transfer of power to the fins, is lost. Gaiters and ankle straps can reduce the volume of this part of a suit, and may also reduce hydrodynamic drag, while ankle weights require acceleration with every fin stroke.
Female divers are reported to have more difficulties with buoyancy and trim. This may be a consequence of a buoyancy distribution not well catered for by most harness, buoyancy compensator and weighting systems, possibly exacerbated by dry suit buoyancy distribution. Many manage with available equipment, but it may take longer to learn to effectively use less ergonomically matched equipment. A similar problem is reported with unusually small divers.
The operating skills for most types of single bladder buoyancy compensator are standardised and portable between models. Familiarisation is rapid and straightforward, and retraining is generally not required, though additional training is provided for adapting to sidemount because of the associated changes in breathing apparatus management. Twin bladder units require more adaptation of procedures, and are associated with more accidents due to human error, as there are more kinds of operator errors that can be made.
== Weights ==
Weighting systems are needed to compensate for the buoyancy of the diver and buoyant equipment. The distribution of buoyancy and ballast affect diver trim, which influences propulsion efficiency breathing gas consumption.
Weight-belts of conventional design are fastened around the waist and load the lower back when the diver is trimmed horizontal. This can cause lower back pain, particularly when the weights are heavy to compensate for the buoyancy of a dry suit with thick undergarments. Weights supported by the harness distribute the load more evenly.
Ankle weights, used to improve trim, add inertia to the feet, which must be accelerated and decelerated with every fin stroke, requiring additional power input for finning and reducing propulsive efficiency. The ability to shed ballast weight is considered a safety feature for scuba diving. It allows the diver to achieve positive buoyancy in an emergency, but the inadvertent loss of ballast when the diver needs to control ascent rate is itself an emergency that can cause decompression illness.
The need to pull weights clear of other equipment when ditching in some orientations is additional task loading in an emergency. The weight belt can become caught in the harness and compound the diver's problems if the need to establish positive buoyancy is urgent.
== Fins ==
Fin design is a compromise between propulsive efficiency and maneuverability. Monofins are the equipment of choice for deep apnea diving and for speed and endurance competitions. Breath hold spearfishers need more maneuverability while retaining the best reasonably practicable efficiency, and they mostly choose long bifins. Professional and recreational scuba and surface-supplied divers will sacrifice more efficiency for better maneuverability. Comfort issues and muscle or joint stress, particularly among less physically fit divers, may bias the choice towards softer fins that produce less thrust and maneuverability. Divers needing maximum maneuverability will usually choose stiff paddle fins which can be effective for reversing out of a tight spot but are inefficient for cruising using flutter kick. These fins work well with the frog kick, which is also less likely to shed vortices downward and disturb silty bottoms, so this style of fin is popular for cave and wreck penetration diving.
Experimental work suggests that larger fin blades are more efficient in converting diver effort to thrust, and are more economical in breathing gas for similar propulsive effect. Larger fins were perceived by the participating divers to be less fatiguing than smaller fins. For each kick stroke the mass of the fin must be accelerated once in each direction, so producing more thrust per stroke will waste less work on accelerations. Inertial effects increasing the work of finning are also caused by heavier fins, boots and ankle weights.
Attachment to the foot follows two basic options: an integral foot pocket enclosing the heel or an open heeled foot pocket with an elastic heel strap. Both systems allow full mobility of the ankle joint for bi-fins, but limit the motion for monofins. Full foot-pockets are softer and more comfortable on bare feet, and spread the loads more evenly, but are often unsuited to wearing over a thick or hard-soled boot capable of crossing rough rocky shores. Fin retainers may be necessary for security if the fit is loose. Open heel foot pockets can be matched with foot width when wearing a boot, and the heel-strap is selected or adjusted to fit. Fin straps may be of fixed or adjustable length. Fixed length straps are always the right length for a single user, and have fewer snag points, moving parts, and other components that can fail. Adjustable straps are quickly adaptable to the feet of different users, a major advantage for rental equipment.
== Gloves ==
Glove fit is important for several reasons. Gloves that are too tight or thick restrict movement and require more effort to grip, which causes early fatigue. Reduced blood flow may cause cramping. Loose gloves may be ineffective against heat loss due to flushing, and may reduce dexterity due to excess bulk.
There is a conflict between insulation and dexterity, and the reduction of tactile sense, grip strength, and early fatigue due to thick gloves or chilled hands. The diver can tolerate greater heat loss through the hands if the rest of the diver is warm, but in some cases such as diving in near-freezing water or where the air temperature at the surface is below freezing, the risk of frostbite or non-freezing cold injury necessitates the use of gloves most of the time. For safety-critical equipment, dexterity can be the difference between managing a problem adequately, or a situation deteriorating beyond recovery. Simple, large control interfaces such as oversize knobs and buttons, large clips, and tools that can be gripped by a heavily gloved hand can reduce risk significantly.
In very cold water there are two problems causing loss of dexterity. The chilling of hands and fingers directly causes loss of feeling and strength of the hands, and thick gloves needed to reduce chilling also reduce the sensitivity of the fingertips, making it more difficult to feel what the fingers are doing. Thick gloves also make the fingertips wider and thicker and a poorer fit to components designed to be used by gloveless hands. This is less of a problem with gloves where the fingertips have a reduced thickness of cover over the contact surface, but few neoprene gloves have this feature. The fingertips of the thumbs and forefingers are most affected, and also wear out faster than the rest of the glove. Some divers wear a thinner, tougher, work glove under the neoprene insulating glove, and cut the tips off the thumbs and forefingers of the neoprene gloves to expose the inner gloves as a workable compromise. Dry gloves allow the diver to tailor the inner insulating glove to suit the task. Insulation can be thicker where it affects dexterity least, and thinner where more sensitivity is needed.
Long term grip strength is reduced by fatigue. If the glove requires effort to close the hand to hold an object, this will eventually tire the hand, and grip will weaken sooner than when affected by cold alone. This is mitigated by gloves with a preform to fit a partly closed hand, and by more flexible glove materials.
== Lifting bags ==
== Surface-supplied gas panels ==
Breathing gas supplied to divers from the surface is routed through a surface control manifold and the gas panel, and may also pass through a manifold in an open or closed diving bell. The surface gas panel may be operated by the diving supervisor or a designated gas man, and the bell panel is the responsibility of the bellman. The gas panels are arranged so that it is clear to the operator which valves and gauges serve each diver. The surface standby diver may be supplied from an independent panel with independent gas supplies, so the standby diver is isolated from gas supply problems that may affect the working divers. Gas panels may be integrated with voice communication equipment.
The gas panel should monitor the depth of each diver in order to provide the right supply pressure. This is done using the pneumofathometer gauge for each diver. It should control the flow rate for free-flow helmets, monitor the supply pressure of connected gasses, make it clear which supply is in use when changing between main and secondary, and confirm that the gas is breathable at the current depth of each diver. Additionally, it should display which part of the system is supplying which diver. Safe and reliable gas provision to the divers depends on the panel operator having a clear and accurate knowledge of the status of the valves and pressures at the panel. This is helped by arranging the components of the panel so that it is immediately obvious which components are dedicated to each diver, what the function of each component is, and the status of each valve. Quarter turn ball valves are generally used because it is immediately obvious from the handle position whether they are open or closed. The spatial arrangement of valves and gauges on the panel is usually either the same for each diver, or mirrored. All operable valves and gauges should be labeled, and colour or shape coding may be useful.
== Communication systems ==
Diver communications are the methods used by divers to communicate with each other or with surface members of the dive team. In professional diving, diver communication is usually voice communications between a single working diver and the diving supervisor at the surface control point, and with the bell for bell operations. This is considered important both for managing the diving work, and as a safety measure for monitoring the condition of the diver. The traditional method of communication by line signals is now used in emergencies when voice communications have failed. Surface supplied divers also often carry a closed circuit video camera on the helmet which allows the surface team to see what the diver is doing and to be involved in inspection tasks. This can also be used to transmit hand signals to the surface if voice communications fails.: Ch.429 Underwater slates may be used to write text messages which can be shown to other divers,: Ch.5 Voice communication is the most generally useful format underwater, as visual forms are more affected by visibility, and written communication and signing are relatively slow and restricted by diving equipment.: 1–2
Diver voice communication equipment does not work with a standard scuba demand valve mouthpiece, so scuba divers generally use hand signals are when visibility allows, and there are a range of commonly used signals, with some variations. These signals are often also used by professional divers to communicate with other divers. There is also a range of other special purpose non-verbal signals, mostly used for safety and emergency communications.
The interface between air and water is an effective barrier to direct sound transmission, and the natural water surface is a barrier to visual communication across the interface due to internal reflection. Hyperbaric speech distortion also hinders sound-based communication.
The process of talking underwater is influenced by the internal geometry of the life support equipment and constraints on the communications systems as well as the physical and physiological influences of the environment on the processes of speaking and vocal sound production.: 6, 16 The use of breathing gases under pressure or containing helium causes problems in intelligibility of diver speech due to distortion caused by the different speed of sound in the gas and the different density of the gas compared to air at surface pressure. These parameters induce changes in the vocal tract formants, which affect the timbre, and a slight change of pitch. Several studies indicate that the loss in intelligibility is mainly due to the change in the formants.
The difference in density of the breathing gas causes a non-linear shift of low-pitch vocal resonance, due to resonance shifts in the vocal cavities, giving a nasal effect, and a linear shift of vocal resonances which is a function of the velocity of sound in the gas, known as the Donald Duck effect. Another effect of higher density is the relative increase in intensity of voiced sounds relative to unvoiced sounds. The contrast between closed and open voiced sounds and the contrast between voiced consonants and adjacent vowels decrease with increased pressure. Change of the speed of sound is relatively large in relation to depth increase at shallower depths, but this effect reduces as the pressure increases, and at greater depths a change in depth makes a smaller difference.
Helium speech unscramblers are a partial technical solution. They improve intelligibility of transmitted speech to surface personnel.
== Instrumentation and displays ==
Diving instrumentation may be for safety or to facilitate the task being performed. Safety-critical information such as gas pressure and decompression status should be presented clearly and unambiguously.
A lack of standardised dive computer user-interfaces can cause confusion under stress. Computer lock-out at times of great need is a potentially fatal design flaw. The meaning of alarms and warnings should be immediately obvious. The diver should be dealing with the problem, not trying to work out what it is. Displays should allow for variations in visual acuity, and be readable with colour-blindness. Ideally, critical displays should be readable without a mask, or allow safe surfacing without a mask. There should not be too much distracting information on the main screen, and returning to the main screen should be automatic by default, or auxiliary screens should continue to display critical decompression data.
Dive computers are safety critical equipment, but there is very little formal training provided for their use. Models also vary considerably in operation, and are often not intuitive, so skills are not transferable when a new unit is used. The user manual is usually all that is available to learn from, and it cannot be taken underwater for convenient reference. Instrument consoles represent a concentrated source of information, and a large potential for operator error.
Dive computers provide a variety of visual dive information to the diver, usually on a LCD or OLED display. More than one screen arrangement may be selectable during a dive, and the primary screen will display by default and contain the safety critical data. Secondary screens are usually selected by pressing one or two buttons one or more times, and may be transient or remain visible until another screen is selected. All safety critical information should be visible on any screen that will not automatically revert within a short period, as the diver may forget how to get back to it and this may put them as significant risk. Some computers use a scroll through system which tends to require more button pushes, but is easier to remember, as eventually the right screen will turn up, others may use a wider selection of buttons, which is quicker when the sequence is known, but easier to forget or become confused, and may demand more of the diver's attention, :
Display and control units for electronically controlled closed circuit rebreathers have very similar requirements and problems to dive computers. This may be reduced when the rebreather controllers and backup dive computer are produced by the same manufacturer.
Head-up displays can be used to provide the diver with a view of critical information which is always visible. These can be mounted on the mask, or on the mouthpiece assembly. Head-up displays require special near-eye 0ptics to allow correct focus on the display. In conditions of very low visibility, a head-up display has the advantage that the diver's ability to see the display is not affected by turbidity. It also lets the diver monitor all displayed dive data without interrupting their work.
== Cutting tools ==
The primary function of diver cutting tools is to deal with entanglement by lines or nets. The tool should be accessible to both hands, and should be capable of cutting the diver free from any entanglement hazard predicted at the dive site. Many divers carry a cutting tool as standard equipment, and it may be required by code of practice as default procedure. When entanglement risk is high, backup cutting tools may be required.
== Dive lights ==
Dive lights may be needed to compensate for insufficient natural illumination or to restore colour. They may be carried in several ways depending on their purpose. Head mount lights are used by divers who need to use both hands for other purposes. With a head mount there is a greater risk of dazzling other divers in the vicinity, as the lights move with the diver's head. As such, this arrangement is more appropriate for divers who work or explore alone. Helmet mounts are appropriate for illuminating work which is monitored via a helmet-mounted closed circuit video camera. Hand-held lights can be directed by the diver independently of the direction the diver is facing and do not require any special mounting equipment. However, they occupy a hand and are at risk of being dropped unless they are clipped on. They are most suitable for incidental lighting, and where precise direction is useful. Glove or Goodman handle mount allows precise direction and allows the hand to perform some other tasks. Canister lights allow the light head to be held in either hand, on a Goodman handle, or looed over the neck to free both hands, and the cable prevents the light from falling far if dropped. It is possible and fairly common to carry more than one of these options. Where light is important for safety, the diver will carry backup lights.
== Buddy lines ==
A buddy line is a line or strap physically tethering two scuba divers together underwater to prevent separation. They can also serve as a means of communication in low visibility conditions. It is usually a short length and may be buoyant to reduce the risk of snagging on the bottom. It does not need to be particularly strong or secure, but should not pull free under moderate loads, such as when used for line signals. Divers may communicate by rope signals, but may just use the line to attract attention before moving closer and communicating by hand signals. The disadvantage of a buddy line is an increased risk of snagging and entanglement, and the risk is increased with a longer or thinner line. Divers may need to disconnect the line quickly at either end in an emergency, which can be done via a quick-release mechanism or by cutting the line, both of which require at least one free hand. A velcro strap requires no tools for release and can be released under tension.
== Clips and attachment points ==
Clips and attachment points should be reliable and must generally be operable by one hand with gloves suitable for the water temperature, without needing to see what is being done, as it may be dark, low visibility, or out of view. Single-hand operation is necessary where only one hand can reach. This is always preferable, as the other hand may be in use for something important. While unlikely, it is possible for most types of clip to become jammed closed, and if this may endanger the diver it should be possible to use an alternative method to disconnect, which does not involve special tools. Cutting loose using the diver's cutting tool is the standard.
A reliable clip is one that does not allow connection or disconnection by accident, instead requiring specific action by the operator to clip or unclip. Unreliable clips may cause loss of equipment or entanglement. Bolt snaps and screw-gate carabiners are examples of clips with a reputation for reliability. The carabiners are more secure, and may be load rated, but are less convenient to operate. Carabiners are approved for attaching the umbilical to a surface supplied diver's harness.
There are usually several attachment points provided on the diving harness or buoyancy compensator for securing accessories and additional diving cylinders. On technical harnesses these are often in the form of stainless steel D-rings or sliders with integral rings, and may be adjustable for position. Plastic D-rings are common on bulk-produced recreational buoyancy compensators, and are usually in fixed positions, held on by bar-tacked webbing straps or tabs, and are not replaceable. Professional harness is usually required to have at least one attachment point capable of lifting the diver out of the water. Attachment rings that are free to swing are less prone to snagging on the surroundings in tight spaces but are more difficult to clip onto one-handed when out of view.
== Diver propulsion vehicles ==
A diver propulsion vehicle (DPV) is a powered device with an integral thruster used by scuba divers to increase their range underwater. Range is restricted by the amount of breathing gas that can be carried, the rate at which that breathing gas is consumed, and the power endurance and speed of the DPV. Time limits imposed on the diver by decompression requirements may also limit safe range in practice. DPVs have recreational, scientific and military applications. They have been produced in a range of configurations from small, easily portable scooter units with a small range and low speed, to faired or enclosed units capable of carrying several divers longer distances at higher speeds.
The most efficient position for towing behind is when the wake of the thruster bypasses the diver. This is usually achieved by using a tow leash from the DPV to a D-ring on the lower front of the diver's harness. The diver also holds a handle on top of the DPV with a dead-man switch that turns off power to the DPV as soon as the diver lets go of the handle. The DPV is commonly steered by one hand, leaving the other hand free for other tasks. This requires good static and dynamic balance of the DPV and diver to avoid excessive diver fatigue. Lights, cameras, navigation, and other instruments may be mounted on a DPV for convenience, but the diver should also carry backups for essential instruments in case the DPV must be abandoned in an emergency. Control of the DPV is additional task loading and can distract the diver. A DPV can increase the risk of a silt-out if the thrust is allowed to wash over the bottom.
DPV operation requires greater situational awareness than simply swimming, as some changes can happen much faster. Operating a DPV requires simultaneous depth control, buoyancy adjustment, monitoring of breathing gas, and navigation. Buoyancy control is vital for diver safety. The DPV has the capacity to dynamically compensate for poor buoyancy control by thrust vectoring while moving, but once it stops the diver may turn out to be dangerously positively or negatively buoyant if adjustments were not made to suit the changes in depth while moving. If the diver does not control the DPV properly, a rapid ascent or descent under power can result in barotrauma or decompression sickness.
== Cameras ==
Underwater cameras are usually popular models encased in a watertight pressure housing. There are a few notable exceptions, such as the Nikonos and Sea & Sea ranges, in which the camera body was the pressure housing. Controls are generally operated by movable links penetrating the watertight case, each requiring reliable seals because they represent a possible leak. Compact and lightweight camera bodies with multiple controls packed into a small space tend to transform into bulky, heavy and expensive units when housed for moderately deep diving. The camera's controls must be operable using thick gloves in cold water. For most underwater photography, a camera that is close to neutral buoyancy will be easier to handle and have less disruptive effect on diver trim. Strobe arms incorporating incompressible buoyancy compartments are the preferred system, as they do not need to be adjusted for changes of depth.
Internal flash is problematic at anything except very close range, as it can cause backscatter in cloudy water, and is the major consumer of battery power at full power. External flash using optical coupling avoids hull penetrations and potential leaks, and video lights give a good preview of exposure, and also provide the diver with a high-power dive light that is already pointing in the right direction to record the scene. With more powerful video lights and low-light sensitivity cameras, flash may not be necessary.
== Surface marker buoys ==
A surface marker buoy is towed to indicate the position of the diver. It should have sufficient buoyancy to reliably remain at the surface so it can be seen. If it is actively towed, it should not develop so much drag that the diver is unable to manage it effectively. The tow line may be a major source of drag (roughly proportional to its diameter); as such, a smaller, smooth line is preferable, and also fits on a more compact reel or spool. Smaller line may need to be of stronger and more abrasion-resistant material like ultra-high-molecular-weight polyethylene for acceptable durability.
A decompression buoy is deployed towards the end of the dive as a signal to the surface that the diver has started to ascend. This kind of buoy is not usually towed, so drag is not a problem. Visibility to a surface observer depends on colour, reflectivity, length above the water, and diameter. A low waterplane area has the advantage of reducing the variation of line tension as waves pass overhead, making it easier to maintain accurate depth under large swells during decompression stops. A larger buoy is more visible at the surface but will pull upward harder if the reel jams during deployment.
== Distance lines and line markers, reels and spools ==
Distance lines are used for underwater navigation where it is either essential to mark the route out of the overhead environment, or necessary or desirable to return to a specific point. Lines are deployed from reels or spools, and may be left in place or recovered on the return. The design and construction of the reel have a large influence on handling during both deployment and recovery of line, which are major parts of the task loading of one of the divers in a wreck or cave penetration team. Good design can minimise effort of winding in the line, and an adjustable brake reduces risk of overruns and loose line in the water while laying the line, which is an entanglement hazard. Highly visible line helps reduce the risk of losing the line in bad visibility, and a near neutral buoyancy of the reel minimises the fatigue caused by carrying it in the hand for long periods. Matching the size of a reel or spool to its intended use allows easy recognition by feel and efficient storage.
Line markers are generally used on permanent guidelines to provide critical information to divers following the line. Slots and notches are used to wrap the line and secure the marker in place. Passing the line through the enlarged area at the base of the two slots allows the marker to slide along the line, or even fall off if brushed by a diver. To more securely fasten the marker, an extra wrap may be added at each slot. It must be possible to fit, interpret, and remove a line marker by feel in total darkness with the line under moderate tension. All of this must happen without dislodging the line. The basic function of these markers is fairly consistent internationally, but procedures may differ by region or team. The protocol for placement and removal should be well understood by the members of a specific team.
A dive reel comprises a spool to hold the line. It is coupled with a winding knob which rotates on an axle attached to a frame, with a handle to hold the assembly in position while in use. A line guide is almost always present to prevent line from unwinding unintentionally, and there is usually a method of clipping the reel to the diver's harness when not in use. Reels may be made from a wide variety of materials, but near neutral buoyancy and resistance to impact damage are desirable features. Reels may also be open or closed. This refers to the presence of a cover around the spool, which is intended to reduce the risk of line tangles on the spool, or line flipping over the side and causing a jam. To some extent this works, but if there is a jam the cover effectively prevents the diver from correcting it. Open reels allow easy access to free jams caused by overwinds or line getting caught between spool and handle, and allow visual checks on the line while winding it in. Reels should be easy to use and lockable to prevent unintentionally unrolling, and have sufficient friction to prevent overruns. Reels used for deploying DSMBs usually have a thumb release ratchet to allow free running deployment and to prevent unwinding when there is tension on the line at other times. A reel with a closed handle is less tiring to hold for long periods, particularly when wearing thick or stiff gloves.
Finger spools are a simple, compact, and low tech alternative to reels that are best suited to relatively short lengths of line. They are a pair of circular flanges with a hole in the middle, connected by a tubular hub, which is sized to use a finger as an axle when unrolling the line. The line is secured by clipping a bolt snap through a hole on one of the flanges and over the line as it leaves the reel. It is reeled in by holding the spool with one hand and simply winding the line onto the spool by hand. Spools are most suitable for reasonably short lines, up to about 50 m, as it becomes tedious to roll up longer lengths. The double end bolt snap for locking the line may also be used as an aid for winding it in, to avoid line abrasion of the fingers or gloves.
== Equipment storage ==
While it is possible for a diver to put on and take off some items of equipment in the water, there is a greater risk of fitting them incorrectly or losing them, particularly when the water is a bit rough. Doing this in the surf is even more risky, and delays at the surface on a boat dive can let the divers drift off site. When possible, kit-up and pre-dive checks should be completed on shore or on the boat, and the kit-up area should facilitate this, or at least make it possible. For recreational diving charter boats, this gives preference to arrangements where each diver can safely and securely stow all their personal dive gear at the same place where they will be putting it on, and where it is not necessary for it to be handled by anyone else except at the diver's request, as unauthorised handling of another person's life-support equipment could have legal consequences if something goes wrong.
Boarding the boat after a dive may require equipment to be removed in the water, and this presents another set of hazards, and the associated risks of injury and damage to or loss of equipment, some of which may be avoided if the diver does not have to take off equipment in the water, and heavy equipment does not have to be lifted over the side of the boat with fragile dangling components exposed to snagging, impact, and crushing hazards by crew or passengers. The necessity to remove fins before climbing some ladders reduces the diver's ability to swim back to the boat if they drift away. When boarding an anchored boat, some way of keeping within reach of the boarding area while removing equipment is required, and it may be necessary to use both hands to ensure secure removal and hand-over of some equipment. Suitable handholds, clip-off points and trailing lines can facilitate this activity.
== Diving chambers ==
Design and construction of pressure vessels for human occupancy are regulated by law, safety standards, and codes of practice. These specify safety and ergonomic requirements, airlock opening sizes, internal dimensions, valve types and arrangement, safety interlocks, pressure gauge types and arrangements, gas inlet silencers, outlet safety covers, seating, illumination, breathing gas supply and monitoring, climate control and communications systems. Other requirements are also specified for structural strength, permitted materials, over-pressure relief, testing, fire suppression and periodical inspection.
A closed bell design must allow access by divers wearing bulky diving suits and bailout sets appropriate for the depth. The amount of gas in the bailout set is calculated for a return rate of 10 metres per minute from the reach of the excursion umbilical. At greater depths, this may require twin sets of high pressure cylinders. It must also be possible for the bellman to hoist an unconscious diver through the lock. A flood-up valve may be provided to allow partial flooding of the bell, so that an unresponsive diver is partially supported by buoyancy while being maneuvered through the opening. Once suspended inside the bell, the water can be blown back down by adding gas. The internal volume must include enough space for divers and equipment including racks for the excursion umbilicals and the bell gas panel. On-board gas cylinders, emergency power packs, tools and hydraulic power supply lines do not have to be stored inside. Access while underwater is through a lock at the bottom, so that the internal gas pressure can keep the water out. This lock can be used for transfer to the saturation habitat, or a side lock can be provided. The side lock does not need to allow passage with harness and bailout cylinders as these are not carried into the habitat area and are serviced at atmospheric pressure.
The splash zone is the region where the bell passes through the surface of the water and where wave action and platform movement can cause the bell to swing around, which can be uncomfortable and dangerous to the occupants. To limit this motion a bell cursor may be used. This is a device used to guide and control the motion of the bell through the air and the splash zone near the surface, where waves can move the bell significantly. It can either be a passive system that relies on additional ballast weight or an active system that uses a controlled drive system to provide vertical motion. The cursor has a cradle which locks onto the bell and moves vertically on rails to constrain lateral movement. The bell is released and locked onto the cursor in the relatively still water below the splash zone.
A bell stage is a rigid frame that may be fitted below a closed bell to ensure that even if the bell is lowered so far as to contact the clump weight or the seabed, there is enough space under the bell for the divers to get in and out through the bottom lock. If all the lifting arrangements fail, the divers must be able to shelter inside the bell while awaiting rescue, and must be able to get out if the rescue is to another bell when the bell is resting on the seabed.
Each compartment of a hyperbaric system for human occupation has an independent externally mounted pressure gauge so that it is not possible to confuse which compartment pressure is being displayed. Where physically practicable, lock doors open towards the side where pressure is normally higher, so that a higher internal pressure will hold them closed and sealed.
Medical and supply lock outer doors generally open outwards due to space constraints, and therefore are fitted with safety interlock systems which prevent them from being opened with internal pressure above atmospheric. This helps avoid the possibility of human error allowing them to be opened while the inner lock is not sealed, as the uncontrolled decompression that would ensue would probably kill the occupants, and possibly also the lock operator.
Internal diameter of hyperbaric living compartments and deck decompression chambers is constrained by codes of practice for reasonable comfort for the occupants. For emergency transfer chambers, there may be overriding logistical constraints on size and mass.
=== Hyperbaric stretchers ===
A hyperbaric stretcher is a lightweight pressure vessel for human occupancy (PVHO) designed to accommodate one person undergoing initial hyperbaric treatment during or while awaiting transport or transfer to a treatment chamber. The stretcher should accommodate most divers without being excessively claustrophobic, be conveniently portable by a reasonable number of bearers, should fit into the available space in the transport likely to be used, and fit through the entry opening of the treatment chamber or lock onto the chamber for transfer under pressure. It should be possible to see and communicate with the person in the chamber, and the occupant should be able to breathe oxygen which is vented to the exterior to keep a constant internal pressure and limit the fire hazard. Breathing gas supplies should also be portable, and it should be possible to disconnect them for a short period when maneuvering in tight spaces.
A saturated diver who needs to be evacuated should be transported without a significant change in ambient pressure. Hyperbaric evacuation requires pressurised transportation equipment, and could be required in a range of situations. The pressure rating and locking mechanism of the evacuation chamber must be compatible with the saturation system it is to serve and the reception facility. This is because both transfers must be under pressure, and it may not be safe to start decompression during the evacuation.
== Access equipment ==
Access equipment is the gear needed to get into and out of the water. In most cases, it refers to diving from a floating platform, but also applies to shore dives where access requires equipment.
=== Diving stages and wet bells ===
Diving stages and wet bells are open platforms used to lower the divers to the work site and to control the ascent and in-water decompression, and to provide safe and easy entry and exit from the water. Design must provide space for the working diver and possibly the bellman. They must be in positions where they are protected from impact during transit and prevented from falling out when above the water. The divers may be seated, but standing during transit is more common.
A stage must have a way to guide the umbilical from the surface tending point to the diver so the diver can be sure of finding the right way back to the stage. This can be provided by having the diver exit the stage on the opposite side to boarding, with the umbilical passing through the frame, but this is not infallible in bad visibility, and a closed fairlead is more reliable. Running the umbilical via the stage may also be needed to ensure the diver cannot approach known hazards, such as the thrusters of a dynamically positioned vessel.
A wet bell has an open-bottomed air space at the top, large enough for the diver and bellman's heads. This space can be used as a place of refuge in an emergency, where some breathing problems can be managed. The air space must be large enough for an unresponsive diver to be suspended by their harness with their head in the air space, as it may be necessary to remove an unresponsive diver's helmet or full-face mask to provide first aid. The bell is also provided with an on-board emergency gas supply, sufficient for any planned or reasonably foreseeable decompression, and a means of safely switching between surface and on-board gas supply. This necessitates an on-board gas distribution manifold and divers' umbilicals that are deployed from and stored on the bell, and someone to operate the panel and tend the working diver's excursion umbilical. The bellman does this, and also serves as standby diver. The buoyancy of the air space may have to be compensated by ballast, as the bell must be negatively buoyant during normal operation.
=== Diver ladders ===
For some applications, dive boat ladders that allow the diver to ascend without removing the fins are preferred. When there is a lot of relative motion between the diver and ladder, it can become difficult to safely remove fins, then get onto the ladder, and not lose the fins. A ladder that can be climbed with fins on the feet avoids this problem. A ladder that slopes at an angle of about 15° from the vertical reduces the load on the arms.
If a ladder must be climbed in full equipment, suitable handholds to brace the diver while climbing are necessary for safety. This also applies if the divers need to climb down a ladder wearing dive gear, and they may need to turn around at the top of the ladder. In the general case, the vessel will be moving in a seaway while the diver is boarding.
=== Dive platforms and diver lifts ===
A dive platform, or swim platform, is a near horizontal surface on a dive boat that gives more convenient access to the water than the deck. It may be large enough for several divers to use simultaneously, or just enough for a single diver. The platform may be fixed, folding, or arranged to lower divers into the water and lift them out again, in which case it is known as a diver lift. Most dive platforms are mounted at the stern, usually on the transom, at a height a short distance above the waterline. They are easily flooded by a following sea, and are self-draining.
Fixed and folding platforms are generally provided with ladders which can be folded or lifted out of the water when not in use. They are also equipped with steps or ladders from the platform to the deck, while lifting platforms may be sufficiently immersible for the divers to swim directly over the platform and stand up to be lifted to a level where they can walk off onto the deck. Lifts are commonly mounted on the transom, or on the side of the boat. Handrails while using steps, ladders and lifts, when crossing or waiting on the platform, or making adjustments to equipment are a valuable safety adjunct as the platform will often be moving when in use, and the divers will usually be encumbered by heavy and bulky diving equipment. Barriers to protect occupants from pinch point hazards may be necessary when there are moving parts. The utility of a lift is enhanced if the diver can use it without having to remove any equipment in the water or on the platform, so an upper position level with the working deck and sufficient space to walk onto the deck fully kitted is preferable.
=== Recovery of an incapacitated diver ===
Professional divers may be required to wear a harness suitable for lifting the diver out of the water in an emergency, and there will usually be an emergency recovery plan and the necessary extraction equipment and personnel available. Recreational divers are not usually required to make any special provisions for an emergency, but recreational diving service providers may have a duty of care to their customers to provide for reasonably foreseeable emergencies with practicable facilities. There may be a regional or membership organisation standard or code of practice. Recovering an incapacitated diver from the water and providing first aid on the boat would usually be considered an expected level of care from a professional service provider.
Recreational divers are not required to wear lifting rated harness, so other plans should be in place. These often necessitate removing equipment from the diver, and the risk of losing the equipment. Details of methods to recover a diver into a boat will vary depending on the geometry of the boat. Simply dragging a diver over the pontoon of an inflatable hull may work in many cases. Larger boats with higher freeboard may have lifting gear that can be used with a rescue sling.
== Tools ==
Tools that are intended for use by divers should take into account the handicaps of the underwater environment on operator stability, mobility, and control, within the full range of conditions in which they are likely to be used. Buoyancy effects on tool and operator, water movement, and reduced sensory input can complicate underwater tool use. Use with gloves is common, and can be a problem when controls are small and clustered.
=== Tool bags, pockets and lanyards ===
Lanyards and clipping points can prevent the loss of tools and equipment like cameras, lights and cutting tools in mid-water or poor visibility, but can increase entanglement risk. Carrying heavy tools can compromise the diver's ability to accurately control ascent and descent rates, so it is common practice for professional divers to have their tools delivered in a bag lowered from the surface, or to transport them in a basket on the stage or bell which transports the diver to the underwater workplace. Tools do not have to be carried inside the pressurised volume of a closed bell, so the basket or rack can be on the bell stage or clump weight.
Pockets for small accessories are common on jacket-style buoyancy compensators. Wing buoyancy compensators generally do not have pockets, as the wing is behind the diver and the harness is usually fairly minimal, but pockets can be added to the waistbelt if there is space. They are supported by the webbing at the top and may be strapped around the thigh to prevent flapping. Cargo pockets on the diving suit are more popular with technical divers, and may be glued to the front or side of the thighs of the suit, or attached in similar positions to wetsuit shorts or a tunic worn over the main suit. Occasionally a chest pocket or internal key pocket may be provided. Sidemount divers may use a butt-pack, a clip-on bag worn behind the diver below the harness and buoyancy comprnsator, that is unclipped and brought forward for access. Position, size, shape, closures, and accessibility are important for the function of carrying equipment, and possible interference with other equipment should also be considered.
Tool bags serve a similar purpose and are available in forms which can be clipped to the diver's harness in a position where access is relatively convenient. Tool bags are used by technical divers for similar purposes to pockets, and professional divers use them to carry small sets of relatively light tools and components in clip-on bags, and heavier tools and components in independent bags which are set down when not being used for the carrying function. Lifting bags of appropriate size may be used to support part of the weight of a bag, heavy tool or installation component.
== Checklists ==
Checklists for preparation of the dive and diving equipment are regarded as important safety tools, and are mandatory in some circumstances. There are several design factors which affect the effectiveness of checklists.
The design of a checklist should fit the purpose of the list. If a checklist is perceived as a top-down means to control behaviour by the organisational hierarchy it is more likely to be rejected and fail in its purpose. A checklist perceived as helping the operator to save time and reduce error is likely to be better accepted. This is more likely to happen when the user is involved in the development of the checklist.
Rae et al. (2018) define safety clutter as "the accumulation and persistence of 'safety' work that does not contribute to operational safety", and state that "when 'safety' rules impose a significant and unnecessary burden on the performance of everyday activities, both work and safety suffer".
An objective in checklist design that it should promote a positive attitude towards the use of the checklist by the operators. For this to happen it must be realistic, convenient and not be regarded as a nuisance. A checklist should be designed to describe and facilitate a physical procedure that is accepted by the operators as necessary, effective, efficient and convenient.
== See also ==
Human factors in diving safety – The influence of physical, cognitive and behavioral characteristics of divers on safety
Ergonomics – Designing systems to suit their users
History of underwater diving – Developments over time in the human activity
Diving equipment – Equipment used to facilitate underwater diving
Timeline of diving technology – Chronological list of notable events in the history of underwater diving equipment
== Notes ==
== References == | Wikipedia/Human_factors_in_diving_equipment_design |
Diving physics, or the physics of underwater diving, is the basic aspects of physics which describe the effects of the underwater environment on the underwater diver and their equipment, and the effects of blending, compressing, and storing breathing gas mixtures, and supplying them for use at ambient pressure. These effects are mostly consequences of immersion in water, the hydrostatic pressure of depth and the effects of pressure and temperature on breathing gases. An understanding of the physics behind is useful when considering the physiological effects of diving, breathing gas planning and management, diver buoyancy control and trim, and the hazards and risks of diving.
Changes in density of breathing gas affect the ability of the diver to breathe effectively, and variations in partial pressure of breathing gas constituents have profound effects on the health and ability to function underwater of the diver.
== Aspects of physics with particular relevance to diving ==
The main laws of physics that describe the influence of the underwater diving environment on the diver and diving equipment include:
=== Buoyancy ===
Archimedes' principle (Buoyancy) - Ignoring the minor effect of surface tension, an object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Thus, when in water, the weight of the volume of water displaced as compared to the weight of the diver's body and the diver's equipment, determine whether the diver floats or sinks. Buoyancy control, and being able to maintain neutral buoyancy in particular, is an important safety skill. The diver needs to understand buoyancy to effectively and safely operate drysuits, buoyancy compensators, diving weighting systems and lifting bags.
=== Pressure ===
The concept of pressure as force distributed over area, and the variation of pressure with immersed depth are central to the understanding of the physiology of diving, particularly the physiology of decompression and of barotrauma.
The absolute pressure on an ambient pressure diver is the sum of the local atmospheric pressure and hydrostatic pressure. Hydrostatic pressure is the component of ambient pressure due to the weight of the water column above the depth, and is commonly described in terms of metres or feet of sea water.
The partial pressures of the component gases in a breathing gas mixture control the rate of diffusion into and out of the blood in the lungs, and their concentration in the arterial blood, and the concentration of blood gases affects their physiological effects in the body tissues. Partial pressure calculations are used in breathing gas blending and analysis
A class of diving hazards commonly referred to as delta-P hazards are caused by a pressure difference other than variation of ambient pressure with depth. This pressure difference causes flow that may entrain the diver and carry them to places where injury could occur, such as the intake to a marine thruster or a sluice gate.
=== Gas property changes ===
Gas equations of state, which may be expressed in combination as the Combined gas law, or the Ideal gas law within the range of pressures normally encountered by divers, or as the traditionally expressed gas laws relating the relationships between two properties when the others are held constant, are used to calculate variations of pressure, volume and temperature, such as: Boyle's law, which describes the change in volume with a change in pressure at a constant temperature. For example, the volume of gas in a non-rigid container (such as a diver's lungs or buoyancy compensation device), decreases as external pressure increases while the diver descends in the water. Likewise, the volume of gas in such non-rigid containers increases on the ascent. Changes in the volume of gases in the diver and the diver's equipment affect buoyancy. This creates a positive feedback loop on both ascent and descent. The quantity of open circuit gas breathed by a diver increases with pressure and depth. Charles's law, which describes the change in volume with a change in temperature at a fixed pressure, Gay-Lussac's second law, which describes the change of pressure with a change of temperature for a fixed volume, (originally described by Guillaume Amontons, and sometimes called Amontons's law). This explains why a diver who enters cold water with a warm diving cylinder, for instance after a recent quick fill, finds the gas pressure of the cylinder drops by an unexpectedly large amount during the early part of the dive as the gas in the cylinder cools.
In mixtures of breathing gases the concentration of the individual components of the gas mix is proportional to their partial pressures and volumetric gas fraction. Gas fraction is constant for the components of a mixture, but partial pressure changes in proportion to changes in the total pressure. Partial pressure is a useful measure for expressing limits for avoiding nitrogen narcosis and oxygen toxicity. Dalton's law describes the combination of partial pressures to form the total pressure of the mixture.
Gases are highly compressible but liquids are almost incompressible. Gas spaces in the diver's body and gas held in flexible equipment contract as the diver descends and expand as the diver ascends. When constrained from free expansion and contraction, gases will exert unbalanced pressure on the walls of their containment, which can cause damage or injury known as barotraum if excessive.
=== Solubility of gases and diffusion ===
Henry's law describes how as pressure increases the quantity of gas that can be dissolved in the tissues of the body increases. This effect is involved in nitrogen narcosis, oxygen toxicity and decompression sickness.
Concentration of gases dissolved in the body tissues affects a number of physiological processed and is influenced by diffusion rates, solubility of the components of the breathing gas in the tissues of the body and pressure. Given sufficient time under a specific pressure, tissues will saturate with the gases, and no more will be absorbed until the pressure increases. When the pressure decreases faster than the dissolved gas can be eliminated, the concentration rises and supersaturation occurs, and pre-existing bubble nuclei may grow. Bubble formation and growth in decompression sickness is affected by surface tension of the bubbles, as well as pressure changes and supersaturation.
=== Density effects ===
The density of the breathing gas is proportional to absolute pressure, and affects the breathing performance of regulators and the work of breathing, which affect the capacity of the diver to work, and in extreme cases, to breathe. Density of the water, the diver's body, and equipment, determines the diver's apparent weight in water, and therefore their buoyancy, and influences the use of buoyant equipment. Density and the force of gravity are the factors in the generation of hydrostatic pressure. Divers use high density materials such as lead for diving weighting systems and low density materials such as air in buoyancy compensators and lifting bags.
=== Viscosity effects ===
The absolute (dynamic) viscosity of water is higher (order of 100 times) than that of air. This increases the drag on an object moving through water, and more effort is required for propulsion in water than air relative to the speed of movement. Viscosity also affects the work of breathing.
=== Heat balance ===
Thermal conductivity of water is higher than that of air. As water conducts heat 20 times more than air, and has a much higher thermal capacity, heat transfer from a diver's body to water is faster than to air, and to avoid excessive heat loss leading to hypothermia, thermal insulation in the form of diving suits, or active heating is used. Gases used in diving have very different thermal conductivities; Heliox, and to a lesser extent, trimix, conducts heat faster than air because of the helium content, and argon conducts heat slower than air, so technical divers breathing gases containing helium may inflate their dry suits with argon. Some thermal conductivity values at 25 °C and sea level atmospheric pressure: argon: 16 mW/m/K; air: 26 mW/m/K; neoprene: 50 mW/m/K; wool felt: 70 mW/m/K; helium: 142 mW/m/K; water: 600 mW/m/K.
=== Underwater vision ===
Underwater vision is affected by the refractive index of water, which is similar to that of the cornea of the eye, and which is about 30% greater than air. Snell's law describes the angle of refraction relative to the angle of incidence. This similarity in refractive index is the reason a diver cannot see clearly underwater without a diving mask with an internal airspace. Absorption of light depends on wavelength, this causes loss of colour underwater. The red end of the spectrum of light is absorbed over a short distance, and is lost even in shallow water. Divers use artificial light underwater to reveal these absorbed colours. In deeper water no light from the surface penetrates, and artificial lighting is necessary to see at all. Underwater vision is also affected by turbidity, which causes scattering, and dissolved materials which absorb light.
=== Underwater acoustics ===
Underwater acoustics affect the ability of the diver to hear through the hood of the diving suit or the helmet, and the ability to judge the direction of a source of sound.
== Environmental physical phenomena of interest to divers ==
The physical phenomena found in large bodies of water that may have a practical influence on divers include:
Effects of weather such as wind, which causes waves, and changes of temperature and atmospheric pressure on and in the water. Even moderately high winds can prevent diving because of the increased risk of becoming lost at sea or injured. Low water temperatures make it necessary for divers to wear diving suits and can cause problems such as freezing of diving regulators.
Haloclines, or strong, vertical salinity gradients. For instance, where fresh water enters the sea, the fresh water floats over the denser saline water and may not mix immediately. Sometimes visual effects, such as shimmering and reflection, occur at the boundary between the layers, because the refractive indices differ.
Ocean currents can transport water over thousands of kilometres, and may bring water with different temperature and salinity into a region. Some ocean currents have a huge effect on local climate, for instance the warm water of the North Atlantic drift moderates the climate of the north west coast of Europe. The speed of water movement can affect dive planning and safety.
Thermoclines, or sudden changes in temperature. Where the air temperature is higher than the water temperature, shallow water may be warmed by the air and the sunlight but deeper water remains cold resulting in a lowering of temperature as the diver descends. This temperature change may be concentrated over a small vertical interval, when it is called a thermocline.
Where cold, fresh water enters a warmer sea the fresh water may float over the denser saline water, so the temperature rises as the diver descends.
In lakes exposed to geothermal activity, the temperature of the deeper water may be warmer than the surface water. This will usually lead to convection currents.
Water at near-freezing temperatures is less dense than slightly warmer water - maximum density of water is at about 4 °C - so when near freezing, water may be slightly warmer at depth than at the surface.
Tidal currents and changes in sea level caused by gravitational forces and the Earth's rotation. Some dive sites can only be dived safely at slack water when the tidal cycle reverses and the current slows. Strong currents can cause problems for divers. Buoyancy control can be difficult when a strong current meets a vertical surface. Divers consume more breathing gas when swimming against currents. Divers on the surface can be separated from their boat cover by currents. On the other hand, drift diving is only possible when there is a reasonable current.
== See also ==
Ambient pressure – Pressure of the surrounding medium
Atmospheric pressure – Static pressure exerted by the weight of the atmosphere
Buoyancy – Upward force that opposes the weight of an object immersed in fluid
Pressure – Force distributed over an area
== References == | Wikipedia/Diving_physics |
Helix Energy Solutions Inc., known as Cal Dive International prior to 2006, is an American oil and gas services company headquartered in Houston, Texas. The company is a global provider of offshore services in well intervention and ROV operations of new and existing oil and gas fields.
== History ==
=== 1980–1989 ===
In 1980, Oceaneering executives, Lad Handleman, John Swinden, Don Sites, and Rick Foreman left the company and named their new company Cal Dive International.
Oceaneering was formed in 1964 when Handelman merged his California oilfield diving company, Cal Dive, with Canadian-based Can-Dive, and upon his departure, Handleman reclaimed his original company name for the new venture. In 1983, Cal Dive Intl. was acquired by Diversified Energy International (DEI) whose financial backing allowed the company to expand with two converted diving vessels.
=== 1990–1999 ===
In 1990, new CEO Jerry Reuhl, led a management team that included future CEO, Owen Kratz, purchased Cal Dive Intl. from DEI for $11 million with Merrill Lynch acting as the financial partner, providing all of the holding a 45% equity position.
In 1992, after it established a business model of acquiring offshore oil and gas properties near the end of their production life in the Gulf of Mexico, Cal Dive Intl. created a subsidiary called Energy Resource Technology (ERT) to manage its growing portfolio of Gulf shelf properties.
In 1993, Cal Dive Intl. management bought out Merrill Lynch in 1993, and then sold 50% of the company to First Reserve Corporation in 1995, to raise more capital to support a growing deepwater program.
In 1994, Cal Dive Intl. acquired the Uncle John semi-submersible drilling rig and extended the company's well intervention capabilities.
In 1997, Kratz succeeded Reuhl as CEO. Kratz had previously served as the COO and Executive Vice President. Kratz was an accomplished oilfield diver who had previously owned his own marine construction company.
=== 2000–2010 ===
In March 2001, Cal Dive Intl. purchased Professional Divers of New Orleans for $11.5 million and in December acquired 85 percent of outstanding Canyon Offshore shares, and purchased the remaining 15 percent over the next three years. With the acquisition of Canyon Offshore, Cal Dive Intl. could now offer operators ROV, intervention, and cable/flowline burial services. In 2002, The world's first deepsea well intervention semi-submersible, the Q4000, is launched into service in the Gulf of Mexico.
In July of that same year, the company changed its corporate name to Helix Energy Solutions Group and moved its stock listing from NASDAQ to the New York Stock Exchange under the new ticker symbol, HLX. In 2009, the Newbuild well intervention vessel, Well Enhancer, was launched into service in the North Sea. In 2010, Helix ESG deployed multiple assets and resources to contain the 2010 Gulf of Mexico Oil Spill.
=== 2011 - 2023 ===
In 2012, Helix ESG announced plans r business unit, Helix Subsea Construction, and the sale of its vessels. Helix ESG also announced that going forward well intervention and ROV services would be its primary contracting businesses and new vessels would be purchased or chartered to meet growing demand in those service sectors. In 2015, Helix Energy Solutions Group saw its profit tumble 78 percent in the fourth quarter as upstreams curb drilling activity. In 2019, the Newbuild Q7000 well intervention semisubmersible vessel is delivered to Helix Energy Solutions In 2022, Helix acquired the Alliance group of companies, based in Louisiana, which added to the decommissioning of oil wells in the Gulf of Mexico.
== Management ==
Owen Kratz is the President and Chief Executive Officer of Helix Energy Solutions Group, Inc.
== See also ==
List of oilfield service companies
== References ==
=== Notes === | Wikipedia/Helix_Energy_Solutions_Group |
Fitness to dive (more specifically medical fitness to dive) refers to the medical and physical suitability of a diver to function safely in an underwater environment using diving equipment and related procedures. Depending on the circumstances, it may be established with a signed statement by the diver that they do not have any of the listed disqualifying conditions. The diver must be able to fulfill the ordinary physical requirements of diving as per the detailed medical examination by a physician registered as a medical examiner of divers following a procedural checklist. A legal document of fitness to dive issued by the medical examiner is also necessary.
The most important medical is the one before starting diving, as the diver can be screened to prevent exposure in the event of an imminent danger. The other important medicals are after some significant illness, where medical intervention is needed and has to be done by a doctor proficient in diving medicine, and can not be done by prescriptive rules.
Psychological factors can affect fitness to dive, particularly where they affect response to emergencies, or risk-taking behavior. The use of medical and recreational drugs can also influence fitness to dive, both for physiological and behavioral reasons. In some cases, prescription drug use might have a net positive effect when viably treating an underlying condition. However, the side effects of viable medication frequently have undesirable influences on the fitness of a diver. Most cases of recreational drug use result in an impaired fitness to dive, and a significantly increased risk of sub-optimal response to emergencies.
== General requirements ==
The medical, mental and physical fitness of professional divers is important for safety at work for the diver and the other members of the diving team.
As a general principle, fitness to dive is dependent on the absence of conditions which would constitute an unacceptable risk for the diver, and for professional divers, to any member of the diving team. General physical fitness requirements are also often specified by a certifying agency, and are usually related to ability to swim and perform the activities that are associated with the relevant type of diving.
The general hazards of diving are much the same for recreational divers and professional divers, but the risks vary with the diving procedures used. These risks are reduced by appropriate skills and equipment.
Medical fitness to dive generally implies that the diver has no known medical conditions that limit the ability to do the job, jeopardize the safety of the diver or the team, that might get worse as an effect of diving, or predispose the diver to diving or occupational illness.
There are three types of diver medical assessment: initial assessments, routine re-assessments and special re-assessments after injury or decompression illness.
=== Fitness of recreational divers ===
Standards for fitness to dive are specified by the diver certification agency that issues the certification following training. Some agencies place the responsibility for assessing fitness largely on the individual diver, while others require an examination by a registered medical practitioner based on specified criteria. These criteria are generally consistent across certification agencies and are adapted from standards for professional divers, though they may be somewhat relaxed for recreational diving.
The purpose of establishing fitness to dive is to reduce risk of a range of diving related medical conditions associated with known or suspected pre-existing conditions, and is not generally an indication of the person's psychological suitability for diving and has no reference to their diving skills.
A certification of fitness to dive is generally for a specified period, (usually a year or less), and may specify limitations or restrictions.
In most cases, a statement or certificate of fitness to dive for recreational divers is only required during training courses. Ordinary recreational diving is at the diver's own risk. The medical literature, anecdotal evidence and small-scale surveys suggest that a significant part of the recreational scuba diving population may have chronic medical conditions that affect their fitness to dive according to the Recreational Scuba Training Council's guidelines, are aware of these, and continue to dive. It has not been established whether the risk associated with these conditions is clinically significant or whether repeated screening is necessary or desirable, or whether the risks traditionally associated with some contraindicated conditions are realistic. It is also not clear whether these conditions were generally present at initial screening but not known or disclosed, or whether they developed afterwards, and if so, whether in some cases they are consequences of diving injury.
In rare cases, state or national legislation may require recreational divers to be examined by registered medical examiners of divers. In France, Norway, Portugal and Israel. recreational divers are required by regulation to be examined for medical fitness to dive.
==== Standard forms for recreational diving ====
Recreational diver certification agencies may provide a standard document which the diver is required to complete, specifying whether any of a range of conditions apply to the diver. If no disqualifying conditions are admitted, the diver is considered to be fit to dive.
The RSTC medical statement is used by all RSTC member affiliates: RSTC Canada, RSTC, RSTC-Europe and IAC (former Barakuda), FIAS, ANIS, SSI Europe, PADI Norway, PADI Sweden, PADI Asia Pacific, PADI Japan, PADI Canada, PADI Americas, PADI Worldwide, IDD Europe, YMCA, IDEA, PDIC, SSI International, BSAC Japan and NASDS Japan.
Other certification agencies may rely on the competence of a general practitioner to assess fitness to dive, either with or without an agency specified checklist.
In some cases the certification agency may require a medical examination by a registered medical examiner of divers.
In 2020-21, a revised World Recreational Scuba Training Council diver participation questionnaire and Diving Medical Guidance to the Physician form were published, following a three-year review by the Diving Medical Screen Committee.
=== Fitness of professional divers ===
The requirements for medical examination and certification of fitness of professional divers is typically regulated by national or state legislation for occupational health and safety
== Fitness testing procedures ==
=== Lung function tests ===
A frequently used test for lung function for divers is spirometry, which measures the amount (volume) and/or speed (flow) of air that can be inhaled and exhaled. Spirometry is an important tool used for generating pneumotachographs, which are helpful in assessing conditions such as asthma, pulmonary fibrosis, cystic fibrosis, and COPD, all of which are contraindications for diving. Sometimes only peak expiratory flow (PEF) is measured, which uses a much simpler apparatus, but is still useful to give an indication of lung overpressure risk.
=== Cardiac stress test ===
The cardiac stress test is done with heart stimulation, either by exercise on a treadmill, or pedaling a stationary exercise bicycle ergometer, with the patient connected to an electrocardiogram (or ECG).
The Harvard Step Test is a type of cardiac stress test for detecting and/or diagnosing cardiovascular disease. It also is a good measurement of fitness, and the ability to recover after a strenuous exercise, and is sometimes used as an alternative for the cardiac stress test.
== Medical examiner of divers ==
The most important medical examination is the one before starting diving, as the diver can be screened to prevent exposure when a dangerous condition exists. The other important medicals are after some significant illness, where medical intervention is needed there and has to be done by a doctor who is competent in diving medicine, and can not be done by prescriptive rules. For medical examinations prescribed in terms of occupational health legislation, the examiner may be required to be registered as a specialist in diving medicine, or be registered as competent to make medical examinations on divers, which implies an awareness of the physiological effects of diving and the mechanisms of diving diseases. Standards and levels of specialization and registration vary considerably between countries, and international recognition is limited. In most cases, medical examination for recreational divers is not compulsory, therefore international recognition of medical examiners is not relevant.
== Disqualifying conditions ==
The general principles for disqualification are that diving causes a deterioration in the medical condition and the medical condition presents an excessive risk for a diving injury to both the individual and the diving partner.
There are some conditions that are considered absolute contraindications for diving. Details vary between recreational and professional diving and in different parts of the world. Those listed below are widely recognized.
=== Permanently disqualifying conditions ===
Stroke and transient ischemic attacks.
Intercranial aneurysm, arterial-venous malformation or tumor.
Exertional angina, postmyocardial infarction with left ventricular dysfunction, congestive heart failure, or dependence on medication to control dysrhythmias.
Postcoronary bypass surgery with violation of pleural spaces.
A history of spontaneous pneumothorax.
=== Temporarily disqualifying conditions ===
Any illness requiring drug treatment may constitute a temporary disqualification if either the illness or the drug may compromise diving safety. Sedatives, tranquilizers, antidepressants, antihistamines, anti-diabetic drugs, steroids, anti-hypertensives, anti-epilepsy drugs, alcohol and hallucinatory
drugs such as marijuana and LSD may increase risk to the diver. Some drugs which affect brain function have unpredictable effects on a diver exposed to high pressure in deep diving.
== Conditions which may disqualify or require restrictions depending on severity and management ==
Some medical conditions may temporarily or permanently disqualify a person from diving depending on severity and the specific requirements of the registration body. These conditions may also require the diver to restrict the scope of activities or take specific additional precautions. They are also referred to as relative contraindications, and may be acute or chronic.
=== Asthma ===
In the past, asthma was generally considered a contraindication for diving due to theoretical concern about an increased risk for pulmonary barotrauma and decompression sickness. The conservative approach was to arbitrarily disqualify asthmatics from diving. This has not stopped asthmatics from diving, and experience in the field and data in the current literature do not support this dogmatic approach. Asthma has a similar prevalence in divers as in the general population.
The theoretical concern for asthmatic divers is that pulmonary obstruction, air trapping and hyperinflation may increase risk for pulmonary barotrauma, and the diver may be exposed to environmental factors that increase the risk of bronchospasm and the development of an acute asthmatic attack which could lead to panic and drowning. As of 2016, there is no epidemiological evidence for an increased relative risk of pulmonary barotrauma, decompression sickness or death among divers with asthma. This evidence only accounts for asthmatics with mild disease and the actual risk for severe or uncontrolled asthmatics, may be higher.
=== Cancers ===
Cancers are generally considered a class of abnormal, fast growing and disordered cells which have the potential to spread to other parts of the body. They may occur in virtually any organ or tissue. The effect of a cancer on fitness to dive can vary considerably, and will depend on several factors. If the cancer or the treatment compromise the diver's ability to perform the normal activities associated with diving, including the necessary physical fitness, and particularly cancers or treatments which compromise fitness to withstand the pressure changes, then the diver should abstain from diving until passed as fit by a diving medical practitioner who is aware of the condition. Specific considerations include whether the tumor or treatment affects organs which are directly affected by pressure changes, whether the person's capacity to manage themselves in an emergency is compromised, including mental awareness and judgement, and that diving should not aggravate the disease. Some cancers, such as lung cancer would be an absolute contraindication.
=== Diabetes ===
Like asthma, the traditional medical response to diabetes was to declare the person unfit to dive, but in a similar way, a significant number of divers with well-managed diabetes have logged sufficient dives to provide statistical evidence that it can be done at acceptable risk, and the recommendations of diving medical researchers and insurers has changed accordingly.
Current (2016) medical opinion of Divers Alert Network (DAN) and the Diving Diseases Research Centre (DDRC) is that diabetics should not dive if they have any of the following complications:
Significant retinopathy increases risk of retinal hemorrhage due to minor mask squeeze or equalizing procedures.
Peripheral vascular disease and/or neuropathy increase risk of sudden death due to coronary artery disease,
Significant autonomic or peripheral neuropathy increases the risk of exaggerated hypotension when leaving the water.
Nephropathy causing proteinuria
Coronary artery disease
Significant peripheral vascular disease may reduce inert gas washout and predispose the diver to limb decompression sickness.
DAN makes the following recommendations for additional precautions by diabetic divers:
Diabetic divers are advised not to dive deeper than 30 msw (100 fsw), to avoid situations where nitrogen narcosis could be confused with hypoglycemia, not to dive for longer than one hour, to limit the time blood glucose levels would remain unmonitored, or to incur compulsory decompression stops, or dive in overhead environments, both of which make direct and immediate access to the surface unavailable.
Diabetic diver's buddy or dive leader who is informed of their condition and knows the appropriate response in the event of a hypoglycemic episode. It is also recommended the buddy does not have diabetes.
Diabetic divers should avoid circumstances that increase risk of hypoglycemic episodes such as prolonged cold and strenuous dives.
=== Epilepsy ===
Epilepsy is a central nervous system disorder in which the person has had at least two seizures, often for no discernible cause. Even if no one with a history of epilepsy dived, a few people would experience their first seizure while diving. As a seizure may involve loss of consciousness, this puts the convulsing diver at significant risk, particularly on scuba with half mask and demand valve, which may become dislodged.
If epilepsy is required to be controlled by medication, diving is contraindicated. A possible acceptable risk would be a history of febrile seizures in infancy, apneic spells or seizures attendant to acute illness such as encephalitis and meningitis, all without recurrence without medication. By 2004 the UK Sport Diving Medical Committee ruled that a person with epilepsy must go 5 years without fits and off medication before being passed to dive. Very little reliable epidemiological evidence exists to suggest that a past history of seizures may correlate with increased risk to recreational scuba divers.
Published literature does not support an association between decompression illness and epilepsy, however, if a seizure occurs underwater it may plausibly lead to an uncontrolled ascent, which is associated with a high risk of decompression illness. A seizure underwater is similarly likely to cause dislodging of the demand valve with consequent high risk of drowning.
There is also no reliable evidence that epileptics are differently sensitive to raised partial pressures of oxygen. It is now known that the mechanism of the epileptic seizure is different to the oxygen toxicity seizure, and epileptics are not more susceptible to convulse under pressure.
No evidence suggests that a person with a history of seizures is likely to be more sensitive to nitrogen narcosis.
No plausible reasons to suggest that antiepileptic drugs would increase the risk of oxygen toxicity have been published. In theory it is possible that they may provide some level of protection.
Most objections to allowing people who have a long history of no seizures to dive are largely theoretical, and in many cases entirely unsupported by reliable evidence.
The British Diving Diseases Research Centre (DDRC) recommendation as of 2019 is that if a person previously had epilepsy but has been off medication without seizure for at least five years they may be fit to dive. If the seizures were exclusively nocturnal, this is reduced to three years. Medical advice from a diving doctor is recommended.
The European Diving Technology Committee guidelines for fitness to dive states that epilepsy is a contraindication to occupational diving, but that
where a diver has been free of seizures for ten years without treatment they may be assessed by an expert for fitness to dive.
=== Pregnancy ===
A study investigating potential links between diving while pregnant and fetal abnormalities by evaluating field data showed that most women are complying with the diving industry recommendation and refraining from diving while pregnant. There were insufficient data to establish significant correlation between diving and fetal abnormalities, and differences in placental circulation between humans and other animals limit the applicability of animal research for pregnancy and diving studies.
The literature indicates that diving during pregnancy does increase the risk to the fetus, but to an uncertain extent. As diving is an avoidable risk for most women, the prudent choice is to avoid diving while pregnant. However, if diving is done before pregnancy is recognized, there is generally no indication for concern.
In addition to possible risk to the fetus, changes in a woman's body during pregnancy might make diving more problematic. There may be problems fitting equipment and the associated hazards of ill fitting equipment. Swelling of the mucous membranes in the sinuses could make ear clearing difficult, and nausea may increase discomfort.
=== Diving after childbirth ===
Divers who want to return to diving after having a child should generally follow the guidelines suggested for other sports and activities, as diving requires a similar level of conditioning and fitness.
After a vaginal delivery, without complications, three weeks is usually sufficient to allow the cervix to close, which reduces the risk of uterine infection. Divers Alert Network recommends as a rule of thumb, to wait four weeks after normal delivery before resuming diving, and at least eight weeks after cesarean delivery. Any complications may indicate a longer wait, and medical clearance is advised.
=== Physical disabilities ===
Adaptive Diving, diving with physical disabilities:
Adaptive diving is a branch of scuba diving that caters to individuals with physical disabilities. It encompasses a range of strategies and modifications to ensure that people with diverse physical challenges can enjoy the freedom of diving. Here are some key aspects of adaptive diving:
Equipment Modifications:
Divers with physical disabilities may require specialized equipment adaptations. For amputees, prosthetic limbs can be fitted with diving attachments. Custom harnesses, buoyancy compensators, and fins are designed to accommodate various physical limitations.
For sight correction, prescription masks or seedeep reading glasses with strong lenses can be used, allowing correction of such limitation, and enabling the needed sight to read your dive gauge and dive watch.
Training and Certification:
Several scuba diving organizations offer adaptive diving courses and certifications. These courses teach divers and instructors how to adapt techniques and equipment to different disabilities, ensuring safe and enjoyable dives.
Buddy System:
The buddy system is crucial in scuba diving, and it's especially important for divers with physical disabilities. Divers work together with their dive buddies to assist each other as needed, ensuring a safe and enjoyable dive experience.
Dive Destinations and Facilities:
Many dive resorts and destinations around the world are equipped to accommodate divers with physical disabilities. They provide accessible entry points, adaptive equipment, and trained staff to assist disabled divers.
Supportive Organizations:
Numerous organizations and foundations are dedicated to promoting adaptive diving and providing resources for individuals with physical disabilities. These organizations often organize dive trips, training programs, and support networks for disabled divers.
=== Patent foramen ovale ===
A patent foramen ovale (PFO), or atrial shunt can potentially cause a paradoxical gas embolism by allowing venous blood containing what would normally be asymptomatic inert gas decompression bubbles to shunt from the right atrium to the left atrium during exertion, and can be then circulated to the vital organs where an embolism may form and grow due to local tissue supersaturation during decompression. This congenital condition is found in roughly 25% of adults, and is not listed as a disqualifier from diving nor as a required medical test for professional or recreational divers. Some training organisations recommend that divers contemplating technical diver training should have themselves tested as a precaution, and to allow informed consent to assume the associated risks.
== Factors which temporarily affect fitness to dive ==
Several factors may temporarily affect fitness to dive by altering the risk of encountering problems during a dive. Some of these depend on conditions that vary according to time or place, and are not addressed in a medical examination. Others are more within the control of the diver. These include:
Fatigue:
Dehydration:
Excessive hydration, particularly in combination with hypertension, is a known risk factor for immersion pulmonary oedema.
Motion sickness:
Menstrual cycle: There is evidence from surveys that there may be a correlation between the stage of the menstrual cycle and the occurrence of decompression illness. The same study indicates the possibility of correlation between the stage of the menstrual cycle with other problems during the dive.
Medications
Recreational drug use and substance abuse
== COVID-19 ==
The long term effects of Coronavirus disease 2019 are highly variable in severity, and the effects on fitness to dive will vary from case to case. Many of these effects influence the lungs and cardiovascular system, and therefore may significantly affect risk of diving injury, or the diver's ability to manage an emergency effectively. A review indicated that people who have recovered from COVID-19 had reduced levels of physical function and fitness compared to healthy controls. Recovery of physical functions tends to be incomplete, with some residual impairments present up to 2 years after infection. There is some evidence that combined aerobic and resistance training can improve physical function and fitness after medical recovery, but further research is required to determine the effectiveness of exercise in restoring fitness.
Diving medicine specialists at Divers Alert Network have advised that divers wishing to return to recreational diving after recovering from COVID-19 should wait until they have regained their previous physical fitness, then consult a qualified diving medical practitioner. This process is similar to the compulsory procedure for professional divers for return to diving after illness. The process takes into account the significant number of people who may have had asymptomatic infections, and treats them as if they did not have COVID.
=== Return to diving after COVID-19 ===
The principles behind the DAN protocol for returning to diving activity after COVID-19 are based on risk. The returning diver should not pose a risk of infecting others, and should not be at elevated risk of barotrauma or decompression illness due to damage to the lungs, or be at reduced capacity to manage problems due to cognitive dysfunction or insufficient physical fitness. Aerobic fitness recommendation for commercial divers is 10 Mets, and for recreational divers 6 Mets.
A grading system based on severity of illness is suggested as a guideline (July 2021), with the understanding that individual circumstances may differ, and that this model is subject to revision as and when further data becomes available.
Grade 0 is people who may or may not have had COVID-19, but if they were infected, did not notice significant symptoms, including those who are identified by screening or diagnostic tests as being infected, but remain asymptomatic. This is about 25% of the people infected. They do not need to undergo any special examination or testing, and can return to diving without restrictions as appropriate to their general health and fitness, provided they are not still infectious. If in doubt, they should remain in precautionary isolation for 14 days.
Grade 1 (mild), is people who had mild symptoms that did not require medical intervention, and recovered after self-isolation or quarantine. These people may return to diving 2 weeks after full recovery, conditional on passing a diving medical examination, a stress ECG, normal lung function tests and a normal lung X-ray.
Grade 2 (moderate), is people who has moderate symptoms which required admission to hospital or supplementary oxygen, but not ventilatory support. X-rays do not indicate more than mild abnormality, and no clotting disorders have manifested. These people may return to diving 3 months after recovery subject to passing a diving medical examination, a stress ECG, normal lung function tests and a normal lung X-ray.
Grade 3 (severe), is people who required admission to intensive care or ventilatory support, or displayed cardiac, neurological or clotting abnormalities, or other complications. These people may return to diving 6 months after recovery subject to passing a diving medical examination, a stress ECG, normal lung function tests, a normal lung X-ray, additional heart tests and a lung CT if indicated. If there are abnormalities, retesting at 12 months is suggested.
The DAN recommendation for diving after vaccination, is not to dive while one is not feeling well in the days after vaccination, to the same extent that one would not dive if not feeling well at any other time.
DAN is conducting research on the long term (5 year) effects of COVID-19 on fitness to dive for recreational scuba and freediving.
The Diving Medical Advisory Council and IMCA have also issued advisory documents on this topic for commercial divers.
== Psychological fitness to dive ==
Psychological fitness has been defined in a military context as "the integration and optimization of mental, emotional, and behavioral abilities and capacities to optimize performance and strengthen resilience". There are other definitions in a self-help/personal growth context, also referred to as emotional or mental fitness, but the military definition is appropriate in the context of the ability to survive and perform in a hostile environment. Psychological fitness to dive is to some extent a characteristic of the person who trains to become a diver, and in recreational diving there is little or no further training, but training for diving in harsher environments and for more demanding tasks often includes elements of training to improve psychological fitness, which allows the diver to better cope with the stresses of emergencies, and in some types of professional diving, the stresses of the job in hand.
Competence, physical health, and fitness are important factors in safe performance, but psychological factors also contribute to human failure or success and should be addressed in the interests of due diligence.
There is little screening for psychological fitness for recreational diving, and not much more for commercial and scientific diving. Technical diving exposes the diver to more unforgiving hazards and higher risks, but it is a recreational activity and to a large extent participation is at the option of the participant.
Psychological profiles indicating intelligence and below average neuroticism tend to correlate with successful diving activity over the long term. These divers tend to be self-sufficient and emotionally stable, and less likely to be involved in accidents unrelated to health problems. Nevertheless, many people with mild neuroses can and do dive with an acceptable safety record. Besides any risks caused by the condition itself, there may be hazards due to the effects of medications taken to manage the condition, either singly or in combination. There are no scientific studies into the safety of diving with most medications, and in most cases the effects of the medication are secondary to the effects of the underlying condition. Drugs with strong effects on moods should be used with care when diving.
A mild state of anxiety can improve performance by making the person more alert and quicker to react, but more severe levels can degrade performance, by narrowing focus and distracting attention, culminating in extreme and debilitating anxiety or panic, where rational response to a developing emergency is lost. A tendency to be generally anxious is known as trait anxiety, as opposed to anxiety brought on by a situation, which is termed state anxiety. Divers who are prone to trait anxiety are more likely to mismanage a developing emergency by panicking and missing the opportunity to recover from the initial incident. Training can help a diver to recognize rising stress levels, and allow them to take corrective action before the situation deteriorates into an injury or fatality. Over-learning appropriate responses to predictable and reasonably foreseeable contingencies allows the diver to react confidently and effectively, which reduces stress as the positive consequences of the appropriate actions are apparent, usually allowing the diver to terminate the dive in a controlled and safe manner.
Statistics from incidents where the circumstances are known implicate panic and inappropriate response in a large proportion of fatalities and near misses. In 1998 the Recreational Scuba Training Council listed "a history of panic disorder" as an absolute contraindication to scuba diving, but the 2001 guideline specifies "a history of untreated panic disorder" as a severe risk condition, which suggests that some people who are being treated for the condition might dive at an acceptable level of risk.
Two personality traits are consistently mentioned across contexts, These are a propensity for adventure or sensation-seeking, and lower trait anxiety than the general population. Both of these characteristics are associated with tolerance to physiological stress and safety implications. Trait anxiety is associated with a tendency to panic, which is implicated in a high proportion of diving incidents, and sensation seeking is associated with risk taking behavior. The current trend in research has moved from describing personality profiles to investigating associations between personality and diving performance.
Some psychological conditions that may affect a person's competence to dive include:
Affective disorders: Depression and manic depression (bipolar disorder). A condition that reduces a person's ability to make appropriate decisions while diving, particularly when things go wrong, can be a danger to themselves and anyone diving with them who may get involved in the consequences of a poor decision. Conditions that require medication also bring the effects of that medication into the situation, and this applies particularly when the medications alter the mood and affect competence to manage an emergency. A decision whether a person with these conditions can be considered fit to dive must take into account the specifics of the case, including the medications used, the response to the medication over time, and the frequency and severity of incidents.
Anxiety and phobias, panic disorder. Episodes of panic or near-panic have been implicated in many diving accidents, particularly in recreational diving, and have probably been the cause of diving fatalities. There is evidence that people who have a high level of underlying anxiety are likely to have greater responses to stresses, and these divers will therefore be exposed to greater risk. More than half of divers in a survey reported experiencing at least one panic or near-panic episode while diving. Panic attacks are commonly triggered by an event that a non-diver would consider serious, such as entanglement, an equipment malfunction or being confronted by an unexpected sea creature they may consider dangerous. Such panic attacks can lead to irrational behavior, which can be life-threatening.Panic attacks can be experienced by both inexperienced and experienced divers, for no apparent reason. In experienced divers, it is believed that panic occurs because the diver becomes disoriented and experiences sensory deprivation. Inexperienced divers are more likely to panic for a specific reason, such as a loss of breathing gas or an encounter with a shark perceived to be dangerous.Panic can occur when the person reacts quickly but irrationally, their attention narrows, and they lose the ability to recognise and select the appropriate available response options. Appropriate training, adequate practice of skills, and attention to the environment can prevent or minimise the occurrence of situations that may trigger panic, and reinforce the ability to respond appropriately to those triggering events which cannot be avoided.
Narcolepsy: Fitness to dive would depend to some extent on the medication used, response to the medication and possible side-effects. The condition may also affect the safety of other divers who may be affected by a diving accident. A full-face mask may be used to reduce risk of drowning in case of loss of consciousness during a dive.
Schizophrenia would be considered case by case. Type of medication and response, and how long the person has been free of the disorder would be taken into account, as some people have responded well to medication over the long term. The person's decision making ability, social responsibility and medication side-effects may affect the person's ability to dive safely.
Substance abuse
=== Recreational diving ===
Recreational diving can have a more beneficial effect on the state of mind of participants than many other physical leisure activities by way of stress reduction and improvement of well-being.
Recreational scuba diving may be considered an extreme sport since personal risk is involved, but it is also a leisure activity conducted for entertainment and relaxation. The diver is free to not dive or to terminate a dive at any time, and to make this physiologically practicable at acceptable risk, there are limitations on the depth, decompression status, and environment in which mainstream recreational diving can take place.
Limited research into the personality characteristics of people choosing to start recreational diving indicate tendencies of self-sufficiency, boldness and impulsiveness (and low scores on conformity, warmth and sensitivity), and are not typical of the personality profiles expected from extreme athletes. Four prevalent personality types were identified, and the results suggested that the risk behavior of the diver would probably depend on the personality type.
Personality types identified were:
The adventurer, a focused and enthusiastic person who appears easy to get along with, but has a tendency to be competitive and seek attention, and may take risks that endanger themselves and their diving partners.
The rationalist, an intelligent person with strong control of their emotional life and general behavior, who will conform when the situation requires it, and will generally persist until they have mastered the necessary skills, will comply with rational rules and procedures, and follow the instructions of people who appear to be competent. They are unlikely to take unnecessary risks.
The dreamer, a person who appears to be unconcerned with everyday matters, or absent minded, and take part in scuba diving as an escape from a bland existence to a more exotic world. Once they recognize the challenges of the activity they may become excessively dependent on the instructor or diving partner and may feel insecure and overwhelmed and frequently seek confirmation of their abilities, which may be annoying.
The passive-aggressive macho diver, a person who initially presents themselves as friendly and pleasant, but as they integrate with the group, start to display consistently critical attitudes towards anyone who may be conceived of as less expert than themselves, whether or not this is objectively realistic. This has been explained as a defense mechanism to disguise their underlying insecurity and an attempt to boost their low self-esteem.
Motivation to continue diving and to travel to dive: Kler and Tribe (2012) hypothesize and present evidence that a major motivation to pursue diving tourism at considerable expense is the participants gain meaning, fulfillment and long-term satisfaction (eudaimonia) through learning and personal growth from their participation.
For most recreational divers the activity is enjoyable and relaxing. The need to focus on the activities and skills and the tendency to become enthralled by the underwater environment enables divers to leave their worries above the surface.
==== Technical diving ====
Technical diving is the extension of recreational diving to higher risk activities. Technical divers operate in the range of activities that are generally beyond the expected competence of recreational diving, and often beyond the legally acceptable range of risk for professional diving. Military and public safety divers may occasionally be exposed to similar levels of risk in the course of their duties, but this will be for compelling operational reasons, whereas the technical diver chooses to accept these risks in the pursuit of a recreational activity. The risks are managed by the use of specialized equipment, avoidance of single points of failure by teamwork and equipment redundancy, the use of procedures known to be effective, maintenance of a high level of skill, sufficient physical fitness to perform effectively in the expected conditions and any reasonably foreseeable contingency, and appropriate reaction to contingencies. The diver makes an informed assessment of the residual risk and accepts the possible consequences. The way in which a diver reacts to the environment is influenced by attitude, awareness, physical fitness, self-discipline, and the ability to distinguish reality from perception.
In a situation where there is no simple and direct escape to safety, reaction to stress can determine the difference between an enjoyable dive and an accident that may lead to death or disability. If uncontrolled, stress may lead to panic. Overhead environments present challenges and choices where an error may be fatal. Time-pressure stress related to matching gas supply to dive duration can increase when the dive plan is compromised and gas supply runs low, or decompression obligation accumulates beyond the planned limit. When this kind of stress causes the diver to increase gas consumption due to overreacting, the problem gets worse and can spiral into an unrecoverable incident. The ability to react calmly, promptly, and correctly to life-threatening situations, and to persistently and rationally strive to deal effectively with the situation can make the difference between life and death.
=== Military diving ===
Studies of the personality traits of navy divers have indicated that although they operate in a military environment, navy divers tend to be non-conformists.
In a comparison between navy and civilian divers, navy divers scored higher than navy non-divers and civilian divers on calmness and self-control in difficult circumstances and were more emotionally controlled and adventurous, less assertive, more practical, more self-controlled and more likely to follow rules and procedures precisely and work together as a team. The navy divers were found to be willing to accept higher risk, and to have a strong sense of control and acceptance of taking personal responsibility for events.
=== Commercial diving ===
Serious injuries in commercial diving can be extremely costly to the employer, and the working environment can be inherently very hazardous. This is combined with a legislative environment which has a low risk tolerance, so commercial divers need to be selected for the ability to follow best practice procedures reliably and work well as members of a team, as well as the requisite work skills needed to work efficiently and profitably.
== Effects of drugs ==
The use of medical and recreational drugs, can also influence fitness to dive, both for physiological and behavioral reasons. In some cases prescription drug use may have a net positive effect, when effectively treating an underlying condition, but frequently the side effects of effective medication may have undesirable influences on the fitness of diver, and most cases of recreational drug use result in an impaired fitness to dive, and a significantly increased risk of sub-optimal response to emergencies.
=== Prescription and non-prescription medication ===
There are no specific studies that give objective values for the effects and risks of most medications if used while diving, and their interactions with the physiological effects of diving. Any advice given by a medical practitioner is based on educated (to a greater or lesser extent), but unproven assumption, and each case is best evaluated by an expert.
Personality differences between divers will cause each to respond differently to the effects of various breathing gases under pressure and abnormal physiological states. Some of the diving disorders can present symptoms similar to those of psychoneurotic reactions or an organic cerebral syndrome.
When considering allowing or barring someone with psychological problems to dive, the certifying physician must be aware of all the possibilities and variations in the specific case.
In many cases an acute illness is best treated in the absence of potential complications caused by diving, but chronic conditions may require medication if the person is to dive at all. Some of the medication types which are commonly or occasionally known to be used by active divers are listed here, along with possible side effects and complications:
Over the counter drugs are generally considered safe for consumer use when the directions for use are followed. They are generally not tested in hyperbaric conditions and may have undesirable side effects, particularly in combination with other drugs.
Motion sickness is a widespread and potentially debilitating reaction of the central nervous system to conflicting input from the vestibular balance organs of the inner ear and the eyes and other parts of the body. The main symptoms are nausea and confusion.
Antihistamines, which include cyclizine, dimenhydrinate, diphenhydramine, and meclizine are the most commonly used medications. They are generally available without a prescription, and have similar side effects, the most common of which is drowsiness, which can adversely affect a diver's situational awareness and reaction speed. There are also other side effects.
Promethazine is chemically related to the tranquilizers, and it also has antihistamine properties. It is generally a prescription drug and drowsiness is a significant side effect, and it may significantly impair ability to perform essential tasks under stressful conditions.
Trans-dermal scopolamine patch has been reported as effective by many divers, but there are undesirable side effects. Dry mouth effects have been reported, which may be more prevalent in divers breathing dry gas from scuba cylinders. Blurred vision is common, and contact contamination of the eye with the medication will cause pupil dilation. The medication is known to occasionally cause hallucinations, confusion, agitation and disorientation, which are not compatible with safe diving.
Phenytoin is an antiepileptic drug which has been shown to be effective against motion sickness, but it has not been approved for the purpose. It is not free of side effects.
Tablet form of scopolamine, by prescription
Malaria is a disease caused by a microorganism carried by mosquitoes. There are several strains and it is widespread in tropical regions. The disease is dangerous and prophylaxis is recommended.
No interactions between antimalarial drugs and diving have been established, and complications are not generally expected, but the use of Mefloquine is not accepted by all diving medicine specialists.
Antimalarial drug prophylaxis recommendations depend on specific regions and may change over time. Current recommendations should be checked.
All of these drugs may have side-effects, and there are known interactions with other drugs. Overdose can be fatal.
Mefloquine is seldom reported to have side-effects, but some people are allergic to it. Side effects include nausea, dizziness and disturbed sleep. Occasional serious side effects include seizures, hallucinations and severe anxiety.
Doxycycline has side effects of skin sensitization to sunburn, and sometimes upset stomach or yeast infections. It is unsuitable for young children and pregnant women as it can cause staining of developing teeth.
Malarone (a combination of atovaquone and proguanil) seldom has side effects, but headache, nausea, vomiting and abdominal pain have been reported. There are contraindications for renal impairment, and it is not recommended in pregnancy or for small children.
Chloroquine
Hydroxychloroquine sulfate
Pyrimethamine
Fansidar (sulfadoxine and pyrimethamine)
Decongestants: Pseudoephedrine has been named in anecdotal reports of possible connections with increased sensitivity to CNS oxygen toxicity. There is a plausible biological mechanism but very little reliable data. The steroid fluticasone propionate and similar medications have been satisfactorily used to treat nasal congestion, but should be used for at least a week before diving to be maximally effective.
Contraceptives
Anxiety, phobias & panic disorders
Diabetes
Asthma
Indigestion
Headaches
Cardiovascular and hypertension medication;
Beta blockers
ACE inhibitors (Angiotension-converting enzyme inhibitors)
Calcium channel blockers
Diuretics
Antiarrhythmic agents
Anticoagulants
Schizophrenia
Clozapine
Quetiapine
Risperidone
Olanzapine
Depression: Little research is available on diving or hyperbaric exposure with depression or while taking antidepressants. Reported side effects include anxiety and panic, thought to be caused by interaction with high partial pressure of nitrogen and side effects of the drugs. Restrictions on instructors or divemasters with duty of care to their clients may be more stringent than for recreational divers, though consideration should be given for the possible degradation of the buddy system. Some antidepressants are known to increase risk of seizure but no data is available on whether they increase sensitivity to CNS oxygen toxicity.
Selective serotonin reuptake inhibitors: SSRIs tend to be more expensive than other antidepressant medications, but are relatively safer for divers. However they do have typical side effects, such as drowsiness, which can affect dive safety. Other side effects may include increased susceptibility to bruising and bleeding, which can increase the apparent severity of injuries. Combined effects with other medications like anti-platelet drugs and non-steroidal anti-inflammatories, (such as aspirin or ibuprofen), can further exacerbate bleeding. In higher doses SSRIs may cause seizures, with the associated high risk of drowning if they occur underwater.
Monoamine oxidase inhibitors: MOAIs can cause dizziness from orthostatic hypotension and drowsiness. Side effects at increased partial pressure of nitrogen are unclear. In combination with some other medications they can cause increased blood pressure, and they should not be take with some types of aged or fermented foods which contain the amino acid tyramine which can cause a hypertensive crisis.
Tricyclics, tetracyclics, heterocyclics: TCAs and HCAs can have side effects of dizziness, drowsiness, and blurred vision, which are not compatible with safe diving if they impair concentration, alertness or decision-making.
bupropion, trazodone and venlafaxine may lower the seizure threshold. Venlafaxine may occasionally cause fainting, excitability and difficulty breathing. Bupropion may cause agitation, CNS stimulation, seizures, psychosis, dry mouth, headache, migraine, nausea, vomiting, rash, tinnitus, muscle pain and dizziness.
Anti-inflammatories and analgesics may be acceptable, subject to some known side effects, sensitivities, interactions and contraindications. These drugs are commonly taken for temporary relief of minor aches and pains, and the underlying condition may still be present. They may mask symptoms of mild decompression sickness, which may delay treatment. Naproxen sodium and ibuprofen may produce side effects such as heartburn, nausea, abdominal pain, headache, dizziness and drowsiness, and they are usually discouraged for people with disorders involving heartburn, gastric ulcers, bleeding problems or asthma. There may be adverse drug interactions with anticoagulants, insulin and nonsteroidal anti-inflammatories.
Aspirin
Diclofenac (Voltaren)
Ibuprofen
Ketoprofen
Naproxen
Paracetamol (Acetaminophen)
=== Recreational drugs and substance abuse ===
Smoking (tobacco)
Alcohol: Although alcohol consumption increases dehydration and therefore may increase susceptibility to DCS, a 2005 study found no evidence that alcohol consumption increases the incidence of DCS.
Alcohol may also increase risk by affecting reaction time, visual tracking, attention, ability to multitask, perception and judgement and performance of psychomotor tasks.
Cannabis may cause side effects that could increase risk when diving, including:
Dizziness is a fairly common side effect, which may reduce with continued use.
Headache, constipation, nervousness, fatigue, insomnia, limb or abdominal pain, and weight loss are less common side effects.
These impairments may not be apparent to the user, which makes the risk greater.
== See also ==
Rubicon Foundation – Non-profit organization for promoting research and information access for underwater diving
Undersea and Hyperbaric Medical Society – US based organisation for research and education in hyperbaric physiology and medicine.
Diving Medical Advisory Council – Independent organisation of diving medical specialists from Northern Europe
== References ==
== External links ==
Health & Medicine - Divers Alert Network
European diving technology committee
Recreational Diving Medical Screening System (2020)
Scuba diving restrictions | Wikipedia/Effects_of_drugs_on_fitness_to_dive |
Ocean Science is an open-access peer-reviewed scientific journal published by Copernicus Publications on behalf of the European Geosciences Union. It covers all aspects of oceanography. The journal is available on-line and in print. Papers are published under the Creative Commons Attribution 4.0 license.
The editor-in-chief is Karen J. Heywood. The founding editors were David Webb (National Oceanography Centre) and John Johnson (University of East Anglia).
== Peer-review process ==
The journal makes use of an open reviewing process
developed for Atmospheric Chemistry and Physics by its editor, Ulrich Pöschl, and colleagues.
Submissions considered suitable for review are first published as unreviewed grey literature in the sister discussion journal Ocean Science Discussions.
They are then subject to interactive public discussion, during which the referees' comments (anonymous or attributed), additional short comments by other members of the scientific community (attributed), and the authors' replies are also published. Authors then have a chance to revise their papers in response to the issues raised and the review process is completed in the normal manner.
After final acceptance, papers are published on-line as soon as authors have approved the typeset version. The printed version of the journal, which is published bimonthly, includes all papers published on-line since the last printed issue.
== Abstracting and indexing ==
The journal is abstracted and indexed in Science Citation Index Expanded, Scopus, Chemical Abstracts, and GeoRef. According to the Journal Citation Reports, the journal has a 2020 impact factor of 3.416.
== See also ==
List of scientific journals in earth and atmospheric sciences
== References ==
== External links ==
Official website | Wikipedia/Ocean_Science_(journal) |
A teaching method is a set of principles and methods used by teachers to enable student learning. These strategies are determined partly by the subject matter to be taught, partly by the relative expertise of the learners, and partly by constraints caused by the learning environment. For a particular teaching method to be appropriate and efficient it has to take into account the learner, the nature of the subject matter, and the type of learning it is supposed to bring about.
The approaches for teaching can be broadly classified into teacher-centered and student-centered, but in practice teachers will often adapt instruction by moving back and forth between these methodologies depending on learner prior knowledge, learner expertise, and the desired learning objectives. In a teacher-centered approach to learning, teachers are the main authority figure in this model. Students are viewed as "empty vessels" whose primary role is to passively receive information (via lectures and direct instruction) with the end goal of testing and assessment. It is the primary role of teachers to pass knowledge and information on to their students. In this model, teaching and assessment are viewed as two separate entities. Student learning is measured through objectively scored tests and assessments. In student-centered learning, while teachers are the authority figure in this model, teachers and students play an equally active role in the learning process. This approach is also called authoritative. The teacher's primary role is to coach and facilitate student learning and overall comprehension of material. Student learning is measured through both formal and informal forms of assessment, including group projects, student portfolios, and class participation. Teaching and assessments are connected; student learning is continuously measured during teacher instruction.
== Methods of teaching ==
=== Lecturing ===
The lecture method is just one of several teaching methods, though in schools it is usually considered the primary one. The lecture method is convenient for the institution and cost-efficient, especially with larger classroom sizes. This is why lecturing is the standard for most college courses when there can be several hundred students in the classroom at once; lecturing lets professors address the most people at once, in the most general manner, while still conveying the information that they feel is most important, according to the lesson plan. While the lecture method gives the instructor or teacher chances to expose students to unpublished or not readily available material, the students play a passive role which may hinder learning. While this method facilitates large-class communication, the lecturer must make a constant and conscious effort to become aware of student problems and engage the students to give verbal feedback. It can be used to arouse interest in a subject provided the instructor has effective writing and speaking skills.
=== Peer Instruction ===
Developed by Eric Mazur, peer instruction is a teaching method designed to improve the lecture. It includes both pre-class and in-class workflows. The in-class workflow intersperses teacher presentations with conceptual questions, called Concept Tests. These are designed to expose common student misconceptions in understanding the material, and lead to student discussion then reteaching if required.
=== Explaining ===
While under-researched, both student and teacher explanations remain one of the most utilized teaching methods in teacher practice. Explaining has many sub-categories including the use of analogies to build conceptual understanding. Some modes of explaining include the ‘thinking together’ style where teachers connect student ideas to scientific models. There are also more narrative styles using examples, and learner explanations which require students to give an explanation of the concept to be learned allowing the teacher to give precise feedback on the quality of the explanation.
=== Demonstrating ===
Demonstrating, which is also called the coaching style or the Lecture-cum-Demonstration method, is the process of teaching through examples or experiments. The framework mixes the instructional strategies of information imparting and showing how. For example, a science teacher may teach an idea by experimenting with students. A demonstration may be used to prove a fact through a combination of visual evidence and associated reasoning.
Demonstrations are similar to written storytelling and examples in that they allow students to personally relate to the presented information. Memorization of a list of facts is a detached and impersonal experience, whereas the same information, conveyed through demonstration, becomes personally relatable. Demonstrations help to raise student interest and reinforce memory retention because they provide connections between facts and real-world applications of those facts. Lectures, on the other hand, are often geared more towards factual presentation than connective learning.
One of the advantages of the demonstration method involves the capability to include different formats and instruction materials to make the learning process engaging. This leads to the activation of several of the learners' senses, creating more learning opportunities. The approach is also beneficial on the part of the teacher because it is adaptable to both group and individual teaching. While demonstration teaching, however, can be effective in teaching Math, Science, and Art, it can prove ineffective in a classroom setting that calls for the accommodation of the learners' individual needs.
=== Collaborating ===
Collaboration allows student to actively participate in the learning process by talking with each other and listening to others opinions. There exist some actions such as Dialogic Literary Gatherings and Interactive Groups which improve learnings by the collaboration and dialogic communication between the participants .Collaboration establishes a personal connection between students and the topic of study and it helps students think in a less personally biased way. Group projects and discussions are examples of this teaching method. Teachers may employ collaboration to assess student's abilities to work as a team, leadership skills, or presentation abilities.
Collaborative discussions can take a variety of forms, such as fishbowl discussions. It is important for teachers to provide students with instruction on how to collaborate effectively. This includes teaching them rules to conversation, such as listening, and how to use argumentation versus arguing. After some preparation and with clearly defined roles, a discussion may constitute most of a lesson, with the teacher only giving short feedback at the end or in the following lesson.
Some examples of collaborative learning tips and strategies for teachers are; to build trust, establish group interactions, keeps in mind the critics, include different types of learning, use real-world problems, consider assessment, create a pre-test, and post-test, use different strategies, help students use inquiry and use technology for easier learning.
==== Classroom discussion ====
The most common type of collaborative method of teaching in a class is classroom discussion. It is also a democratic way of handling a class, where each student is given equal opportunity to interact and put forth their views. A discussion taking place in a classroom can be either facilitated by a teacher or by a student. A discussion could also follow a presentation or a demonstration. Class discussions can enhance student understanding, add context to academic content, broaden student perspectives, highlight opposing viewpoints, reinforce knowledge, build confidence, and support community in learning. The opportunities for meaningful and engaging in-class discussion may vary widely, depending on the subject matter and format of the course. Motivations for holding planned classroom discussion, however, remain consistent. An effective classroom discussion can be achieved by probing more questions among the students, paraphrasing the information received, using questions to develop critical thinking with questions like "Can we take this one step further?;" "What solutions do you think might solve this problem?;" "How does this relate to what we have learned about..?;" "What are the differences between ... ?;" "How does this relate to your own experience?;" "What do you think causes .... ?;" "What are the implications of .... ?"
It is clear from "the impact of teaching strategies on learning strategies in first-year higher education cannot be overlooked nor over interpreted, due to the importance of students' personality and academic motivation which also partly explain why students learn the way they do" that Donche agrees with the previous points made in the above headings but he also believes that student's personalities contribute to their learning style. The way a student interprets and executes the instruction given by a teacher allows them to learn in a more effective and personal way. This interactive instruction is designed for the students to share their thoughts about a wide range of subjects.
Class discussions have also proven to be an effective method of bullying prevention and intervention when teachers discuss the issue of bullying and its negative consequences with the entire class. These discussions have shown to increase the number of students who would help other students when they are victimized.
==== Debriefing ====
The term "debriefing" refers to conversational sessions that revolve around the sharing and examining of information after a specific event has taken place. Depending on the situation, debriefing can serve a variety of purposes. It takes into consideration the experiences and facilitates reflection and feedback. Debriefing may involve feedback to the students or among the students, but this is not the intent. The intent is to allow the students to "thaw" and to judge their experience and progress toward change or transformation. The intent is to help them come to terms with their experience. This process involves a cognizance of cycle that students may have to be guided to completely debrief. Teachers should not be overly critical of relapses in behaviour. Once the experience is completely integrated, the students will exit this cycle and get on with the next.
Debriefing is a daily exercise in most professions. It might be in psychology, healthcare, politics, or business. This is also accepted as an everyday necessity.
==== Classroom Action Research ====
Classroom Action Research is a method of finding out what works best in your own classroom so that you can improve student learning. We know a great deal about good teaching in general (e.g. McKeachie, 1999; Chickering and Gamson, 1987; Weimer, 1996), but every teaching situation is unique in terms of content, level, student skills, and learning styles, teacher skills and teaching styles, and many other factors. To maximize student learning, a teacher must find out what works best in a particular situation. Each teaching and research method, model and family is essential to the practice of technology studies. Teachers have their strengths and weaknesses, and adopt particular models to complement strengths and contradict weaknesses. Here, the teacher is well aware of the type of knowledge to be constructed. At other times, teachers equip their students with a research method to challenge them to construct new meanings and knowledge. In schools, the research methods are simplified, allowing the students to access the methods at their own levels.
=== Questioning ===
Questioning is one of the oldest documented teaching methods, and can be used by teachers in a variety of ways for a variety of purposes including, checking for understanding, clarifying terms, exposing misconceptions, and gathering evidence of learning to inform subsequent instructional decisions.
==== Socratic questioning ====
Named after Socrates, socratic questioning is described by his pupil Plato as a form of questioning where the teacher probes underlying misconceptions to lead students towards deeper understanding.
==== Cold calling ====
Cold calling is a teaching methodology based around the teacher asking questions to students without letting the students know beforehand who will be called upon to answer by the teacher. Cold calling aims to increase inclusion in the classroom and active learning as well as student engagement and participation. Cold calling in education is distinct from cold-calling in sales which is a form of business solicitation. Cold calling as a teaching methodology has been linked to increased student participation, increased student voluntary participation, increased student engagement, increased student in class gender equity and no decrease in student comfort levels in class. There is some evidence that the effectiveness of cold calling as teaching method is connected to the use of covert retrieval practice.
=== Feedback ===
Feedback is targeted information given to students about their current performance relative to their desired learning goals. It should aim to (and be capable of producing) improvement in students’ learning, as well as being bidirectional by giving teachers feedback on student performance which in turn helps teachers plan the next steps in learning. Feedback in its various forms can be a potent teaching method with potentially large impacts on student achievement. It can also have some negative side effects under certain conditions.
== Effectiveness of teaching methods ==
Small effects or lack of statistically significant effects have been found when evaluating many teaching methods rigorously with randomized controlled trials. Many teaching methods targeting cognitive skills show quickly disappearing impacts.
== Evolution of teaching methods ==
=== Ancient education ===
About 3000 BC, with the advent of writing, education became more conscious or self-reflecting, with specialized occupations such as scribe and astronomer requiring particular skills and knowledge. Philosophy in ancient Greece led to questions of educational method entering national discourse.
In his literary work The Republic, Plato described a system of instruction that he felt would lead to an ideal state. In his dialogues, Plato described the Socratic method, a form of inquiry and debate intended to stimulate critical thinking and illuminate ideas.
Many commentators on the Christian New Testament make reference to the teaching methodology of Jesus Christ, who "used a variety of teaching techniques to impress his teaching on his hearers". It has been the intent of many educators since Plato, such as the Roman educator Quintilian, who lived shortly after Jesus, to find specific, interesting ways to encourage students to use their intelligence and to help them to learn.
=== Medieval education ===
Comenius, in Bohemia, wanted all children to learn. In his The World in Pictures, he created an illustrated textbook of things children would be familiar with in everyday life and used it to teach children. Rabelais described how the student Gargantua learned about the world, and what is in it.
Much later, Jean-Jacques Rousseau in his Emile, presented methodology to teach children the elements of science and other subjects. During Napoleonic warfare, the teaching methodology of Johann Heinrich Pestalozzi of Switzerland enabled refugee children, of a class believed to be unteachable, to learn. He described this in his account of an educational experiment at Stanz.
=== 19th century ===
The Prussian education system was a system of mandatory education dating to the early 19th century. Parts of the Prussian education system have served as models for the education systems in a number of other countries, including Japan and the United States. The Prussian model required classroom management skills to be incorporated into the teaching process.
The University of Oxford and the University of Cambridge in England developed their distinctive method of teaching, the tutorial system, in the 19th century. This involves very small groups, from one to three students, meeting on a regular basis with tutors (originally college fellows, and now also doctoral students and post-docs) to discuss and debate pre-prepared work (either essays or problems). This is the central teaching method of these universities in both arts and science subjects, and has been compared to the Socratic method.
=== Experimental pedagogy ===
Experimental pedagogy is a pedagogical trend that appeared at the end of the 19th and the beginning of the 20th century, whose task was to introduce, in addition to observation, the experimental method into the study of teaching. This field of study employs scientific methods to investigate teaching and learning, aiming to improve educational practices by testing different approaches and measuring their effectiveness.
The main credit for the constitution of experimental pedagogy as a special direction and the development of its theoretical foundations belongs to two German pedagogues, Ernst Meumann and Wilhelm August Lay, who are also considered the founders of experimental pedagogy. There are also Alfred Binet and Théodore Simon in France, Joseph Mayer Rice, Edward Thorndike and G. Stanley Hall in America, Édouard Claparède and Robert Dottrens in Switzerland, Alexander Petrovich Nechaev in Russia, etc.
Key characteristics of experimental pedagogy include being evidence-based, rigorous in study design, and oriented towards improvement. The field investigates the effectiveness of various teaching methods, the impact of instructional materials, and factors influencing student learning.
Experimental pedagogy has the potential to significantly impact education by offering evidence-based support for effective practices. Examples of its application include studies on the use of technology in the classroom, the influence of different teaching methods on student motivation, and the examination of factors affecting student achievement.
Examples of experimental pedagogy in educational action include:
A study on the effectiveness of using technology in the classroom, comparing the learning outcomes of students using tablets with those who do not.
A study on the impact of different teaching methods on student motivation, comparing motivation levels in classes using different approaches.
A study on the factors influencing student achievement, examining factors such as student background, family income, and resource access.
=== 20th century ===
Newer teaching methods may incorporate television, radio, internet, multi media, and other modern devices. Some educators believe that the use of technology, while facilitating learning to some degree, is not a substitute for educational methods that encourage critical thinking and a desire to learn. Inquiry learning is another modern teaching method. A popular teaching method that is being used by many teachers is hands on activities. Hands-on activities are activities that require movement, talking, and listening.
== See also ==
== References ==
== Further reading ==
Highet G (1989). The Art of Teaching. Vintage Books. ISBN 978-0-679-72314-1.
Monroe P (1915). A Text-Book in the History of Education. Macmillan. OL 1540509W.
== External links ==
"Experimental pedagogy and experimental psychology". psycnet.apa.org. APA PsycNet. Retrieved 2024-02-07.
Jahrling R (1923). "Experimental Pedagogy, the Science of Education". The Pedagogical Seminary. 30 (1): 40–44. doi:10.1080/08919402.1923.10532906. ISSN 0891-9402.
Deines AG (2019), "Experimental Pedagogy: The Connection Between Teaching and Social Impact", Teaching and Designing in Detroit, Routledge, doi:10.4324/9780429290596-10, ISBN 978-0-429-29059-6, retrieved 2024-02-07 | Wikipedia/Teaching_method |
Canadian Armed Forces (CAF) divers are specialists trained to perform underwater operations within their respective environmental commands. CAF divers are qualified in several sub-categories, including: Clearance Divers (CL Diver), Search and Rescue Technicians (SAR Tech), Port Inspection Divers (PID), Ship's Team Divers, and Combat Divers.
== Training ==
The CAF training agencies authorized to conduct CAF diving programs are:
Fleet Diving Unit (Atlantic) (FDU (A))
Fleet Diving Unit (Pacific) (FDU (P))
Army Dive Centre (ADC)
== Clearance Divers ==
Royal Canadian Navy Clearance Divers are trained to perform a variety of diving operations. These operations include the use of traditional open-circuit diving equipment (SCUBA), lightweight portable surface-supplied diving systems, commercial-grade mixed-gas surface-supplied systems and mixed-gas rebreather systems such as the CCDA and CUMA sets.
Clearance Divers are also equipped to operate fixed and portable hyperbaric chambers, enabling them to conduct complex underwater tasks, including diving medicine and decompression operations.
Canada currently has two operational diving units; RCN Clearance Diving Officers and Clearance Divers and Port Inspection Divers. Both units perform a variety of core capabilities.
These core capabilities are:
Battle Damage Repair (BDR)
Maritime Explosive Ordnance Disposal (MEOD)
Mine Countermeasures (MCM)
Force Protection Support (FPS)
They also perform secondary or support functions to these core capabilities that include:
Improvised Explosive Device Disposal (IEDD) for devices found in military establishments within defined areas of responsibility in Canada;
Submarine Search and Rescue (SUBSAR) first line response (RCC and light-weight Surface Supplied Diving equipment)
Second line response (ROVs and/or diving);
Provision of a minimum six-person 45 metre CABA diving team on each coast for emergencies.
Diving Support Roles (which amplifies Para 13 b.) consist of:
Underwater ship and infrastructure maintenance
Light salvage
Seabed search
Underwater demolitions
Inspection, maintenance and repair of critical diver life support equipment.
Operation of Working Class Remote Operated Vehicle (ROV), Inspection Class ROV, ROV Simulator, Diver Evaluation Systems, and side scan sonar (SSS)
Support for medical treatment in hyperbolic chamber
The two operational naval diving units are:
Fleet Diving Unit Pacific based at CFB Esquimalt, British Columbia.
Fleet Diving Unit Atlantic based near Halifax in CFB Shearwater, Nova Scotia.
The Royal Canadian Clearance Diver motto is "Strength in depth".
Clearance Diving Officers and Divers also serve at:
the Experimental Diving Unit (EDU) at Defence Research and Development Canada
the EOD School in CFB Gagetown, New Brunswick.
Director of Diving Safety (D Dive S), at the National Defence Headquarters (NDHQ) in Ottawa, Ontario.
Royal Canadian Navy Clearance Divers' Prayer
On 30 April 2015 the RCN Clearance Diving occupation adopted the following prayer as their official occupation prayer. The prayer was originally written by Padre David Jackson, the unit chaplain of Fleet Diving Unit Atlantic, for the occasion of the 60th Anniversary of the RCN Clearance Diving occupation. The prayer is based on Psalm 146:6. & 139:9-10. and also incorporates the occupation motto "Strength in Depth".
English: Lord God Almighty, who made heaven and earth, the sea, and all that is in them; we ask You to look with favour upon us, the members of the Royal Canadian Navy Clearance Diving Branch, that as we dwell in the uttermost parts of the sea, even there Your hand may lead us, and your right hand may hold us. Be our strength in depth and preserve us from all the perils of the sea and the assaults of the enemy; that we may serve Queen, Country and Branch with loyalty, courage and honour. Amen.
French: Dieu Tout-Puissant, Toi qui a créé le ciel et la terre, la mer avec tout ce qu'elle contient; Nous te demandons de tourner ton regard vers nous les membres de la Branche des Plongeurs Démineurs de la Marine Royale Canadienne surtout lorsque nous sommes dans les profondeurs de la mer. Là aussi ta main puisse nous conduire, Et ta droite nous saisir. Sois notre force dans les profondeurs et préserve-nous de tous les dangers de la mer et de nos ennemis; pour que nous puissions servir la Reine, notre pays et la Branche avec loyauté, courage et honneur. Amen
== Combat divers ==
=== History ===
Diving in the Canadian Army began in the 1960s when, as a result of the introduction of amphibious vehicles, it was essential to provide a diving capability to the safety organization for the swimming of the vehicles. Amphibious operations also required better underwater reconnaissance of crossing sites. Following trials in 1966, diving sections were established in engineer units in 1969. Once diving was established, additional tasks were added to make combat diving an extension of combat engineering, such as obstacle construction and breaching, employing and detecting landmines, and limited underwater construction.
=== General Description ===
Combat divers equip the Army with the ability to execute combat engineer tasks underwater. As combat engineers first and foremost, their diving responsibilities are considered secondary to their primary role. When a specific task is identified and assigned, they are organised into mission-specific teams to provide targeted support for operations.
=== Niche area ===
Combat divers primarily operate on inland waterways, working both on the surface and underwater using breathing apparatus. Their tasks usually take place near shorelines and riverbanks, supporting the Army during land operations. Occasionally, they may operate in saltwater environments to provide support for Army missions. In certain scenarios, combat divers may be tasked with conducting reconnaissance near enemy forces. These reconnaissance missions are carried out with the backing of maneuver forces, which can provide observation support and suppressive fire to aid the dive team.
Canada's Combat Divers are an Occupation Sub-Specialisation (OSS) in its Army Combat Engineer Regiments.
== See also ==
Professional Diving
== References ==
== External links ==
Canadian Forces Diving
DAOD 8009-1, Canadian Forces Diving - Organization and Operating Principles
Canadian Naval Divers Association
Physical Fitness Standards for CF Diving Personnel
Fleet Diving Unit (Pacific) | Wikipedia/Canadian_Armed_Forces_Divers |
Hierarchy of hazard control is a system used in industry to prioritize possible interventions to minimize or eliminate exposure to hazards. It is a widely accepted system promoted by numerous safety organizations. This concept is taught to managers in industry, to be promoted as standard practice in the workplace. It has also been used to inform public policy, in fields such as road safety. Various illustrations are used to depict this system, most commonly a triangle.
The hazard controls in the hierarchy are, in order of decreasing priority:
Elimination
Substitution
Engineering controls
Administrative controls
Personal protective equipment
The system is not based on evidence of effectiveness; rather, it relies on whether the elimination of hazards is possible. Eliminating hazards allows workers to be free from the need to recognize and protect themselves against these dangers. Substitution is given lower priority than elimination because substitutes may also present hazards. Engineering controls depend on a well-functioning system and human behaviour, while administrative controls and personal protective equipment are inherently reliant on human actions, making them less reliable.
== History ==
During the 1990s TB outbreak, resulting from the HIV epidemic in the United States, the hierarchy of controls was described as a way for healthcare workers to mitigate their exposure to TB. The hierarchy can be summarized, from most to least preferable, as the following list states:
"Substitution": Avoids the hazard, which is not possible in a healthcare setting.
"Contain [the hazards] at their source": Using administrative controls, screen for a given health hazard (in this case, TB).
This can include source control, which can involve masking an infected patient.
"Engineering controls": This usually involves configuring isolation rooms and HVAC systems to prevent the spread of infection.
"Establish barriers": Personal protective equipment, with respirators.
Today's hierarchy has several differences, however keeping the original idea.
== Components of the hierarchy ==
=== Elimination ===
Physical removal of the hazard is the most effective hazard control. For example, if employees must work high above the ground, the hazard can be eliminated by moving the piece they are working on to ground level to eliminate the need to work at heights. However, often elimination of the hazard is not possible because the task explicitly involves handling a hazardous agent. For example, construction professionals cannot remove the danger of asbestos when handling the hazardous agent is the core of the task.
The most effective control measure is eliminating the hazard and its associated risks entirely. The simplest way to do this is by not introducing the hazard in the first place. For instance, the risk of falling from a height can be eliminated by performing the task at ground level. Eliminating hazards is often more cost-effective and feasible during the design or planning phase of a product, process, or workplace. At this stage, there’s greater flexibility to design out hazards or incorporate risk controls that align with the intended function. Employers can also eliminate hazards by completely removing them—such as clearing trip hazards or disposing of hazardous chemicals, thus eliminating the risks they pose. If eliminating a hazard compromises the ability to produce the product or deliver the service, it's crucial to eliminate as many risks associated with the hazard as possible.
=== Substitution ===
Substitution, the second most effective hazard control, involves replacing something that produces a hazard with something that does not produce a hazard or produces a lesser hazard. However, to be an effective control, the new product must not produce unintended consequences. For example, if a product can be purchased with a larger particle size, the smaller product may effectively be substituted with the larger product due to airborne dust having the possibility of being hazardous.
Eliminating hazards and substituting safer alternatives can be challenging to implement within existing processes. These strategies are most effective when applied during the design or development phases of a workplace, tool, or procedure. At this stage, they often represent the most straightforward and cost-effective solutions. Additionally, they present a valuable opportunity when selecting new equipment or methods. The Prevention through Design approach emphasizes integrating safety considerations into the design of work tools, operations, and environments to enhance overall safety and efficiency.
=== Engineering controls ===
The third most effective means of controlling hazards is engineered controls. These do not eliminate hazards, but rather isolate people from hazards. Capital costs of engineered controls tend to be higher than less effective controls in the hierarchy, however they may reduce future costs. A main part of engineering controls, "enclosure and isolation," creates a physical barrier between personnel and hazards, such as using remotely controlled equipment. As an example, fume hoods can remove airborne contaminants as a means of engineered control.
Effective engineering controls are integral to the original equipment design and work to eliminate or block hazards at the source before they reach workers. They are designed to prevent users from modifying or tampering with the controls and require minimal action from users to function effectively. These controls operate seamlessly without disrupting the workflow or complicating tasks. While they may have higher initial costs compared to administrative controls or personal protective equipment (PPE), they often result in lower long-term operating expenses, especially when safeguarding multiple workers and potentially saving costs in other operational areas.
=== Administrative controls ===
Administrative controls are changes to the way people work. Examples of administrative controls include procedure changes, employee training, and installation of signs and warning labels, such as those in the Workplace Hazardous Materials Information System. Administrative controls do not remove hazards, but limit or prevent people's exposure to the hazards, such as completing road construction at night when fewer people are driving.
Administrative controls are ranked lower than elimination, substitution, and engineering controls because they do not directly remove or reduce workplace hazards. Instead, they manage workers' exposure by setting rules like limiting work times in contaminated areas. However, these measures have limitations since they don't address the hazard itself. Where possible, administrative controls should be combined with other control measures.
Examples of administrative controls include:
Implementing job rotation or work-rest schedules to limit individual exposure.
Establishing a preventive maintenance program to ensure equipment is functioning properly.
Scheduling high-exposure tasks during off-peak times when fewer workers are present.
Restricting access to hazardous areas.
Assigning tasks only to qualified personnel.
Posting warning signs to alert workers of potential hazards.
=== Personal protective equipment ===
Personal protective equipment (PPE) includes gloves, Nomex clothing, overalls, Tyvek suits, respirators, hard hats, safety glasses, high-visibility clothing, and safety footwear. PPE is often the most important means of controlling hazards in fields such as health care and asbestos removal. However, considerable efforts are needed to use PPE effectively, such as training in donning and doffing or testing the equipment. Additionally, some PPE, such as respirators, increase physiological effort to complete a task and, therefore, may require medical examinations to ensure workers can use the PPE without risking their health.
Employers should not depend solely on personal protective equipment (PPE) to manage hazards when more effective controls are available. While PPE can be beneficial, its effectiveness relies on correct and consistent use, and it may incur significant costs over time, especially when used daily for multiple workers. Employers must provide PPE when other control measures are still being developed or cannot adequately reduce hazardous exposure to safe levels. Personal Protective Equipment (PPE) minimizes risks to health and safety when worn correctly, including items like earplugs, goggles, respirators, and gloves. However, PPE and administrative controls don't eliminate hazards at their source, relying instead on human behavior and supervision. As a result, they are among the least effective methods for risk reduction when used alone.
== Role in prevention through design ==
The hierarchy of controls is a core component of Prevention through Design, the concept of applying methods to minimize occupational hazards early in the design process. Prevention through Design emphasizes addressing hazards at the top of the hierarchy of controls (mainly through elimination and substitution) at the earliest stages of project development.
NIOSH’s Prevention through Design Initiative comprises “all of the efforts to anticipate and design out hazards to workers in facilities, work methods and operations, processes, equipment, tools, products, new technologies, and the organization of work.”
== Variations on the NIOSH control hierarchy ==
While the control hierarchy shown above is traditionally used in the United States and Canada, other countries or entities may use a slightly different structure. In particular, some add isolation above engineering controls instead of combining the two. The variation of the hierarchy used in the ARECC decision-making framework and process for industrial hygiene (IH) includes modification of the material or procedure to reduce hazards or exposures (sometimes considered a subset of the hazard substitution option but explicitly considered there to mean that the efficacy of the modification for the situation at hand must be confirmed by the user). The ARECC version of the hierarchy also includes warnings as a distinct element to clarify the nature of the warning. In other systems, warnings are sometimes considered part of engineering controls and sometimes part of administrative controls.
=== Use of hierarchical controls ===
The hierarchy of controls serves as a valuable tool for safety professionals to determine the most effective methods for managing specific hazards. By following this hierarchy, employers can ensure they are implementing the best measures to protect their employees from potential risks.
When encountering a hazard in the workplace, the hierarchy of hazard control provides a systematic approach to identify the most appropriate actions for controlling or eliminating that hazard. Additionally, it aids in developing a comprehensive hazard control plan for implementing the chosen measures effectively in the workplace.
It is important to be aware of the following when using the hierarchy of controls:
Use interim controls: If more time is needed to implement long-term solutions, the hierarchy of controls should be used from the top down as interim controls in the meantime.
Avoid introducing new hazards: Keep in mind is that the selected controls should never directly or indirectly introduce new hazards. Make sure to perform a thorough safety analysis before implementing the selected controls.
Use a combination of controls: If there is no single method that will fully protect workers, then a combination of controls should be used.
== See also ==
ARECC - Decision-making framework and process used in the field of industrial hygiene (IH) to anticipate and recognize hazards, evaluate exposures, and control and confirm protection from risks
Prevention through design – Reduction of occupational hazards by early planning in the design process
Occupational exposure banding – Process to assign chemicals into categories corresponding to permissible exposure concentrations
Control banding – Approach to promoting OHS
Job safety analysis – Procedure to integrate safety practices into a particular task
Normalization of deviance – one reason people stop using effective prevention measures
Safety engineering – Engineering discipline which assures that engineered systems provide acceptable levels of safety
== Notes ==
== References ==
This article incorporates public domain material from websites or documents of the National Institute for Occupational Safety and Health.
== External links ==
Canadian Centre for Occupational Health & Safety document
Hierarchy of prevention and control measures on OSH Wiki (EU) | Wikipedia/Hierarchy_of_hazard_controls |
A diving team is a group of people who work together to conduct a diving operation. A characteristic of professional diving is the specification for minimum personnel for the diving support team. This typically specifies the minimum number of support team members and their appointed responsibilities in the team based on the circumstances and mode of diving, and the minimum qualifications for specified members of the diving support team. The minimum team requirements may be specified by regulation or code of practice. Some specific appointments within a professional dive team have defined competences and registration may be required.
There is considerable difference in the diving procedures of professional divers, where a diving team with formally appointed members in specific roles and with recognised competence is required by law, and recreational diving, where in most jurisdictions the diver is not constrained by specific laws, and in many cases is not required to provide any evidence of competence. In recreational diving there may be no team at all for a solo diver, a dive buddy is the default arrangement, a three diver team is fairly common for technical diving, and a major technical dive or expedition may have a fairly complex team including surface support personnel made up to suit the requirements of the dive plan. Recreational diving instructors often use an assistant to increase the number of learners they can safely manage in the water, and dive guides may use an assistant to help keep the group together and assist the customers in an emergency.
The members of a diving team are part of a larger class of diving support personnel, which includes diving instructors, equipment maintenance technicians, operators of equipment and vessels used in support of a diving operation, and specialised medical staff.
== Professional diving ==
Professional divers operate as a team. The minimum composition of the team is usually specified by some combination of national, federal or state regulations, standing orders, codes of practice, and operations manual.
=== Core diving team ===
These are the personnel that are generally required to be present at a professional dive site during the diving operation.
==== Working diver ====
Also referred to as 'the diver', this is the person who does the underwater work planned for the dive. There may be more than one working diver, and the working diver and bellman may alternate during a dive. Diving skills required depend on the mode of diving and equipment used, and work skills required depend on the job to be done. A working diver is by default necessary for a diving operation. Without the diver there is no diving operation.
==== Diving supervisor ====
The diving supervisor is the professional diving team member who is directly responsible for the diving operation's safety and the management of any incidents or accidents that may occur during the operation; the supervisor is required to be available at the control point of the diving operation for the diving operation's duration, and to manage the planned dive and any contingencies that may occur.
Details of competence, requirements, qualifications, registration and formal appointment differ depending on jurisdiction and relevant codes of practice. Diving supervisors are used in commercial diving, military diving, public safety diving and scientific diving operations. A diving supervisor is required for every diving operation. The supervisor must remain in the control area and be in control at all times during the diving operation. This generally implies being able to communicate with the divers and other team members.
==== Standby diver ====
The diver who is at all times during the dive ready to go to the assistance of the working diver and perform a rescue to recover the diver to the surface if necessary. Diving competence requirements are identical to those of the working diver, but underwater work skills are not relevant while acting as standby diver. In surface oriented diving the standby diver may wait at the diving operation control point, and in saturation diving the bellman is the standby diver, though an additional surface standby diver may be required to assist with technical problems at shallow depths. A standby diver is required for every diving operation, though in some circumstances two working divers may act as standby to each other when working in close proximity, in an arrangement similar to the buddy system.
==== Diver's tender ====
The diver's tender, or dive attendant, is a person who may or may not be a qualified diver who assists the diver or standby diver to dress in and out, assists them entering and exiting the water, boarding the stage or wet bell, and manages the diver's umbilical at the surface where applicable. The bellman acts as the working diver's umbilical attendant from a wet or closed bell.
In some circumstances, when untethered scuba is used, there may not be a requirement for a tender, and appropriate assistance may be provided by one of the other team members. In other cases, where the working diver is required to enter a confined space underwater, an additional underwater tender may be needed to handle the diver's umbilical at the entrance or other place where the risk of snagging is high. In some cases the stand-by diver may do this job. In these cases the underwater tender must be a suitably equipped and qualified diver, and will generally also need a surface tender in addition to the working diver's surface tender.
==== Diving medical practitioner ====
A registered diving medical practitioner (DMP) competent to manage diving injuries may be required to be available on standby off-site during diving operations. The DMP should have certified skills and basic practical experience in assessment of medical fitness to dive, management of diving accidents, safety planning for professional diving operations, advanced life support, acute trauma care and general wound care. Depending on jurisdiction, a DMP may be required on telephonic standby for all commercial diving operations. For mixed gas and saturation diving the DMP should be competent to manage treatment for injuries associated with that class of diving.
=== Additional members depending on circumstances ===
The use of more complex equipment or diving modes may necessitate the inclusion of additional members in the diving team. Some of these are required to be registered operators, others are only required to be competent at their allocated tasks.
==== Compressor operator ====
For surface-supplied air diving using a low pressure compressor a competent person is needed to set up, start run and check the compressor and air delivery to the distribution panel. There may also be a high-pressure compressor for filling scuba cylinders and high pressure reserve air cylinders for divers or decompression chambers, and this too should be operated by a competent person.
==== Bellman ====
If an open or closed bell which provides gas to the diver from a bell panel is to be used to convey the divers to the worksite, a bellman is required. The bellman is a diver who acts as standby diver and diver's attendant from the bell during the dive, and may alternate as working diver during the dive if appropriately competent for the diving task. The bellman normally stays in the bell during the dive and operates the bell gas panel, but may be required to leave the bell to go to the assistance of the working diver, recover a disabled diver to the bell and provide first aid in the bell. Diving competence requirements are identical to those of the working diver, but underwater work skills are not relevant while acting as the bellman. Diver competence for bell operations includes competence at all skills required of the bellman.
==== Launch and recovery system operator ====
A competent person responsible for operating the bell or stage lifting winch and launch and recovery system (LARS) is needed when such equipment is used. This is not a diving post.
==== Chamber operator ====
A chamber operator is needed if there is a decompression chamber on site. The chamber operator is a person competent to operate a hyperbaric chamber with a compressed air atmosphere under the direction of a diving supervisor. This is not a diving post, but the chamber operator may also be a diver, and many surface supplied air divers are also qualified as chamber operators. The chamber operator is competent to prepare the chamber for an operation, blow it down to depth, communicate with the occupants and the supervisor, operate the main and medical locks, provide decompression gases on the built-in breathing system, monitor and maintain the chamber atmosphere composition and pressure within the prescribed limits, manage contingencies, decompress to follow a specified surface decompression or recompression treatment schedule, and perform basic maintenance procedures, including cleaning and inspecting the components for correct function.
==== Gas man ====
A gas man, also called gas panel operator, or rack operator, is required when gas mixtures other than air are to be provided to the diver. This person controls the gas supply to the diver and may also handle communications as a direct assistant to the supervisor. The gas man may also be a diver, but the specific activity is not a diving post.
==== Diving medical technician ====
A diving medical technician is necessary where the diving operation is remote from hospital facilities, such as in offshore work. A diver medic or diving medical technician (DMT) is a member of a dive team who is trained in advanced first aid. A Diver Medic recognised by IMCA must be capable of administering first aid and emergency treatment, and carrying out the directions of a doctor pending the arrival of more skilled medical aid, and therefore must be able to effectively communicate with a doctor who is not on site, and be familiar with diving procedures and compression chamber operation. The Diver Medic must also be able to assist the diving supervisor with decompression procedures, provide advice as to when more specialised medical help should be requested, and must be fit to provide treatment in a hyperbaric chamber in an emergency, and must therefore hold a valid certificate of medical fitness to dive. The diver medic may also be a diver, but this is not a diving appointment. Training standards for Diver Medic are described in the IMCA Scheme for Recognition of Diver Medic Training.
==== Systems technician ====
A person competent to maintain, repair and test the function of the diving and support systems and components for which they are appointed as systems technician. A systems technician would typically be required for a team operating a saturation system, or a surface supplied diving operation with a significant amount of support equipment, or relatively complex support equipment, or where a large number of dives are planned, and on-site maintenance and repair work is likely to be needed. This is not a diving appointment, though the technician may also be a diver.
==== Diving superintendent ====
The diving superintendent is the management position covering diving operations. The superintendent is usually a qualified supervisor, but depending on the organisation, may not be required to supervise dives. The superintendent may oversee saturation and surface oriented diving operations on air or mixed gases, develop and implement dive plans and diving related company procedures and manage diving related activities to minimise health, safety and environmental risks and impacts. This is not a diving appointment and the superintendent may not be directly involved in the actual diving operations.
==== Life-support technician ====
A life support technician is a person registered as competent to operate the life-support systems of a mixed gas saturation diving system. Divers living in saturation conditions must be continuously monitored and the pressure, oxygen and carbon dioxide content of their breathing gas, and temperature and humidity of the environment must be monitored and controlled. Functions such as feeding and sewage disposal and locking stores and equipment into and out of the chambers are also controlled from outside by life support personnel. Responsibilities include communication with the divers in saturation, supervising transfer of personnel into and out of the accommodation chambers, maintaining the hyperbaric rescue craft and hyperbaric evacuation of the divers in an emergency. This is a non-diving post.
==== Life-support supervisor ====
The life support supervisor is a senior life support technician appointed by the diving contractor to supervise operation of the saturation life support systems. This is a non-diving post.
=== ROV team ===
Whenever a remotely operated underwater vehicle is operated at a dive site when a diving operation is taking place, competent personnel are required to run the ROV, and as the safety of the divers is affected, the ROV team is under the authority of the diving supervisor. The ROV can be both a hazard because of its mass, power and moving parts, and a benefit to diver safety, as it can monitor the divers on closed circuit video, and give some kinds of assistance in contingencies. There are a range of tasks where a ROV is more suitable than a diver, and others which a diver can do better. The ROV team are not necessarily divers, though it is possible. ROV operation requires a different set of skills and knowledge to diving.
==== ROV pilot ====
A person trained and competent to operate a remotely controlled underwater vehicle. In diving operations the pilot must be competent to safely operate the ROV with divers in the water. ROV pilots are usually also trained in routine maintenance and minor repair of the ROV.
==== ROV supervisor ====
A senior ROV pilot appointed to supervise the ROV team. The ROV supervisor is under the authority of the diving supervisor when divers are in the water, but may work autonomously when there is no diving taking place.
== Legal status ==
When the minimum personnel in a diving team is regulated in terms of national or state legislation, the legal status and responsibilities of the members is generally defined in the legislation. These responsibilities often relate to occupational safety and health and specify a duty of care for the team members.
== Recreational and technical diving ==
In mainstream recreational diving, team diving is the exception. Support functions are carried out by operators such as dive boat charter operators, dive shops and dive schools, for their customers, on a commercial basis. Duty of care may be specifically limited by terms of use and waivers. Groups of divers may also associate in clubs and informal groups to finance or otherwise provide mutual services such as boats and filling facilities, and may dive together in informal groups. Club members may provide training and dive leadership to other club members, often on a not-for-profit cost sharing basis.
Technical divers may form teams where this is appropriate to support each other for complex or hazardous dives. This can include surface co-coordinators, equipment handlers, gas blenders, support and standby divers, and any other function that may seem useful to them. The team members are not usually contractually bound and have no duty of care beyond what they may have voluntarily assumed and that of ordinary citizens. The divers remain responsible for their own assumption of risk and are not under the direction of anyone other than themselves and the dive plan by group consensus. Technical divers may also refer to team diving where a group of three divers assume the roles of dive buddies to each other.
Primary dive team or diver is the diver or group of divers who will take part in the main dive. For example, the diver or divers who intend to explore new territory in a cave, penetrate a wreck, or attempt a depth record.
Support divers may place and recover drop cylinders, meet returning divers at per-arranged depths, provide support to decompressing divers by relaying communications with the surface team, or assisting divers in the water.
Stand-by divers are support divers at the surface ready to go to the assistance of team members in the water when requested
Surface co-ordinators are team members who keep track of team activities and assist in scheduling and recording the dive and support activities.
=== Team redundancy ===
In complex dive operations such as deep cave penetrations, technical divers will often use team redundancy to limit the amount of equipment carried. The concept is that equipment that is important to safety, but has a very low risk of failure does not have to be backed up by every member. Dive computers are team redundant when two divers each have one if they both dive the same profile on the same gases, one spare mask is considered sufficient, as they very seldom break or get lost, fin straps, cutting tools and the like may be also be considered sufficiently backed up if one spare is carried by the team. Backup gas may also be shared, as may a backup scooter. Sometimes the team members will each carry backup. Backup lights and gas are commonly carried by each member, but are available to be shared if necessary. As a general rule, once team redundancy has been exhausted and no spares are left, the dive is turned, so sometimes more spares are carried so that a single item failure does not prevent the operation from being completed. Much of the DIR philosophy is based on facilitating team redundancy. To be effective, the redundant team equipment must be available to any member of the team in time to safely mitigate the loss of function of the original item.
== Freediving ==
=== Buddy teams ===
The buddy system is recommended by freediver training agencies and schools for risk management by freedivers as they are at risk of hypoxic blackout for various reasons, and a competent buddy following recommended procedures may be able to intervene successfully.
The buddy system is a procedure in which two individuals, the "buddies", operate together as a team so that they are able to monitor and help each other.
Appropriate training is recommended as the most effective way to develop the necessary competence, which includes both knowledge and practical experience, and understanding of personal limitations. Certification is provided as evidence that a diver has been trained and was assessed as competent within the scope of the certification. It is also necessary to be sufficiently fit for the planned dives at the time. Training in first aid with CPR is also recommended.
=== Competition safety ===
Following the deaths of two freedivers in competitions, AIDA has a system set up for monitoring and if necessary, recovering competitors who lose consciousness underwater.
As of 2022 the incidence of adverse events in depth competitions varies between 3 and 4%, This rate is considered relatively low and is expected during competitions where divers push their breath-hold limits. Almost all of these divers are successfully assisted and recover completely. There is a much lower incidence of more serious injuries due to the established safety system at the competitions.
==== Safety divers ====
The safety team is usually made up of volunteers, but in major events may be paid staff. The work can be challenging as many dives are done in a day. The safety diver will descend in time to meet the competitor during their ascent, and monitor them for the rest of the ascent. They will intervene if necessary, typically by securing the airway and swimming them up to the surface. There is usually a rotating team of safety divers to ensure that they are not overtasked. Each competitor is monitored by a team of several breath hold safety divers. The first will meet the diver at somewhere around 1/3 to 1/4 of the target depth, usually with a maximum of 30m The second will meet them about 10m shallower, and a third will be on standby in case of an emergency.
In case of a deeper incident, the competitor is clipped to the downline, which can be rapidly raised by the surface support team, which includes a medical support group.
== References == | Wikipedia/Diving_systems_technician |
Atrial septal defect (ASD) is a congenital heart defect in which blood flows between the atria (upper chambers) of the heart. Some flow is a normal condition both pre-birth and immediately post-birth via the foramen ovale; however, when this does not naturally close after birth it is referred to as a patent (open) foramen ovale (PFO). It is common in patients with a congenital atrial septal aneurysm (ASA).
After PFO closure the atria normally are separated by a dividing wall, the interatrial septum. If this septum is defective or absent, then oxygen-rich blood can flow directly from the left side of the heart to mix with the oxygen-poor blood in the right side of the heart; or the opposite, depending on whether the left or right atrium has the higher blood pressure. In the absence of other heart defects, the left atrium has the higher pressure. This can lead to lower-than-normal oxygen levels in the arterial blood that supplies the brain, organs, and tissues. However, an ASD may not produce noticeable signs or symptoms, especially if the defect is small. Also, in terms of health risks, people who have had a cryptogenic stroke are more likely to have a PFO than the general population.
A cardiac shunt is the presence of a net flow of blood through a defect, either from left to right or right to left. The amount of shunting present, if any, determines the hemodynamic significance of the ASD. A right-to-left-shunt results in venous blood entering the left side of the heart and into the arterial circulation without passing through the pulmonary circulation to be oxygenated. This may result in the clinical finding of cyanosis, the presence of bluish-colored skin, especially of the lips and under the nails.
During development of the baby, the interatrial septum develops to separate the left and right atria. However, a hole in the septum called the foramen ovale allows blood from the right atrium to enter the left atrium during fetal development. This opening allows blood to bypass the nonfunctional fetal lungs while the fetus obtains its oxygen from the placenta. A layer of tissue called the septum primum acts as a valve over the foramen ovale during fetal development. After birth, the pressure in the right side of the heart drops as the lungs open and begin working, causing the foramen ovale to close entirely. In about 25% of adults, the foramen ovale does not entirely seal. In these cases, any elevation of the pressure in the pulmonary circulatory system (due to pulmonary hypertension, temporarily while coughing, etc.) can cause the foramen ovale to remain open.
== Types ==
The six types of atrial septal defects are differentiated from each other by whether they involve other structures of the heart and how they are formed during the developmental process during early fetal development.
=== Ostium secundum ===
The ostium secundum atrial septal defect is the most common type of atrial septal defect and comprises 6–10% of all congenital heart diseases. It involves a patent ostium secundum (that is, a patent foramen secundum).
The secundum atrial septal defect usually arises from an enlarged foramen ovale, inadequate growth of the septum secundum, or excessive absorption of the septum primum. About 10 to 20% of individuals with ostium secundum ASDs also have mitral valve prolapse.
An ostium secundum ASD accompanied by an acquired mitral valve stenosis is called Lutembacher's syndrome.
==== Natural history ====
Most individuals with an uncorrected secundum ASD do not have significant symptoms through early adulthood. More than 70% develop symptoms by about 40 years of age. Symptoms are typically decreased exercise tolerance, easy fatigability, palpitations, and syncope.
Complications of an uncorrected secundum ASD include pulmonary hypertension, right-sided congestive heart failure.
While pulmonary hypertension is unusual before 20 years of age, it is seen in 50% of individuals above the age of 40. Progression to Eisenmenger's syndrome occurs in 5 to 10% of individuals late in the disease process.
=== Patent foramen ovale ===
A patent foramen ovale (PFO) is a remnant opening of the fetal foramen ovale, which often closes after a person's birth. This remnant opening is caused by the incomplete fusion of the septum primum and the septum secundum; in healthy hearts, this fusion forms the fossa ovalis, a portion of the interatrial septum which corresponds to the location of the foramen ovale in the fetus. In medical use, the term "patent" means open or unobstructed. In about 25% of people, the foramen ovale does not close, leaving them with a PFO or at least with what some physicians classify as a "pro-PFO", which is a PFO that is normally closed, but can open under increased right atrial pressure. On echocardiography, shunting of blood may not be noted except when the patient coughs.
PFO is linked to stroke, sleep apnea, migraine with aura, cluster headache, decompression sickness, Raynaud's phenomenon, hyperventilation syndrome, transient global amnesia (TGA), and leftsided carcinoid heart disease (mitral valve). No cause is established for a foramen ovale to remain open instead of closing, but heredity and genetics may play a role. In rats research showed a link to the amount of Cryptosporidium infestation and the number of newborn rats that failed to close their foramen ovale. PFO is not treated in the absence of other symptoms.
The mechanism by which a PFO may play a role in stroke is called paradoxical embolism. In the case of PFO, a blood clot from the venous circulatory system is able to pass from the right atrium directly into the left atrium via the PFO, rather than being filtered by the lungs, and thereupon into systemic circulation toward the brain. Also multiple substances – including the prothrombotic agent serotonin – are shunted bypassing the lungs. PFO is common in patients with an atrial septal aneurysm (ASA), a much rarer condition, which is also linked to cryptogenic (i.e., of unknown cause) stroke.
PFO is more common in people with cryptogenic stroke than in those with a stroke of known cause. While PFO is present in 25% in the general population, the probability of someone having a PFO increases to about 40 to 50% in those who have had a cryptogenic stroke, and more so in those who have a stroke before the age of 55. Treatment with anticoagulant and antiplatelet medications in this group appear similar.
=== Ostium primum ===
A defect in the ostium primum is occasionally classified as an atrial septal defect, but it is more commonly classified as an atrioventricular septal defect. Ostium primum defects are less common than ostium secundum defects. This type of defect is usually associated with Down syndrome.
=== Sinus venosus ===
A sinus venosus ASD is a type of atrial septum defect in which the defect involves the venous inflow of either the superior vena cava or the inferior vena cava.
A sinus venosus ASD that involves the superior vena cava makes up 2 to 3% of all interatrial communication. It is located at the junction of the superior vena cava and the right atrium. It is frequently associated with anomalous drainage of the right-sided pulmonary veins into the right atrium (instead of the normal drainage of the pulmonary veins into the left atrium).
=== Common or single atrium ===
Common (or single) atrium is a failure of development of the embryologic components that contribute to the atrial septal complex. It is frequently associated with heterotaxy syndrome.
=== Mixed ===
The interatrial septum can be divided into five septal zones. If the defect involves two or more of the septal zones, then the defect is termed a mixed atrial septal defect.
== Presentation ==
=== Complications ===
Due to the communication between the atria that occurs in ASDs, disease entities or complications from the condition are possible. Patients with an uncorrected atrial septal defect may be at increased risk for developing a cardiac arrhythmia, as well as more frequent respiratory infections.
==== Decompression sickness ====
ASDs, and particularly PFOs, are a predisposing venous blood carrying inert gases, such as helium or nitrogen does not pass through the lungs.
The only way to release the excess inert gases from the body is to pass the blood carrying the inert gases through the lungs to be exhaled. If some of the inert gas-laden blood passes through the PFO, it avoids the lungs and the inert gas is more likely to form large bubbles in the arterial blood stream causing decompression sickness.
==== Eisenmenger's syndrome ====
If a net flow of blood exists from the left atrium to the right atrium, called a left-to-right shunt, then an increase in the blood flow through the lungs happens. Initially, this increased blood flow is asymptomatic, but if it persists, the pulmonary blood vessels may stiffen, causing pulmonary hypertension, which increases the pressures in the right side of the heart, leading to the reversal of the shunt into a right-to-left shunt. Reversal of the shunt occurs, and the blood flowing in the opposite direction through the ASD is called Eisenmenger's syndrome, a rare and late complication of an ASD.
==== Paradoxical embolus ====
Venous thrombus (clots in the veins) are quite common. Embolizations (dislodgement of thrombi) normally go to the lung and cause pulmonary emboli. In an individual with ASD, these emboli can potentially enter the arterial system, which can cause any phenomenon attributed to acute loss of blood to a portion of the body, including cerebrovascular accident (stroke), infarction of the spleen or intestines, or even a distal extremity (i.e., finger or toe).
This is known as a paradoxical embolus because the clot material paradoxically enters the arterial system instead of going to the lungs.
==== Migraine ====
Some recent research has suggested that a proportion of cases of migraine may be caused by PFO. While the exact mechanism remains unclear, closure of a PFO can reduce symptoms in certain cases. This remains controversial; 20% of the general population has a PFO, which for the most part, is asymptomatic. About 20% of the female population has migraines, and the placebo effect in migraine typically averages around 40%. The high frequency of these facts make finding statistically significant relationships between PFO and migraine difficult (i.e., the relationship may just be chance or coincidence). In a large randomized controlled trial, the higher prevalence of PFO in migraine patients was confirmed, but migraine headache cessation was not more prevalent in the group of migraine patients who underwent closure of their PFOs.
== Causes ==
Down syndrome – patients with Down syndrome have higher rates of ASDs, especially a particular type that involves the ventricular wall. As many as one half of Down syndrome patients have some type of septal defect.
Ebstein's anomaly – about 50% of individuals with Ebstein anomaly have an associated shunt between the right and left atria, either an atrial septal defect or a patent foramen ovale.
Fetal alcohol syndrome – about one in four patients with fetal alcohol syndrome has either an ASD or a ventricular septal defect.
Holt–Oram syndrome – both the osteium secundum and osteum primum types of ASD are associated with Holt–Oram syndrome
Lutembacher's syndrome – the presence of a congenital ASD along with acquired mitral stenosis
== Mechanisms ==
In unaffected individuals, the chambers of the left side of the heart are under higher pressure than the chambers of the right side because the left ventricle has to produce enough pressure to pump blood throughout the entire body, while the right ventricle needs only to produce enough pressure to pump blood to the lungs.
In the case of a large ASD (> 9 mm), which may result in a clinically remarkable left-to-right shunt, blood shunts from the left atrium to the right atrium. This extra blood from the left atrium may cause a volume overload of both the right atrium and the right ventricle. If untreated, this condition can result in enlargement of the right side of the heart and ultimately heart failure.
Any process that increases the pressure in the left ventricle can cause worsening of the left-to-right shunt. This includes hypertension, which increases the pressure that the left ventricle has to generate to open the aortic valve during ventricular systole, and coronary artery disease which increases the stiffness of the left ventricle, thereby increasing the filling pressure of the left ventricle during ventricular diastole. The left-to-right shunt increases the filling pressure of the right heart (preload) and forces the right ventricle to pump out more blood than the left ventricle. This constant overloading of the right side of the heart causes an overload of the entire pulmonary vasculature. Eventually, pulmonary hypertension may develop.
The pulmonary hypertension will cause the right ventricle to face increased afterload. The right ventricle is forced to generate higher pressures to try to overcome the pulmonary hypertension. This may lead to right ventricular failure (dilatation and decreased systolic function of the right ventricle).
If the ASD is left uncorrected, the pulmonary hypertension progresses and the pressure in the right side of the heart becomes greater than the left side of the heart. This reversal of the pressure gradient across the ASD causes the shunt to reverse – a right-to-left shunt. This phenomenon is known as Eisenmenger's syndrome. Once right-to-left shunting occurs, a portion of the oxygen-poor blood gets shunted to the left side of the heart and ejected to the peripheral vascular system. This causes signs of cyanosis.
== Diagnosis ==
Most individuals with a significant ASD are diagnosed in utero or in early childhood with the use of ultrasonography or auscultation of the heart sounds during physical examination. Some individuals with an ASD have surgical correction of their ASD during childhood. The development of signs and symptoms due to an ASD are related to the size of the intracardiac shunt. Individuals with a larger shunt tend to present with symptoms at a younger age.
Adults with an uncorrected ASD present with symptoms of dyspnea on exertion (shortness of breath with minimal exercise), congestive heart failure, or cerebrovascular accident (stroke). They may be noted on routine testing to have an abnormal chest X-ray or an abnormal ECG and may have atrial fibrillation. If the ASD causes a left-to-right shunt, the pulmonary vasculature in both lungs may appear dilated on chest X-ray, due to the increase in pulmonary blood flow.
=== Physical examination ===
The physical findings in an adult with an ASD include those related directly to the intracardiac shunt and those that are secondary to the right heart failure that may be present in these individuals.
In unaffected individuals, respiratory variations occur in the splitting of the second heart sound (S2). During respiratory inspiration, the negative intrathoracic pressure causes increased blood return into the right side of the heart. The increased blood volume in the right ventricle causes the pulmonic valve to stay open longer during ventricular systole. This causes a normal delay in the P2 component of S2. During expiration, the positive intrathoracic pressure causes decreased blood return to the right side of the heart. The reduced volume in the right ventricle allows the pulmonic valve to close earlier at the end of ventricular systole, causing P2 to occur earlier.
In individuals with an ASD, a fixed splitting of S2 occurs because the extra blood return during inspiration gets equalized between the left and right atria due to the communication that exists between the atria in individuals with ASD.
The right ventricle can be thought of as continuously overloaded because of the left-to-right shunt, producing a widely split S2. Because the atria are linked via the atrial septal defect, inspiration produces no net pressure change between them, and has no effect on the splitting of S2. Thus, S2 is split to the same degree during inspiration as expiration, and is said to be "fixed".
=== Echocardiography ===
In transthoracic echocardiography, an atrial septal defect may be seen on color flow imaging as a jet of blood from the left atrium to the right atrium.
If agitated saline is injected into a peripheral vein during echocardiography, small air bubbles can be seen on echocardiographic imaging. Bubbles traveling across an ASD may be seen either at rest or during a cough. (Bubbles only flow from right atrium to left atrium if the right atrial pressure is greater than left atrial). Because better visualization of the atria is achieved with transesophageal echocardiography, this test may be performed in individuals with a suspected ASD which is not visualized on transthoracic imaging.
Newer techniques to visualize these defects involve intracardiac imaging with special catheters typically placed in the venous system and advanced to the level of the heart. This type of imaging is becoming more common and involves only mild sedation for the patient typically.
If the individual has adequate echocardiographic windows, use of the echocardiogram to measure the cardiac output of the left ventricle and the right ventricle independently is possible. In this way, the shunt fraction can be estimated using echocardiography.
=== Transcranial doppler bubble study ===
A less invasive method for detecting a PFO or other ASDs than transesophagal ultrasound is transcranial Doppler with bubble contrast. This method reveals the cerebral impact of the ASD or PFO.
=== Electrocardiogram ===
The ECG findings in atrial septal defect vary with the type of defect the individual has. Individuals with atrial septal defects may have a prolonged PR interval (a first-degree heart block). The prolongation of the PR interval is probably due to the enlargement of the atria common in ASDs and the increased distance due to the defect itself. Both of these can cause an increased distance of internodal conduction from the SA node to the AV node.
In addition to the PR prolongation, individuals with a primum ASD have a left axis deviation of the QRS complex, while those with a secundum ASD have a right axis deviation of the QRS complex. Individuals with a sinus venosus ASD exhibit a left axis deviation of the P wave (not the QRS complex).
A common finding in the ECG is the presence of incomplete right bundle branch block, which is so characteristic that if it is absent, the diagnosis of ASD should be reconsidered.
== Treatment ==
=== Patent foramen ovale ===
Most patients with a PFO are asymptomatic and do not require any specific treatment. However, those who develop a stroke require further workup to identify the etiology. In those where a comprehensive evaluation is performed and an obvious etiology is not identified, they are defined as having a cryptogenic stroke. The mechanism for stroke is such individuals is likely embolic due to paradoxical emboli, a left atrial appendage clot, a clot on the inter-atrial septum, or within the PFO tunnel.
==== PFO closure ====
Until recently, patients with PFO and cryptogenic stroke were treated with antiplatelet therapy only. Previous studies did not identify a clear benefit of PFO closure over antiplatelet therapy in reducing recurrent ischemic stroke. However, based on new evidence and systematic review in the field, percutaneous PFO closure in addition to antiplatelet therapy is suggested for all who meet all the following criteria:
Age ≤ 60 years at onset of first stroke,
Embolic-appearing cryptogenic ischemic stroke (i.e., no evident source of stroke despite a comprehensive evaluation), and
PFO with a right-to-left interatrial shunt detected by bubble study (echocardiogram)
A variety of PFO closure devices may be implanted via catheter-based procedures.
==== Medical therapy ====
Based on the most up to date evidence, PFO closure is more effective at reducing recurrent ischemic stroke when compared to medical therapy. In most of these studies, antiplatelet and anticoagulation were combined in the medical therapy arm. Although there is limited data on the effectiveness of anticoagulation in reducing stroke in this population, it is hypothesized that based on the embolic mechanism, that anticoagulation should be superior to antiplatelet therapy at reducing risk of recurrent stroke. A recent review of the literature supports this hypothesis recommending anticoagulation over the use of antiplatelet therapy in patients with PFO and cryptogenic stroke. However, more evidence is required comparing of PFO closure with anticoagulation or anticoagulation with antiplatelet therapy.
=== Atrial septal defect ===
Once someone is found to have an atrial septal defect, a determination of whether it should be corrected is typically made. If the atrial septal defect is causing the right ventricle to enlarge a secundum atrial septal defect should generally be closed. If the ASD is not causing problems the defect may simply be checked every two or three years. Methods of closure of an ASD include surgical closure and percutaneous closure.
==== Evaluation prior to correction ====
Prior to correction of an ASD, an evaluation is made of the severity of the individual's pulmonary hypertension (if present at all) and whether it is reversible (closure of an ASD may be recommended for prevention purposes, to avoid such a complication in the first place. Pulmonary hypertension is not always present in adults who are diagnosed with an ASD in adulthood).
If pulmonary hypertension is present, the evaluation may include a right heart catheterization. This involves placing a catheter in the venous system of the heart and measuring pressures and oxygen saturations in the superior vena cava, inferior vena cava, right atrium, right ventricle, and pulmonary artery, and in the wedge position. Individuals with a pulmonary vascular resistance (PVR) less than 7 wood units show regression of symptoms (including NYHA functional class). However, individuals with a PVR greater than 15 wood units have increased mortality associated with closure of the ASD.
If the pulmonary arterial pressure is more than two-thirds of the systemic systolic pressure, a net left-to-right shunt should occur at least 1.5:1 or evidence of reversibility of the shunt when given pulmonary artery vasodilators prior to surgery. (If Eisenmenger's physiology has set in, the right-to-left shunt must be shown to be reversible with pulmonary artery vasodilators prior to surgery.)
Surgical mortality due to closure of an ASD is lowest when the procedure is performed prior to the development of significant pulmonary hypertension. The lowest mortality rates are achieved in individuals with a pulmonary artery systolic pressure less than 40 mmHg. If Eisenmenger's syndrome has occurred, a significant risk of mortality exists regardless of the method of closure of the ASD. In individuals who have developed Eisenmenger's syndrome, the pressure in the right ventricle has raised high enough to reverse the shunt in the atria. If the ASD is then closed, the afterload that the right ventricle has to act against has suddenly increased. This may cause immediate right ventricular failure, since it may not be able to pump the blood against the pulmonary hypertension.
==== Surgical closure ====
Surgical closure of an ASD involves opening up at least one atrium and closing the defect with a patch under direct visualization.
==== Catheter procedure ====
Percutaneous device closure involves the passage of a catheter into the heart through the femoral vein guided by fluoroscopy and echocardiography. An example of a percutaneous device is a device which has discs that can expand to a variety of diameters at the end of the catheter. The catheter is placed in the right femoral vein and guided into the right atrium. The catheter is guided through the atrial septal wall and one disc (left atrial) is opened and pulled into place. Once this occurs, the other disc (right atrial) is opened in place and the device is inserted into the septal wall. This type of PFO closure is more effective than drug or other medical therapies for decreasing the risk of future thromboembolism.
The most common adverse effect of PFO device closure is new-onset atrial fibrillation. Other complications, all rare, include device migration, erosion and embolization and device thrombosis or formation of an inflammatory mass with risk for recurrent ischemic stroke.
Percutaneous closure of an ASD is currently only indicated for the closure of secundum ASDs with a sufficient rim of tissue around the septal defect so that the closure device does not impinge upon the superior vena cava, inferior vena cava, or the tricuspid or mitral valves. The Amplatzer Septal Occluder (ASO) is commonly used to close ASDs. The ASO consists of two self-expandable round discs connected to each other with a 4-mm waist, made up of 0.004– to 0.005-inch Nitinol wire mesh filled with Dacron fabric. Implantation of the device is relatively easy. The prevalence of residual defect is low. The disadvantages are a thick profile of the device and concern related to a large amount of nitinol (a nickel-titanium compound) in the device and consequent potential for nickel toxicity.
Percutaneous closure is the method of choice in most centres. Studies evaluating percutaneous ASD closure among pediatric and adult population show that this is relatively safer procedure and has better outcomes with increasing hospital volume.
== Epidemiology ==
As a group, atrial septal defects are detected in one child per 1500 live births. PFOs are quite common (appearing in 10–20% of adults), but when asymptomatic go undiagnosed. ASDs make up 30 to 40% of all congenital heart diseases that are seen in adults.
The ostium secundum atrial septal defect accounts for 7% of all congenital heart lesions. This lesion shows a male:female ratio of 1:2.
== References ==
This article incorporates public domain material from National Heart, Lung, and Blood Institute. United States Department of Health and Human Services.
=== Additional references ===
Goldman, Lee (2011). Goldman's Cecil Medicine (24th ed.). Philadelphia: Elsevier Saunders. pp. 270, 400–401. ISBN 978-1437727883.
== Further reading ==
Germonpre, Peter; Hastir, Francis; Dendale, Paul; Marroni, Alessandro; Nguyen, Anne-Florence; Balestra, Costantino (1 April 2005). "Evidence for increasing patency of the foramen ovale in divers". The American Journal of Cardiology. 95 (7). Elsevier:Science direct: 912–915. doi:10.1016/j.amjcard.2004.12.026. PMID 15781033.
== External links ==
Atrial septal defect Archived 2013-05-11 at the Wayback Machine information for parents. | Wikipedia/Atrial_septal_defect |
Sir John Murray (3 March 1841 – 16 March 1914) was a pioneering Canadian-born British oceanographer, marine biologist and limnologist. He is considered to be the father of modern oceanography.
== Early life and education ==
Murray was born on 3 March 1841, at Cobourg, Canada West (now Ontario). He was the second son of Robert Murray, an accountant, and Elizabeth Macfarlane. His parents had emigrated from Scotland to Ontario in about 1834. He went to school in London, Ontario and later to Cobourg College. In 1858, at the age of 17 he moved to Stirling to live with his grandfather, John Macfarlane, and continue his education at Stirling High School. In 1864, he enrolled at University of Edinburgh to study medicine however he did not complete his studies and did not graduate.
In 1868, he joined the whaling ship, Jan Mayen, as ship's surgeon and visited Spitsbergen and Jan Mayen Island. During the seven-month trip, he collected marine specimens and recorded ocean currents, ice movements and the weather.
On his return to Edinburgh he re-entered the University to complete his studies (1868–72) in geology under Sir Archibald Geikie.
== Challenger Expedition ==
In 1872, Murray assisted in preparing scientific apparatus for the Challenger Expedition under the direction of the expedition's chief scientist, Charles Wyville Thomson. When a position on the expedition became available Murray joined the crew as a naturalist. During the four-year voyage, he assisted in the research of the oceans including collecting marine samples, making and noting observations, and making improvements to marine instrumentation. After the expedition, Murray was appointed Chief Assistant at the Challenger offices in Edinburgh where he managed and organised the collection. After Thomson's death in 1882, Murray became Director of the office and in 1896 published The Report on the Scientific Results of the Voyage of HMS Challenger, a work of more than 50 volumes of reports.
Murray renamed his house, on Boswall Road in northern Edinburgh, Challenger Lodge in recognition of the expedition. The building now houses St Columba's Hospice.
== Marine Laboratory, Granton ==
In 1884, Murray set up the Marine Laboratory at Granton, Edinburgh, the first of its kind in the United Kingdom. In 1894, this laboratory was moved to Millport, Isle of Cumbrae, on the Firth of Clyde, and became the University Marine Biological Station, Millport, the forerunner of today's Scottish Association for Marine Science at Dunstaffnage, near Oban, Argyll and Bute.
== Bathymetrical survey of the fresh-water lochs of Scotland ==
After completing the Challenger Expedition reports, Murray began work surveying the freshwater lochs of Scotland. He was assisted by Frederick Pullar and over a period of three years, they surveyed 15 lochs together. In 1901, Pullar drowned as a result of an ice-skating accident which caused Murray to consider abandoning the survey work. However, Pullar's father, Laurence Pullar, persuaded him to continue and gave £10,000 towards the completion of the survey. Murray coordinated a team of nearly 50 people who took more than 60,000 individual depth soundings and recorded other physical characteristics of the 562 lochs. The resulting 6 volume Bathymetrical Survey of the Fresh-Water Lochs of Scotland was published in 1910. The cartographer John George Bartholomew, who strove to advance geographical and scientific understanding through his cartographic work, drafted and published all the maps of the Survey.
== North Atlantic oceanographic expedition ==
In 1909, Murray indicated to the International Council for the Exploration of the Sea that an oceanographic survey of the North Atlantic should be undertaken. After Murray agreed to pay all expenses, the Norwegian Government lent him the research ship Michael Sars and its scientific crew. He was joined on board by the Norwegian marine biologist Johan Hjort and the ship departed Plymouth in April 1910 for a four-month expedition to take physical and biological observations at all depths between Europe and North America. Murray and Hjort published their findings in The Depths of the Ocean in 1912 and it became a classic for marine naturalists and oceanographers.
He was the first to note the existence of the Mid-Atlantic Ridge and of oceanic trenches. He also noted the presence of deposits derived from the Saharan desert in deep ocean sediments and published many papers on his findings.
== Awards, recognition and legacy ==
Fellow of the Royal Society of Edinburgh (1877)
Neill Medal from the Royal Society of Edinburgh (1877)
Makdougall Brisbane Prize from the Royal Society of Edinburgh (1884)
Founder's Medal from the Royal Geographical Society (1895)
Fellow of the Royal Society (1896)
Knight Commander of the Order of the Bath (1898)
Cullum Geographical Medal from the American Geographical Society (1899)
Clarke Medal from the Royal Society of New South Wales (1900)
International Honorary Member of the American Academy of Arts and Sciences (1900)
Livingstone Medal from the Royal Scottish Geographical Society (1910)
International Member of the American Philosophical Society (1911)
Vega Medal from the Swedish Society for Anthropology and Geography (1912)
International Member of the United States National Academy of Sciences (1912)
Other awards included the Cuvier Prize and Medal from the Institut de France and the Humboldt Medal of the Gesellschaft für Erdkunde zu Berlin.
He was president of the Royal Scottish Geographical Society from 1898 to 1904.
In 1911, Murray founded the Alexander Agassiz Medal which is awarded by the National Academy of Sciences, in memory of his friend Alexander Agassiz (1835–1910).
After his death his estate funded the John Murray Travelling Studentship Fund and the 1933 John Murray ''Mabahiss'' Expedition to the Indian Ocean.
== Death ==
Murray lived at Challenger Lodge (renamed after his expedition) on Boswall Road in Trinity, Edinburgh, with commanding views over the Firth of Forth. This house is now the St Columba's Hospice, a palliative care facility.
Murray was killed when his car overturned 10 miles (16 km) west of his home on 16 March 1914 at Kirkliston near Edinburgh. He is buried in Dean Cemetery in Edinburgh on the central path of the north section in the original cemetery.
== Tribute ==
The John Murray Laboratories at the University of Edinburgh, the John Murray Society at the University of Newcastle and the Scottish Environment Protection Agency research vessel, the S.V. Sir John Murray, and the Murray Glacier are named after him.
== Taxa named in his honor ==
Animals named in his honor include the entire Murrayonida order of sea sponges.
Anthoptilum murrayi Kölliker, 1880
Bathyraja murrayi Günther, 1880
Bythotiara murrayi Günther, 1903
Cirrothauma murrayi Chun, 1911
Culeolus murrayi Herdman, 1881
Deltocyathus murrayi Gardiner & Waugh, 1938
Halieutopsis murrayi H. C. Ho, 2022
Lanceola murrayi Norman, 1900
Lithodes murrayi Henderson, 1888
Melanocetus murrayi, commonly known as Murray's abyssal anglerfish, is a deep sea anglerfish in the family Melanocetidae, found in tropical to temperate parts of the world's oceans at depths down to over 2,000 m (6,600 ft).
Mesothuria murrayi Théel, 1886
Millepora murrayi Quelch, 1886
Munneurycope murrayi Walker, 1903
Munnopsurus murrayi Walker, 1903
Murrayona Kirkpatrick, 1910
Phallonemertes murrayi Brinkmann, 1912
Phascolion murrayi Stephen, 1941
†Pipistrellus murrayi Andrews, 1900
Potamethus murrayi M'Intosh, 1916
Psammastra murrayi Sollas, 1886
Pythonaster murrayi Sladen, 1889
Silvascincus murrayi Boulenger, 1887
Sophrosyne murrayi Stebbing, 1888
Stellitethya murrayi Sarà & Bavestrello, 1996
Trachyrhynchus murrayi Günther, 1887
Triglops murrayi Günther, 1888
== Botanical references ==
== See also ==
European and American voyages of scientific exploration
== References ==
== External links ==
Works by or about John Murray at Wikisource
Works by or about John Murray at the Internet Archive
Works by John Murray at LibriVox (public domain audiobooks)
On the 1910 Murray and Hjort expedition and the Cirrothauma murrayi octopus | Wikipedia/John_Murray_(oceanographer) |
A diving regulator or underwater diving regulator is a pressure regulator that controls the pressure of breathing gas for underwater diving. The most commonly recognised application is to reduce pressurized breathing gas to ambient pressure and deliver it to the diver, but there are also other types of gas pressure regulator used for diving applications. The gas may be air or one of a variety of specially blended breathing gases. The gas may be supplied from a scuba cylinder carried by the diver, in which case it is called a scuba regulator, or via a hose from a compressor or high-pressure storage cylinders at the surface in surface-supplied diving. A gas pressure regulator has one or more valves in series which reduce pressure from the source, and use the downstream pressure as feedback to control the delivered pressure, or the upstream pressure as feedback to prevent excessive flow rates, lowering the pressure at each stage.
The terms "regulator" and "demand valve" (DV) are often used interchangeably, but a demand valve is the final stage pressure-reduction regulator that delivers gas only while the diver is inhaling and reduces the gas pressure to approximately ambient. In single-hose demand regulators, the demand valve is either held in the diver's mouth by a mouthpiece or attached to the full-face mask or helmet. In twin-hose regulators the demand valve is included in the body of the regulator which is usually attached directly to the cylinder valve or manifold outlet, with a remote mouthpiece supplied at ambient pressure.
A pressure-reduction regulator is used to control the delivery pressure of the gas supplied to a free-flow helmet or full-face mask, in which the flow is continuous, to maintain the downstream pressure which is limited by the ambient pressure of the exhaust and the flow resistance of the delivery system (mainly the umbilical and exhaust valve) and not much influenced by the breathing of the diver. Diving rebreather systems may also use regulators to control the flow of fresh gas, and demand valves, known as automatic diluent valves, to maintain the volume in the breathing loop during descent. Gas reclaim systems and built-in breathing systems (BIBS) use a different kind of regulator to control the flow of exhaled gas to the return hose and through the topside reclaim system, or to the outside of the hyperbaric chamber, these are of the back-pressure regulator class.
The performance of a regulator is measured by the cracking pressure and added mechanical work of breathing, and the capacity to deliver breathing gas at peak inspiratory flow rate at high ambient pressures without excessive pressure drop, and without excessive dead space. For some cold water diving applications the capacity to deliver high flow rates at low ambient temperatures without jamming due to regulator freezing is important.
== Purpose ==
The diving regulator is a mechanism which reduces the pressure of the supply of breathing gas and provides it to the diver at approximately ambient pressure. The gas may be supplied on demand, when the diver inhales, or as a constant flow past the diver inside the helmet or mask, from which the diver uses what is necessary, while the remainder goes to waste.: 49
The gas may be provided directly to the diver, or to a rebreather circuit, to make up for used gas and volume changes due to depth variations. Gas supply may be from a high-pressure scuba cylinder carried by the diver, or from a surface supply through a hose connected to a compressor or high pressure storage system.
== Types ==
An open circuit demand valve provides gas flow only while the diver inhales, a free flow regulator provides a constant flow rate at the delivery pressure, reclaim and built-in-breathing-systems regulators allow exhaust outflow only during exhalation. Rebreathers use demand regulators to make up a volume deficit in the loop, and may use constant mass flow regulators to refresh the oxygen content of the loop gas mixture. A scuba diving regulator is used to supply a scuba diver from a scuba cylinder, while a diving helmet demand valve may supply gas from surface supply or a bailout scuba cylinder.
=== Open circuit demand valve ===
A demand valve detects the pressure drop when the diver starts inhaling and supplies the diver with a breath of gas at ambient pressure. When the diver stops inhaling, the demand valve closes to stop the flow. The demand valve has a chamber, which in normal use contains breathing gas at ambient pressure, which is connected to a bite-grip mouthpiece, a full-face mask, or a diving helmet, either direct coupled or connected by a flexible low-pressure hose. On one side of the chamber is a flexible diaphragm to sense the pressure difference between the gas in the chamber on one side and the surrounding water on the other side, and control the operation of the valve which supplies pressurised gas into the chamber.
This is done by a mechanical system linking the diaphragm to a valve which is opened to an extent proportional to the displacement of the diaphragm from the closed position. The pressure difference between the inside of the mouthpiece and the ambient pressure outside the diaphragm required to open the valve is known as the cracking pressure. This cracking pressure difference is usually negative relative to ambient, but may be slightly positive on a positive pressure regulator (a regulator that maintains a pressure inside the mouthpiece, mask or helmet, which is slightly greater than the ambient pressure). Once the valve has opened, gas flow should continue at the smallest stable pressure difference reasonably practicable while the diver inhales, and should stop as soon as gas flow stops. Several mechanisms have been devised to provide this function, some of them extremely simple and robust, and others somewhat more complex, but more sensitive to small pressure changes.: 33 The diaphragm is protected by a cover with holes or slits through which outside water can enter freely. This cover reduces sensitivity of the diaphragm to water turbulence and dynamic pressure due to movement, which might otherwise trigger gas flow when it is not needed.
When the diver starts to inhale, the removal of gas from the casing lowers the pressure inside the chamber, and the external water pressure moves the diaphragm inwards operating a lever which lifts the valve off its seat, releasing gas into the chamber. The inter-stage gas, at about 8 to 10 bars (120 to 150 psi) over ambient pressure, expands through the valve orifice as its pressure is reduced to ambient and supplies the diver with more gas to breathe. When the diver stops inhaling the chamber fills until the external pressure is balanced, the diaphragm returns to its rest position and the lever releases the valve to be closed by the valve spring and gas flow stops.
When the diver exhales, one-way valves made from a flexible air-tight material flex outwards under the pressure of the exhalation, letting gas escape from the chamber. They close, making a seal, when the exhalation stops and the pressure inside the chamber reduces to ambient pressure.: 108
The vast majority of demand valves are used on open circuit breathing apparatus, which means that the exhaled gas is discharged into the surrounding environment and lost. Reclaim valves can be fitted to helmets to allow the used gas to be returned to the surface for reuse after removing the carbon dioxide and making up the oxygen. This process, referred to as "push-pull", is technologically complex and expensive and is only used for deep commercial diving on heliox mixtures, where the saving on helium compensates for the expense and complications of the system, and for diving in contaminated water, where the gas is not reclaimed, but the system reduces the risk of contaminated water leaking into the helmet through an exhaust valve.
=== Open circuit free-flow regulator ===
These are generally used in surface supply diving with free-flow masks and helmets. They are usually a large high-flow rated industrial gas regulator that is manually controlled at the gas panel on the surface to the pressure required to provide the desired flow rate to the diver. Free flow is not normally used on scuba equipment as the high gas flow rates are inefficient and wasteful.
In constant-flow regulators the pressure regulator provides a constant reduced pressure, which provides gas flow to the diver, which may be to some extent controlled by an adjustable orifice controlled by the diver. These are the earliest type of breathing set flow control. The diver must physically open and close the adjustable supply valve to regulate flow. Constant flow valves in an open circuit breathing set consume gas less economically than demand valve regulators because gas flows even when it is not needed, and must flow at the rate required for peak inhalation. Before 1939, self contained diving and industrial open circuit breathing sets with constant-flow regulators were designed by Le Prieur, but did not get into general use due to very short dive duration. Design complications resulted from the need to put the second-stage flow control valve where it could be easily operated by the diver.
=== Reclaim regulators ===
The cost of breathing gas containing a high fraction of helium is a significant part of the cost of deep diving operations, and can be reduced by recovering the breathing gas for recycling. A reclaim helmet is provided with a return line in the diver's umbilical, and exhaled gas is discharged to this hose through a reclaim regulator, which ensures that gas pressure in the helmet cannot fall below the ambient pressure.: 150–151 The gas is processed at the surface in the helium reclaim system by filtering, scrubbing and boosting into storage cylinders until needed. The oxygen content may be adjusted when appropriate.: 151–155 : 109 The same principle is used in built-in breathing systems used to vent oxygen-rich treatment gases from a hyperbaric chamber, though those gases are generally not reclaimed. A diverter valve is provided to allow the diver to manually switch to open circuit if the reclaim valve malfunctions, and an underpressure flood valve allows water to enter the helmet to avoid a squeeze if the reclaim valve fails suddenly, allowing the diver time to switch to open circuit without injury.: 151–155 Reclaim valves for deep diving may use two stages to give smoother flow and lower work of breathing. The reclaim regulator works on a similar principle to the demand regulator, in that it allows flow only when the pressure difference between the interior of the helmet and the ambient water opens the valve, but uses the upstream over-pressure to activate the valve, where the demand valve uses downstream underpressure.
Reclaim regulators are also sometimes used for hazmat diving to reduce the risk of backflow of contaminated water through the exhaust valves into the helmet. In this application there would not be an underpressure flood valve, but the pressure differences and the squeeze risk are relatively low.: 109 The breathing gas in this application would usually be air and would not actually be recycled.
=== Built-in breathing systems ===
BIBS regulators for hyperbaric chambers have a two-stage system at the diver similar to reclaim helmets, though for this application the outlet regulator dumps the exhaled gas through an outlet hose to the atmosphere outside the chamber.
These are systems used to supply breathing gas on demand in a chamber which is at a pressure greater than the ambient pressure outside the chamber. The pressure difference between chamber and external ambient pressure makes it possible to exhaust the exhaled gas to the external environment, but the flow must be controlled so that only exhaled gas is vented through the system, and it does not drain the contents of the chamber to the outside. This is achieved by using a controlled exhaust valve which opens when a slight over-pressure relative to the chamber pressure on the exhaust diaphragm moves the valve mechanism against a spring. When this over-pressure is dissipated by the gas flowing out through the exhaust hose, the spring returns this valve to the closed position, cutting off further flow, and conserving the chamber atmosphere. A negative or zero pressure difference over the exhaust diaphragm will keep it closed. The exhaust diaphragm is exposed to the chamber pressure on one side, and exhaled gas pressure in the oro-nasal mask on the other side. The supply of gas for inhalation is through a demand valve which works on the same principles as a regular diving demand valve second stage. Like any other breathing apparatus, the dead space must be limited to minimise carbon dioxide buildup in the mask.
In some cases the outlet suction must be limited and a back-pressure regulator may be required. This would usually be the case for use in a saturation system. Use for oxygen therapy and surface decompression on oxygen would not generally need a back-pressure regulator. When an externally vented BIBS is used at low chamber pressure, a vacuum assist may be necessary to keep the exhalation backpressure down to provide an acceptable work of breathing.
The major application for this type of BIBS is supply of breathing gas with a different composition to the chamber atmosphere to occupants of a hyperbaric chamber where the chamber atmosphere is controlled, and contamination by the BIBS gas would be a problem. This is common in therapeutic decompression, and hyperbaric oxygen therapy, where a higher partial pressure of oxygen in the chamber would constitute an unacceptable fire hazard, and would require frequent ventilation of the chamber to keep the partial pressure within acceptable limits. Frequent ventilation is noisy and expensive, but can be used in an emergency.
=== Rebreather regulators ===
Rebreather systems used for diving recycle most of the breathing gas, but are not based on a demand valve system for their primary function. Instead, the breathing loop is carried by the diver and remains at ambient pressure while in use. Regulators may be used in scuba rebreathers to make up a deficit in loop gas volume, and to provide oxygen-rich gas to compensate for metabolic use.
The automatic diluent valve (ADV) is used in a rebreather to add gas to the loop to compensate automatically for volume reduction due to pressure increase with greater depth or to make up gas lost from the system by the diver exhaling through the nose while clearing the mask or as a method of flushing the loop. They are often provided with a purge button to allow manual flushing of the loop. The ADV is similar in concept and function to the open circuit demand valve and may use many similar components, but does not have an integral exhaust valve. An equivalent function to the exhaust valve is provided by the loop overpressure valve. Some passive semi-closed circuit rebreathers use the ADV to add gas to the loop to compensate for a portion of the gas discharged automatically during the breathing cycle as a way of maintaining a suitable oxygen concentration.
The bailout valve (BOV) is an open circuit demand valve built into a rebreather mouthpiece or other part of the breathing loop. It can be isolated while the diver is using the rebreather to recycle breathing gas, and opened, while at the same time isolating the breathing loop, when a problem causes the diver to bail out onto open circuit. The main distinguishing feature of the BOV is that the same mouthpiece is used for open and closed-circuit, and the diver does not have to shut the dive/surface valve (DSV), remove it from their mouth, and find and insert the bailout demand valve in order to bail out onto open circuit. Although costly, this reduction in critical steps makes the integrated BOV a significant safety advantage, particularly when there is a high partial pressure of carbon dioxide in the loop, as hypercapnia can make it difficult or impossible for the diver to hold their breath even for the short period required to swap mouthpieces.
Constant mass flow addition valves are used to supply a constant mass flow of fresh gas to an active type semi-closed rebreather to replenish the gas used by the diver and to maintain an approximately constant composition of the loop mix. Two main types are used: the fixed orifice and the adjustable orifice (usually a needle valve). The constant mass flow valve is usually supplied by a gas regulator that is isolated from the ambient pressure so that it provides an absolute pressure regulated output (not compensated for ambient pressure). This limits the depth range in which constant mass flow is possible through the orifice, but provides a relatively predictable gas mixture in the breathing loop. An over-pressure relief valve in the first stage is used to protect the output hose. Unlike most other diving gas supply regulators, constant mass flow orifices do not control the downstream pressure, but they do regulate the flow rate.
Manual and electronically controlled addition valves are used on manual and electronically controlled closed circuit rebreathers (mCCR, eCCR) to add oxygen to the loop to maintain oxygen partial pressure set-point. A manually or electronically controlled valve is used to release oxygen from the outlet of a standard scuba regulator first stage into the breathing loop. An over-pressure relief valve on the first stage is necessary to protect the hose in case of first stage leaks. Strictly speaking, these are not pressure regulators, they are flow control valves.
== History ==
The first recorded demand valve was invented in 1838 in France and forgotten in the next few years; another workable demand valve was not invented until 1860. On 14 November 1838, Dr. Manuel Théodore Guillaumet of Argentan, Normandy, France, filed a patent for a twin-hose demand regulator; the diver was provided air through pipes from the surface to a back mounted demand valve and from there to a mouthpiece. The exhaled gas was vented to the side of the head through a second hose. The apparatus was demonstrated to and investigated by a committee of the French Academy of Sciences:
On 19 June 1838, in London, William Edward Newton filed a patent (no. 7695: "Diving apparatus") for a diaphragm-actuated, twin-hose demand valve for divers. However, it is believed that Mr. Newton was merely filing a patent on behalf of Dr. Guillaumet.
In 1860 a mining engineer from Espalion (France), Benoît Rouquayrol, invented a demand valve with an iron air reservoir to let miners breathe in flooded mines. He called his invention régulateur ('regulator'). In 1864 Rouquayrol met the French Imperial Navy officer Auguste Denayrouze and they worked together to adapt Rouquayrol's regulator to diving. The Rouquayrol-Denayrouze apparatus was mass-produced with some interruptions from 1864 to 1965. As of 1865 it was acquired as a standard by the French Imperial Navy, but never was entirely accepted by the French divers because of a lack of safety and autonomy.
In 1926 Maurice Fernez and Yves Le Prieur patented a hand-controlled constant flow regulator (not a demand valve), which used a full-face mask (the air escaping from the mask at constant flow).
In 1937 and 1942 the French inventor, Georges Commeinhes from Alsace, patented a diving demand valve supplied with air from two gas cylinders through a full-face mask. Commeinhes died in 1944 during the liberation of Strasbourg and his invention was soon forgotten. The Commeinhes demand valve was an adaptation of the Rouquayoul-Denayrouze mechanism, not as compact as was the Cousteau-Gagnan apparatus.
It was not until December 1942 that the demand valve was developed to the form which gained widespread acceptance. This came about after French naval officer Jacques-Yves Cousteau and engineer Émile Gagnan met for the first time in Paris. Gagnan, employed at Air Liquide, had miniaturized and adapted a Rouquayrol-Denayrouze regulator used for gas generators following severe fuel restrictions due to the German occupation of France; Cousteau suggested it be adapted for diving, which in 1864 was its original purpose.
The single hose regulator, with a mouth held demand valve supplied with low pressure gas from the cylinder valve mounted first stage, was invented by Australian Ted Eldred in the early 1950s in response to patent restrictions and stock shortages of the Cousteau-Gagnan apparatus in Australia. In 1951 E. R. Cross invented the "Sport Diver," one of the first American-made single-hose regulators. Cross' version is based on the oxygen system used by pilots. Other early single-hose regulators developed during the 1950s include Rose Aviation's "Little Rose Pro," the "Nemrod Snark" (from Spain), and the Sportsways "Waterlung," designed by diving pioneer Sam LeCocq in 1958. In France, in 1955, a patent was taken out by Bronnec & Gauthier for a single hose regulator, later produced as the Cristal Explorer. The "Waterlung" would eventually become the first single-hose regulator to be widely adopted by the diving public. Over time, the convenience and performance of improved single hose regulators would make them the industry standard.: 7 Performance still continues to be improved by small increments, and adaptations have been applied to rebreather technology.
The single hose regulator was later adapted for surface supplied diving in lightweight helmets and full-face masks in the tradition of the Rouquayrol-Denayrouze equipment to economise on gas usage. By 1969 Kirby-Morgan had developed a full-face mask - the KMB-8 Bandmask - using a single hose regulator. This was developed into the Kirby-Morgan SuperLite-17B by 1976, making use of the neck dam seal invented by Joe Savoie.
Secondary (octopus) demand valves, submersible pressure gauges and low pressure inflator hoses were added to the first stage.
In 1994 a reclaim system was developed in a joint project by Kirby-Morgan and Divex to recover expensive helium mixes during deep operations.
== Mechanism and function ==
Both free-flow and demand regulators use mechanical feedback of the downstream pressure to control the opening of a valve which controls gas flow from the upstream, high-pressure side, to the downstream, low-pressure side of each stage. Flow capacity must be sufficient to allow the downstream pressure to be maintained at maximum demand, and sensitivity must be appropriate to deliver maximum required flow rate with a small variation in downstream pressure, and for a large variation in supply pressure. Open circuit scuba regulators must also deliver against a variable ambient pressure. They must be robust and reliable, as they are life-support equipment which must function in the relatively hostile seawater environment.
Diving regulators use mechanically operated valves. In most cases there is ambient pressure feedback to both first and second stage, except where this is avoided to allow constant mass flow through an orifice in a rebreather, which requires a constant upstream pressure.
The parts of a regulator are described here as the major functional groups in downstream order as following the gas flow from the diving cylinder to its final use.
=== Connection to the diving cylinder ===
The first-stage of the scuba regulator will usually be connected to the cylinder valve by one of two standard types of fittings. The CGA 850 connector, also known as an international connector, which uses a yoke clamp, or a DIN screw fitting. There are also European standards for scuba regulator connectors for gases other than air, and adapters to allow use of regulators with cylinder valves of a different connection type.
CGA 850 Yoke connectors (sometimes called A-clamps from their shape) are the most popular regulator connection in North America and several other countries. They clamp the high pressure inlet opening of the regulator against the outlet opening of the cylinder valve, and are sealed by an O-ring in a groove in the contact face of the cylinder valve. The user screws the clamp in place finger-tight to hold the metal surfaces of cylinder valve and regulator first stage in contact, compressing the o-ring between the radial faces of valve and regulator. When the valve is opened, gas pressure presses the O-ring against the outer cylindrical surface of the groove, completing the seal. The diver must take care not to screw the yoke down too tightly, or it may prove impossible to remove without tools. Conversely, failing to tighten sufficiently can lead to O-ring extrusion under pressure and a major loss of breathing gas. This can be a serious problem if it happens when the diver is at depth. Yoke fittings are rated up to a maximum of 240 bar working pressure.
The DIN fitting is a type of screw-in connection to the cylinder valve. The DIN system is less common worldwide, but has the advantage of withstanding greater pressure, up to 300 bar, allowing use of high-pressure steel cylinders. They are less susceptible to blowing the O-ring seal if banged against something while in use. DIN fittings are the standard in much of Europe and are available in most countries. The DIN fitting is considered more secure and therefore safer by many technical divers.: 117 It is more compact than the yoke fitting and less exposed to impact with an overhead.
==== Conversion kits ====
Several manufacturers market an otherwise identical first stage varying only in the choice of cylinder valve connection. In these cases it may be possible to buy original components to convert yoke to DIN and vice versa. The complexity of the conversion may vary, and parts are not usually interchangeable between manufacturers. The conversion of Apeks regulators is particularly simple and only requires an Allen key and a ring spanner.
==== Adaptors ====
Adaptors are available to allow connection of DIN regulators to yoke cylinder valves (A-clamp or yoke adaptor), and to connect yoke regulators to DIN cylinder valves. There are two types of adaptors for DIN valves: plug adaptors and block adaptors. Plug adaptors are screwed into a 5-thread DIN valve socket, are rated for 232/240 bar, and can only be used with valves which are designed to accept them. These can be recognised by a dimple recess opposite to the outlet opening, used to locate the screw of an A-clamp. Block adaptors are generally rated for 200 bar, and can be used with almost any 200 bar 5-thread DIN valve. A-clamp or yoke adaptors comprise a yoke clamp with a DIN socket in line. They are slightly more vulnerable to O-ring extrusion than integral yoke clamps, due to greater leverage on the first stage regulator.
=== Single-hose demand regulators ===
Most contemporary diving regulators are single-hose two-stage demand regulators. They consist of a first-stage regulator and a second-stage demand valve connected by a low pressure hose to transfer breathing gas, and allow relative movement within the constraints of hose length and flexibility.
The first stage is mounted to the cylinder valve or manifold via one of the standard connectors (Yoke or DIN), and reduces cylinder pressure to an intermediate pressure, usually about 8 to 11 bars (120 to 160 psi) higher than the ambient pressure, also called interstage pressure, medium pressure or low pressure.: 17–20
A balanced regulator first stage automatically keeps a constant pressure difference between the interstage pressure and the ambient pressure even as the tank pressure drops with consumption. The balanced regulator design allows the first stage orifice to be as large as needed without incurring performance degradation as a result of changing tank pressure.: 17–20
The first stage regulator body generally has several low-pressure outlets (ports) for second-stage regulators and BCD and dry suit inflators, and one or more high-pressure outlets, which allow a submersible pressure gauge (SPG), gas-integrated diving computer or remote pressure tranducer to read the cylinder pressure. One low-pressure port with a larger bore may be designated for the primary second stage as it will give a higher flow at maximum demand for lower work of breathing.: 50
The mechanism inside the first stage can be of the diaphragm or piston type, and can be balanced or unbalanced. Unbalanced regulators produce an interstage pressure which varies slightly as the cylinder pressure changes and to limit this variation the high-pressure orifice size is small, which decreases the maximum capacity of the regulator. A balanced regulator maintains a constant interstage pressure difference for all cylinder pressures.: 17–20
The second stage, or demand valve reduces the pressure of the interstage air supply to ambient pressure on demand from the diver. The operation of the valve is triggered by a drop in downstream pressure as the diver breathes in. In an upstream valve, the valve is held closed by the interstage pressure and opens by moving into the flow of gas. They are often made as tilt-valves, which are mechanically extremely simple and reliable, but are not amenable to fine tuning.: 14
Most modern demand valves use a downstream valve mechanism, where the valve poppet moves in the same direction as the flow of gas to open and is kept closed by a spring. The poppet is lifted away from the crown by a lever operated by the diaphragm.: 13–15 Two patterns are commonly used. One is the classic push-pull arrangement, where the actuating lever goes onto the end of the valve shaft and is held on by a nut. Any deflection of the lever is converted to an axial pull on the valve shaft, lifting the seat off the crown and allowing air to flow.: 13 The other is the barrel poppet arrangement, where the poppet is enclosed in a tube which crosses the regulator body and the lever operates through slots in the sides of the tube. The far end of the tube is accessible from the side of the casing and a spring tension adjustment screw may be fitted for limited diver control of the cracking pressure. This arrangement also allows relatively simple pressure balancing of the second stage.: 14, 18
A downstream valve will function as an over-pressure valve when the inter-stage pressure is raised sufficiently to overcome the spring pre-load. If the first stage leaks and the inter-stage over-pressurizes, the second stage downstream valve opens automatically. If the leak is bad this could result in a "freeflow", but a slow leak will generally cause intermittent "popping" of the DV, as the pressure is released and slowly builds up again.
If the first stage leaks and the inter-stage over-pressurizes, the second stage upstream valve will not release the excess pressure, This might hinder the supply of breathing gas and possibly result in a ruptured hose or the failure of another second stage valve, such as one that inflates a buoyancy device. When a second stage upstream valve is used a relief valve will be included by the manufacturer on the first stage regulator to protect the hose.: 9
If a shut-off valve is fitted between the first and second stages, as is found on scuba bailout systems used for commercial diving and in some technical diving configurations, the demand valve will normally be isolated and unable to function as a relief valve. In this case an overpressure valve must be fitted to the first stage. They are available as aftermarket accessories which can be screwed into any available low pressure port on the first stage.
Some demand valves use a small, sensitive pilot valve to control the opening of the main valve. The Poseidon Jetstream and Xstream and Oceanic Omega second stages are examples of this technology. They can produce very high flow rates for a small pressure differential, and particularly for a relatively small cracking pressure. They are generally more complicated and expensive to service.: 16
Exhaled gas leaves the demand valve housing through one or two exhaust ports. Exhaust valves are necessary to prevent the diver inhaling water, and to allow a negative pressure difference to be induced over the diaphragm to operate the demand valve. The exhaust valves should operate at a very small positive pressure difference, and cause as little resistance to flow as reasonably possible, without being cumbersome and bulky. Elastomer mushroom valves serve the purpose adequately.: 108 Where it is important to avoid leaks back into the regulator, such as when diving in contaminated water, a system of two sets of valves in series can reduce the risk of contamination. A more complex option which can be used for surface supplied helmets, is to use a reclaim exhaust system which uses a separate flow regulator to control the exhaust which is returned to the surface in a dedicated hose in the umbilical.: 109 The exhaust manifold (exhaust tee, exhaust cover, whiskers) is the ducting that protects the exhaust valve(s) and diverts the exhaled air to the sides so that it does not bubble up in the diver's face and obscure the view.: 33
A standard fitting on single-hose second stages, both mouth-held and built into a full-face mask or demand helmet, is the purge-button, which allows the diver to manually deflect the diaphragm to open the valve and cause air to flow into the casing. This is usually used to purge the casing or full-face mask of water if it has flooded. This will often happen if the second stage is dropped or removed from the mouth while under-water.: 108 It is either a separate part mounted in the front cover or the cover itself may be made flexible and serves as the purge button. Depressing the purge button presses against the diapragm directly over the lever of the demand valve, and this movement of the lever opens the valve to release air through the regulator. The tongue may be used to block the mouthpiece during purging to prevent water or other matter in the regulator from being blown into the diver's airway by the air blast. This is particularly important when purging after vomiting through the regulator. The purge button is also used by recreational divers to inflate a delayed surface marker buoy or lifting bag. Any time that the purge button is operated, the diver must be aware of the potential for a freeflow and be ready to deal with it.
It may be desirable for the diver to have some manual control over the flow characteristics of the demand valve. The usual adjustable aspects are cracking pressure and the feedback from flow rate to internal pressure of the second stage housing. The inter-stage pressure of surface supplied demand breathing apparatus is controlled manually at the control panel, and does not automatically adjust to the ambient pressure in the way that most scuba first stages do, as this feature is controlled by feedback to the first stage from ambient pressure. This has the effect that the cracking pressure of a surface supplied demand valve will vary slightly with depth, so some manufacturers provide a manual adjustment knob on the side of the demand valve housing to adjust spring pressure on the downstream valve, which controls the cracking pressure. The knob is known to commercial divers as "dial-a-breath". A similar adjustment is provided on some high-end scuba demand valves, to allow the user to manually tune the breathing effort at depth: 17
Scuba demand valves which are set to breathe lightly (low cracking pressure, and low work of breathing) may tend to free-flow relatively easily, particularly if the gas flow in the housing has been designed to assist in holding the valve open by reducing the internal pressure. The cracking pressure of a sensitive demand valve is often less than the hydrostatic pressure difference between the inside of an air-filled housing and the water below the diaphragm when the mouthpiece is pointed upwards. To avoid excessive loss of gas due to inadvertent activation of the valve when the DV is out of the diver's mouth, some second stages have a desensitising mechanism which causes some back-pressure in the housing, by impeding the flow or directing it against the inside of the diaphragm.: 21
=== Twin-hose demand regulators ===
The "twin", "double" or "two" hose configuration of scuba demand valve was the first in general use. This type of regulator has two large bore corrugated breathing tubes. One tube is to supply air from the regulator to the mouthpiece, and the second tube delivers the exhaled gas to a point near the demand diaphragm where the ambient pressure is the same, and where it is released through a rubber duck-bill one-way valve, to escape out of the holes in the cover. Advantages of this type of regulator are that the bubbles leave the regulator behind the diver's head, increasing visibility, reducing noise and producing less load on the diver's mouth, They remain popular with some underwater photographers and Aqualung brought out an updated version of the Mistral in 2005.
The mechanism of the twin hose regulator is packaged in a usually circular metal housing mounted on the cylinder valve behind the diver's neck. The demand valve component of a two-stage twin hose regulator is thus mounted in the same housing as the first stage regulator, and in order to prevent free-flow, the exhaust valve must be located at the same depth as the diaphragm, and the only reliable place to do this is in the same housing. The air flows through a pair of corrugated rubber hoses to and from the mouthpiece. The supply hose is connected to one side of the regulator body and supplies air to the mouthpiece through a non-return valve, and the exhaled air is returned to the regulator housing on the outside of the diaphragm, also through a non-return valve on the other side of the mouthpiece and usually through another non-return exhaust valve in the regulator housing - often a "duckbill" type.
A non-return valve is usually fitted to the breathing hoses where they connect to the mouthpiece. This prevents any water that gets into the mouthpiece from going into the inhalation hose, and ensures that once it is blown into the exhalation hose that it cannot flow back. This slightly increases the flow resistance of air, but makes the regulator easier to clear.: 341
Ideally the delivered pressure is equal to the resting pressure in the diver's lungs as this is what human lungs are adapted to breathe. With a twin hose regulator behind the diver at shoulder level, the delivered pressure changes with diver orientation. if the diver rolls on his or her back the released air pressure is higher than in the lungs. Divers learned to restrict flow by using their tongue to close the mouthpiece. When the cylinder pressure was running low and air demand effort rising, a roll to the right side made breathing easier. The mouthpiece can be purged by lifting it above the regulator (shallower), which will cause a free flow.: 341 Twin hose regulators have been superseded almost completely by single hose regulators and became obsolete for most diving since the 1980s. Raising the mouthpiece above the regulator increases the delivered pressure of gas and lowering the mouthpiece reduces delivered pressure and increases breathing resistance. As a result, many aqualung divers, when they were snorkeling on the surface to save air while reaching the dive site, put the loop of hoses under an arm to avoid the mouthpiece floating up causing free flow.
The original twin-hose regulators usually had no ports for accessories, though some had a high pressure port for a submersible pressure gauge. Some later models have one or more low-pressure ports between the stages, which can be used to supply direct feeds for suit or BC inflation and/or a secondary single-hose demand valve, and a high pressure port for a submersible pressure gauge. The new Mistral is an exception as it is based on the Aqualung Titan first stage. which has the usual set of ports.
Some early twin hose regulators were of single-stage design. The first stage functions in a way similar to the second stage of two-stage demand valves, but would be connected directly to the cylinder valve and reduced high pressure air from the cylinder directly to ambient pressure on demand. This could be done by using a longer lever and larger diameter diaphragm to control the valve movement, but there was a tendency for cracking pressure, and thus work of breathing, to vary as the cylinder pressure dropped.
The twin-hose arrangement with a bite-grip mouthpiece or full-face mask is common in rebreathers, but as part of the breathing loop, not as part of a regulator. The associated demand valve comprising the open-circuit bail-out valve is a second stage single hose regulator.
== Performance ==
The breathing performance of regulators is a measure of the ability of a breathing gas regulator to meet the demands placed on it at varying ambient pressures and under varying breathing loads, for the range of breathing gases it may be expected to deliver. Performance is an important factor in design and selection of breathing regulators for any application, but particularly for underwater diving, as the range of ambient operating pressures and variety of breathing gases is broader in this application. It is desirable that breathing from a regulator requires low effort even when supplying large amounts of breathing gas as this is commonly the limiting factor for underwater exertion, and can be critical during diving emergencies. It is also preferable that the gas is delivered smoothly without any sudden changes in resistance while inhaling or exhaling. Although these factors may be judged subjectively, it is convenient to have a standard by which the many different types and manufactures of regulators may be compared.
The original Cousteau twin-hose diving regulators could deliver about 140 litres of air per minute at continuous flow and that was officially thought to be adequate, but divers sometimes needed a higher instantaneous rate and had to learn not to "beat the lung", i.e. to breathe faster than the regulator could supply. Between 1948 and 1952 Ted Eldred designed his Porpoise single hose regulator to supply up to 300 liters per minute.
Various breathing machines have been developed and used for assessment of breathing apparatus performance. ANSTI Test Systems Ltd (UK) has developed a testing machine that measures the inhalation and exhalation effort in using a regulator at all realistic water temperatures. Publishing results of the performance of regulators in the ANSTI test machine has resulted in big performance improvements.
At higher gas densities associated with greater depth and pressure, breathing may be physiologically limited by the capacity of the diver to move gas through the breathing passages of the lungs against dynamic airway compression.
=== Ergonomics ===
Several factors affect the comfort and effectiveness of diving regulators. Work of breathing has been mentioned, and can be critical to diver performance under high workload and when using dense gas at depth.
Mouth-held demand valves may exert forces on the teeth and jaws of the user that can lead to fatigue and pain, occasionally repetitive stress injury, and early rubber mouthpieces often caused an allergic reaction of contact surfaces in the mouth, which has been largely eliminated by the use of hypoallergenic silicone rubber. Various designs of mouthpiece have been developed to reduce this problem. The feel of some mouthpieces on the palate can induce a gag reflex in some divers, while in others it causes no discomfort. The style of the bite surfaces can influence comfort and various styles are available as aftermarket accessories. Personal testing is the usual way to identify what works best for the individual, and in some models the grip surfaces can be moulded to better fit the diver's bite. The lead of the low-pressure hose can also induce mouth loads when the hose is of an unsuitable length or is forced into small radius curves to reach the mouth. This can usually be avoided by careful adjuctment of hose lead and sometimes a different hose length.
Regulators supported by helmets and full-face masks eliminate the load on the lips, teeth and jaws, but add mechanical dead space, which can be reduced by using an orinasal inner mask to separate the breathing circuit from the rest of the interior air space. This can also help reduce fogging of the viewport, which can seriously restrict vision. Some fogging will still occur, and a means of defogging is necessary. The internal volume of a helmet or full-face mask may exert unbalanced buoyancy forces on the diver's neck, or if compensated by ballast, weight loads when out of the water. The material of some orinasal mask seals and full-face mask skirts can cause allergic reactions, but newer models tend to use hypoallegenic materials and are seldom a problem.
=== Malfunctions and failure modes ===
Most regulator malfunctions involve improper supply of breathing gas or water leaking into the gas supply. There are two major gas supply failure modes, where the regulator shuts off delivery, which is extremely rare, and free-flow, where the delivery will not stop and can quickly exhaust a scuba supply. Various lesser malfunctions mostly involve partial reductions in supply, non-catastrophic leaks, and ergonomic faults that make the regulator difficult, uncomfortable, or dangerous to use. Some malfunctions can be quickly and easily corrected by the user if they know what to do, others may require professional servicing, troubleshooting, or replacement of parts. Some may simply be the consequence of using it beyond its specified operating range.
Inlet filter blockage
The inlet to the first stage is usually protected by a filter to prevent corrosion products or other contaminants in the cylinder from getting into the fine between moving parts of the first and second stage and jamming them, either open or closed. If enough dirt gets into these filters, they themselves can be blocked sufficiently to reduce performance, but are unlikely to result in a total or sudden catastrophic failure. Sintered bronze filters can also gradually clog with corrosion products if they get wet. Inlet filter blockage will become more noticeable as the cylinder pressure drops or depth increases.
Sticking valves
The moving parts in first and second stages have fine tolerances in places, and some designs are more susceptible to contaminants causing friction between the moving parts. this may increase cracking pressure, reduce flow rate, increase work of breathing or induce free-flow, depending on what part is affected.
Free-flow
Either of the stages may get stuck in the open position, causing a continuous flow of gas from the regulator known as a free-flow. This can be triggered by a range of causes, some of which can be easily remedied, others not. Possible causes include incorrect interstage pressure setting, incorrect second stage valve spring tension, damaged or sticking valve poppet, damaged valve seat, valve freezing, wrong sensitivity setting at the surface and in Poseidon servo-assisted second stages, low interstage pressure.
Freezing
In cold conditions the cooling effect of gas expanding through a valve orifice may cool either first or second stage sufficiently to cause ice to form. External icing may lock up the spring and exposed moving parts of first or second stage, and freezing of moisture in the stored gas may cause icing on internal surfaces. Either may cause the moving parts of the affected stage to jam open or closed. If the valve freezes closed, it will usually defrost quite rapidly and start working again, and may freeze open soon after. Freezing open is more of a problem, as the valve will then free-flow and cool further in a positive feedback loop, which can normally only be stopped by closing the cylinder valve and waiting for the ice to thaw. If not stopped, the cylinder will rapidly be emptied.
Intermediate pressure creep
This is a slow leak of the first stage valve, often caused by a worn, damaged or dirty valve seat. The effect is for the interstage pressure to rise until either the next breath is drawn, or the pressure exerts more force on the second stage valve than can be resisted by the spring, and the valve opens briefly, often with a popping sound, to relieve the pressure. the frequency of the popping pressure relief depends on the flow in the second stage, the back pressure, the second stage spring tension and the magnitude of the leak. It may range from occasional loud pops to a constant hiss.
Gas leaks
Gas leaks can be caused by burst or leaky hoses, defective or blown o-rings, particularly in yoke connectors, loose connections, and several of the previously listed malfunctions. Low pressure inflation hoses may fail to connect properly, or the non-return valve may leak.: 185 A relatively common o-ring failure occurs when the yoke clamp seal extrudes due to insufficient clamp force or elastic deformation of the clamp by impact with the surroundings.
Wet breathing
Wet breathing is caused by water getting into the regulator and compromising breathing comfort and safety. Water can leak into the second stage body through damaged soft parts like torn mouthpieces, damaged exhaust valves and perforated diaphragms, through cracked housings, or through poorly sealing or fouled exhaust valves.
Excessive work of breathing
High work of breathing can be caused by high inhalation resistance, high exhalation resistance or both. High inhalation resistance can be caused by high cracking pressure, low inter-stage pressure, friction in second stage valve moving parts, excessive spring loading, or sub-optimum valve design. It can usually be improved by servicing and tuning, but some regulators cannot deliver high flow at great depths without high work of breathing. High exhalation resistance is usually due to a problem with the exhaust valves, which can stick, stiffen due to deterioration of the materials, or may have an insufficient flow passage area for the service. Work of breathing increases with gas density, and therefore with depth. Total work of breathing for the diver is a combination of physiological work of breathing and mechanical work of breathing. It is possible for this combination to exceed the capacity of the diver, who can then suffocate due to carbon dioxide toxicity.
Juddering, shuddering and moaning
This is caused by an irregular and unstable flow from the second stage, It may be caused by an unstable feedback between flow rate in the second stage body and diaphragm deflection opening the valve, which is not sufficient to cause free-flow, but enough to cause the system to hunt. Juddering may also be caused by excessive but irregular friction of valve moving parts.
Physical damage to the housing or components
Damage such as cracked housings, torn or dislodged mouthpieces, damaged exhaust fairings, can cause gas flow problems or leaks, or can make the regulator uncomfortable to use or difficult to breathe from. Use of a contaminated or non-compatible regulator with high oxygen fraction gas at high pressure can lead to internal ignition, which may merely destroy a seal or other minor component, or burn up a significant part of the equipment and surroundings.
== Accessories and special features ==
A variety of accessories may be fitted to most diving regulators, some of which are considered standard equipment. Many of them are attached to a port on the first stage. Two types of port are provided – high pressure ports for pressure measurement, with a 7/16" UNF thread and O-ring seal, and low-pressure ports to supply gas to the accessory, which are usually 3/8" UNF with O-ring seal, but a few models used 1/2" UNF for the primary regulator. When not used these ports are sealed by screw-in plugs.
=== Anti-freezing modification ===
As gas leaves the cylinder it decreases in pressure in the first stage, becoming very cold due to adiabatic expansion. Where the ambient water temperature is less than 5 °C any water in contact with the regulator may freeze. If this ice jams the diaphragm or piston spring, preventing the valve closing, a free-flow may ensue that can empty a full cylinder within a minute or two, and the free-flow causes further cooling in a positive feedback loop. Generally the water that freezes is in the ambient pressure chamber around a spring that keeps the valve open and not moisture in the breathing gas from the cylinder, but that is also possible if the air is not adequately filtered. The modern trend of using plastics to replace metal components in regulators encourages freezing because it insulates the inside of a cold regulator from the warmer surrounding water. Some regulators are provided with heat exchange fins in areas where cooling due to air expansion is a problem, such as around the second stage valve seat on some regulators.
Cold water kits can be used to reduce the risk of freezing inside the regulator. Some regulators come with this as standard, and some others can be retrofitted. Environmental sealing of the diaphragm main spring chamber using a soft secondary diaphragm and hydrostatic transmitter: 195 or a silicone, alcohol or glycol/water mixture antifreeze liquid in the sealed spring compartment can be used for a diaphragm regulator. Silicone grease in the spring chamber can be used on a piston first stage. The Poseidon Xstream first stage insulates the external spring and spring housing from the rest of the regulator, so that it is less chilled by the expanding air, and provides large slots in the housing so that the spring can be warmed by the water, thus avoiding the problem of freezing up the external spring.
Kirby Morgan have developed a stainless steel tube heat exchanger ("Thermo Exchanger") to warm the gas from the first stage regulator to reduce the risk of second stage scuba regulator freeze when diving in extremely cold water at temperatures down to −2.2 °C (28.0 °F). The length and relatively good thermal conductivity of the tubing, and the thermal mass of the block allows sufficient heat from the water to warm the air to within one to two degrees of the surrounding water.
=== Shut-off valve ===
Some divers install a sliding sleeve type shut-off valve between the low-pressure hose and the demand valve, so they can shut off the flow to a free-flowing second stage, usually when it ices up. This prevents the pressure relief function of the second stage, so a pressure relief valve must be fitted to the first stage to prevent the hose from bursting as pressure increases. Interstage pressure can rise to cylinder pressure if the first stage does not seal.
=== Pressure relief valve ===
A downstream demand valve serves as a fail safe for over-pressurization: if a first stage with a demand valve malfunctions and jams in the open position, the demand valve will be over-pressurized and will "free flow". Although it presents the diver with an imminent "out of air" crisis, this failure mode lets gas escape directly into the water without inflating buoyancy devices. The effect of unintentional inflation might be to carry the diver quickly to the surface causing the various injuries that can result from an over-fast ascent. There are circumstances where regulators are connected to inflatable equipment such as a rebreather's breathing bag, a buoyancy compensator, or a drysuit, but without the need for demand valves. Examples of this are argon suit inflation sets and "off board" or secondary diluent cylinders for closed-circuit rebreathers. When no demand valve is connected to a regulator, it should be equipped with a pressure relief valve, unless it has a built in over pressure valve, so that over-pressurization does not inflate any buoyancy devices connected to the regulator or burst the low-pressure hose.
=== Pressure monitoring ===
A scuba regulator first stage has one or two high pressure ports upstream of all pressure-reducing valves to monitor the gas pressure remaining in the diving cylinder, provided that the valve is open. The standard connection is an O-ring sealed 7/16" UNF inside thread. There are several types of pressure gauge.
==== Standard submersible pressure gauge ====
The standard arrangement has a high pressure hose leading to a submersible pressure gauge (SPG) (also called a contents gauge). This is an analog mechanical gauge, usually with a Bourdon tube mechanism. It displays with a pointer moving over a dial, usually about 50 millimetres (2.0 in) diameter. Sometimes they are mounted in a console, which is a plastic or rubber case that holds the breathing gas pressure gauge and other instruments such as a depth gauge, dive computer and/or compass.
The high pressure port usually has 7/16"-20 tpi UNF internal thread with an O-ring seal. This makes it impossible to connect a low pressure hose to the high pressure port. Early regulators occasionally used other thread sizes, including 3/8" UNF and 1/8" BSP (Poseidon Cyklon 200), and some of these allowed connection of low-pressure hose to high pressure port, which is dangerous with an upstream valve second stage or a BC or dry suit inflation hose, as the hose could burst under pressure.
==== High pressure hose ====
The high pressure hose is a small bore flexible hose with permanently swaged end fittings that connects the submersible pressure gauge to the HP port of the regulator first stage. The HP hose end that fits the HP port usually has a very small bore orifice to restrict flow. This both reduces shock loads on the pressure gauge when the cylinder valve is opened, and reduces the loss of gas through the hose if it bursts or leaks for any reason. This tiny hole is vulnerable to blocking by corrosion products if the regulator is flooded, or by dust particles or corrosion products from a contaminated cylinder.: 185 At the other end of the hose the fitting to connect to the SPG usually has a swivel, allowing the gauge to be rotated on the hose under pressure. The seal between hose and gauge uses a small component generally referred to as a spool, which seals with an O-ring at each end that fits into the hose end and gauge with a barrel seal. This swivel can leak if the O-rings deteriorate, which is quite common, particularly with oxygen-rich breathing gas. The failure is seldom catastrophic, but the leak will get worse over time.: 185 High pressure hose lengths vary from about 150 millimetres (6 in) for sling and side-mount cylinders to about 750 millimetres (30 in) for back mounted scuba. Other lengths may be available off the shelf or made to order for special applications such as rebreathers or back mount with valve down.
==== Button gauges ====
These are coin-sized analog pressure gauges directly mounted to a high-pressure port on the first stage. They are compact, have no dangling hoses, and few points of failure. They are generally not used on back mounted cylinders because the diver cannot see them there when underwater. They are sometimes used on side slung stage cylinders. Due to their small size, it can be difficult to read the gauge to a resolution of less than 20 bars (300 psi). As they are rigidly mounted to the first stage there is no flexibility in the connection, and they may be vulnerable to impact damage.
==== Air integrated computers ====
Some dive computers are designed to measure, display, and monitor pressure in the diving cylinder. This can be very beneficial to the diver, but if the dive computer fails the diver can no longer monitor his or her gas reserves. Most divers using a gas-integrated computer will also have a standard air pressure gauge, though, the SPG and hose have several potential points of failure. The computer is either connected to the first stage by a high pressure hose, or has two parts - the pressure transducer on the first stage and the display at the wrist or console, which communicate by wireless data transmission link; the signals are encoded to eliminate the risk of one diver's computer picking up a signal from another diver's transducer or radio interference from other sources. Some dive computers can receive a signal from more than one remote pressure transducer. The Ratio iX3M Tech and others can process and display pressures from up to 10 transmitters.
=== Handedness ===
Almost all single hose demand regulators are designed to be used with the hose approaching the mouth from the right hand side. In this orientation the exhaust ports are at the lowest point and drainage is effective. There are a few models, notably those made by Poseidon Diving Systems AB, but historically also from other manufacturers, which have side exhausts and work equally well in either orientation. In effect they have no functional top or bottom. They are more sensitive to lateral tilt, which can affect drainage, but is seldom a problem in practice. A few earlier models were left handed, and at least one Apeks model can be modified for left handed use by rebuilding using the original components. The Mares Loop 15x is unique in having the low pressure hose enter the second stage from the bottom, which allows it to be used with the hose routed under either arm.
=== Secondary demand valve (Octopus) ===
As a nearly universal standard practice in modern recreational diving, the typical single-hose regulator has a second demand valve fitted for emergency use, mainly for the diver's buddy, typically referred to as the octopus because of the extra hose, or secondary demand valve. The origins of the secondary demand valve are obscure, and it may have been independently invented several times, but it was used by Dave Woodward at UNEXSO around 1965–6 to support the freedive attempts of Jacques Mayol. Woodward believed that having the safety divers carry two second stages would be a safer and more practical approach than buddy breathing in the event of an emergency.
The secondary demand valve can be a hybrid of a demand valve and a buoyancy compensator inflation valve. Both types may be called alternate air sources. When the secondary demand valve is integrated with the buoyancy compensator inflation valve, since the inflation valve hose is short (usually just long enough to reach mid-chest), in the event of a diver running out of air, the diver with air remaining would give their primary second stage to the out-of-air diver, and switch to their own integrated inflation valve.
A demand valve on a regulator connected to a separate independent diving cylinder can also be called an alternate air source, and is also a fully redundant air source, as it is totally independent of the primary air source, which has safety advantages.
==== Configuration ====
The low pressure hose on the secondary demand valve is usually longer than the low pressure hose on the primary DV that the diver uses, and the secondary DV and/or its hose may be colored yellow to aid in locating it in an emergency. The secondary regulator should be clipped to the diver's harness in a position where it can be easily seen and reached by both the diver and the potential sharer of air, with a breakaway connection. The longer hose is used for convenience when sharing air, so that the divers are not forced to stay in an awkward position relative to each other. Technical divers frequently extend this feature and use a 5-foot or 7-foot (1.5 m or 2 m) hose, which allows divers to swim in single file while sharing air, which may be necessary in restricted spaces inside wrecks or caves.
In the most common recreational configuration, divers wear the secondary demand valve on the right side, ready for rapid deployment if the buddy runs out of breathing gas. According to an article on the Divers Alert website, the arrangement was originally for the secondary DV to be worn and be deployed on the left side, which allows a standard right handed DV to be used by the recipient without a reverse bend in the hose, which takes maximum advantage of hose length. There is little reliable documentation on whether this was the case, and if so, why it was changed. A comparison of the left and right mountings with reference to the primary function as an emergency gas supply shows some ergonomic advantages the left mount option. These comparisons do not apply with the long hose and necklace or with BCD inflator integrated systems, or with DVs with side exhaust which work upside down.
Advantages claimed for the left side mounting are: It is easier to hand off to another diver, using the left hand, and leaving the right hand free, it does not put an additional bend in the hose, which makes better use of the available length, and gives a smooth unstressed lead for face to face sharing and receiver to the left parallel positioning. Face to face positioning allows eye contact, which is useful during ascent, and side by side is useful if the return requires horizontal travel. The purge button is more accessible to the rescuer, as it is on the thumb side of the donating hand. Disadvantages are that it is an awkward arrangement if the diver needs to use it themself, as the hose then needs to be routed round the back of the head, or it may develop a tight bend putting stress on the jaw. It may also lead to confusion if the receiver has only been exposed to right handed donation.
=== Mouthpiece ===
The mouthpiece is a part that the user grips in the mouth to make a watertight seal. It is a short flattened-oval tube that goes in between the lips, with a curved flange that fits between the lips and the teeth and gums, and seals against the inner surface of the lips. On the inner ends of the flange there are two tabs with enlarged ends, which are gripped between the teeth. These tabs also keep the teeth apart sufficiently to allow comfortable breathing through the gap. Most recreational diving regulators are fitted with a mouthpiece. In twin-hose regulators and rebreathers, "mouthpiece" may refer to the whole assembly between the two flexible tubes. A mouthpiece prevents clear speech, so a full-face mask is preferred where voice communication is needed.
In a few models of scuba regulator the mouthpiece also has an outer rubber flange that fits outside the lips and extends into two straps that fasten together behind the neck.: 184 This helps to keep the mouthpiece in place if the user's jaws go slack through unconsciousness or distraction. The mouthpiece safety flange may also be a separate component.: 154 The attached neck strap also allows the diver to keep the regulator hanging under the chin where it is protected and ready for use. Recent mouthpieces do not usually include an external flange, but the practice of using a neck strap has been revived by technical divers who use a bungee or surgical rubber "necklace" which can come off the mouthpiece without damage if pulled firmly.
The original mouthpieces were usually made from natural rubber and could cause an allergic reaction in some divers. This has been overcome by the use of hypo-allergenic synthetic elastomers such as silicone rubbers.
=== Swivel hose adaptors ===
Adaptors are available to modify the lead of the low pressure hose where it attaches to the demand valve. There are adaptors which provide a fixed angle and those which are variable while in use. Other swivel adaptors are made to be fitted between the low pressure hose and low pressure port on the first stage to provide hose leads otherwise not possible for the specific regulator. As with all additional moving parts, they are an additional possible point of failure, so should only be used where there is sufficient advantage to offset this risk. They are mainly useful to improve the hose lead on regulators used with sidemount and sling mounted cylinders.
=== Full-face mask or helmet ===
This is stretching the concept of accessory a bit, as it would be equally valid to call the regulator an accessory of the full face mask or helmet, but the two items are closely connected and generally found in use together.
Most full face masks and probably most diving helmets currently in use are open circuit demand systems, using a demand valve (in some cases more than one) and supplied from a scuba regulator or a surface supply umbilical from a surface supply panel using a surface supply regulator to control the pressure of primary and reserve air or other breathing gas.
Lightweight demand diving helmets are almost always surface supplied, but full face masks are used equally appropriately with scuba open circuit, scuba closed circuit (rebreathers), and surface supplied open circuit.
The demand valve is usually firmly attached to the helmet or mask, but there are a few models of full face mask that have removable demand valves with quick connections allowing them to be exchanged under water. These include the Dräger Panorama and Kirby-Morgan 48 Supermask.
==== Positive pressure ====
For some applications it is desirable for the gas inside the mask or helmet to remain at a pressure slightly above ambient at all times while in the water, as this will prevent any contamination from leaking into the gas space during inhalation if the face or neck seal, or the exhaust valve system, does not seal perfectly. In clean water such a leak is a minor problem, but leaks of contaminated water can be a hazard to health, and even life-threatening. A positive pressure inside a free-flow helmet is easily achieved by slightly increasing the opening pressure of the exhaust valve, provided it is adjustable, but for a demand system the cracking pressure of the demand valve must also be adjusted, so that it delivers gas before the internal pressure drops below external ambient pressure. This is not difficult, as a slight adjustment to second stage valve spring pressure is all that is required. The problem is that when the mask or helmet is off the diver, and the gas supply is pressurised, the demand valve will leak continuously, and a large amount of gas can be lost. The Interspiro Divator Mk II mask has a second stage regulator which has a manual lock on the demand valve to prevent free-flow when the mask is not in use, which unlocks when a breath is taken, and must be reset when the mask is taken off.
=== Buoyancy compensator and dry suit inflation hoses ===
Hoses may be fitted to low pressure ports of the regulator first stage to provide gas for inflating buoyancy compensators and/or dry suits. These hoses usually have a quick-connector end with an automatically sealing valve which blocks flow if the hose is disconnected from the buoyancy compensator or suit.: 50 There are two basic styles of connector, which are not compatible with each other. The high flow rate CEJN 221 fitting has a larger bore and allows gas flow at a fast enough rate for use as a connector to a demand valve. This is sometimes seen in a combination BC inflator/deflator mechanism with integrated secondary DV (octopus), such as in the AIR II unit from Scubapro. The low flow rate Seatec connector is more common and is the industry standard for BC inflator connectors, and is also popular on dry suits, as the limited flow rate reduces the risk of a blow-up if the valve sticks open. The high flow rate connector is used by some manufacturers on dry suits.
Various minor accessories are available to fit these hose connectors. These include interstage pressure gauges, which are used to troubleshoot and tune the regulator (not for use underwater), noisemakers, used to attract attention underwater and on the surface, and valves for inflating tires and inflatable boat floats, making the air in a scuba cylinder available for other purposes.
=== Instrument consoles ===
Also called combo consoles, these are usually hard rubber or tough plastic moldings which enclose the submersible pressure gauge and have mounting sockets for other diver instrumentation, such as decompression computers, underwater compass, timer and/or depth gauge and occasionally a small plastic slate on which notes can be written either before or during the dive. These instruments would otherwise be carried somewhere else such as strapped to the wrist or forearm or in a pocket and are only regulator accessories for convenience of transport and access, and at greater risk of damage during handling.
=== Automatic closure device ===
The auto-closure device (ACD) is a mechanism for closing off the inlet opening of a regulator first stage when it is disconnected from a cylinder. A spring-loaded plunger in the inlet is mechanically depressed by contact with the cylinder valve when the regulator is fitted to the cylinder, which opens the port through which air flows into the regulator. In the normally closed condition when not mounted, this valve prevents ingress of water and other contaminants to the first stage interior which could be caused by negligent handling of the equipment or by accident. This is claimed by the manufacturer to extend the service life of the regulator and reduce risk of failure due to internal contamination. However, it is possible for an incorrectly installed ACD to shut off gas supply from a cylinder still containing gas during a dive, and water or other contaminants held in the cylinder valve outlet will not be prevented from entering the first stage.
=== Breathing gas heating ===
Surface supplied divers operating for long periods in cold water, or using helium based breathing gas mixtures, commonly use a hot-water suit to maintain body temperature. Part of the water used to heat the suit can be routed through a water jacket (shroud) around part of the breathing gas supply tubing on the helmet, typically the metal tube between the bailout valve block and the demand valve inlet. This heats the gas just before delivery through the demand valve, and as a large part of body heat loss is in heating the inspired air to body temperature on every breath, which is proportional to breathing rate and gas density, this can reduce heat loss significantly on deep dives in cold water.
== Gas compatibility ==
=== Recreational scuba nitrox service ===
Standard air regulators are considered to be suitable for nitrox mixtures containing 40% or less oxygen by volume, both by NOAA, which conducted extensive testing to verify this, and by most recreational diving agencies.: 25
=== Surface supplied nitrox service ===
When surface supplied equipment is used the diver does not have the option of simply taking out the DV and switching to an independent system, and gas switching may be done during a dive, including use of pure oxygen for accelerated decompression. To reduce the risk of confusion or getting the system contaminated, surface supplied systems may be required to be oxygen clean for all services except straight air diving.
=== Oxygen service ===
Regulators to be used with pure oxygen and nitrox mixtures containing more than 40% oxygen by volume should use oxygen compatible components and lubricants, and be cleaned for oxygen service.
=== Helium service ===
Helium is an exceptionally nonreactive gas and breathing gases containing helium do not require any special cleaning or lubricants. However, as helium is generally used for deep dives, it will normally be used with high performance regulators, with low work of breathing at high ambient pressures when the gas is relatively dense.
== Manufacturers and their brands ==
Air Liquide: La Spirotechnique, Apeks and Aqua Lung
American Underwater Products (ROMI Enterprises, of San Leandro, Calif.): Aeris (scuba), which has merged with Oceanic in 2014.Hollis Gear and Oceanic Worldwide
Atomic Aquatics, American manufacturer of diving regulators and basic diving equipment. The company was acquired by Huish Outdoors in September 2011.
Beuchat – French manufacturer of underwater diving equipment
Cressi-Sub – Italian manufacturer of recreational diving and swimming equipment.
Dive Rite
Dräger – German manufacturer of breathing equipment
Halcyon Diving System
HTM Sports: Dacor and Mares
Poseidon Diving Systems AB
ScubaPro – American manufacturer of scuba equipment
Seac Sub
Tusa
Tecline
Zeagle
== See also ==
Breathing performance of regulators – Capacity of breathing regulators to function as specified
Built-in breathing system – System for supply of breathing gas on demand within a confined space
Diving helmet – Rigid head enclosure for underwater diving
Full-face diving mask – Diving mask that covers the mouth as well as the eyes and nose
Human factors in diving equipment design – Influence of the interaction between the user and the equipment on design
Mechanism of diving regulators – Arrangement and function of the components of regulators for underwater diving
== References ==
== External links ==
Rare Vintage Two Hose Regulators: images | Wikipedia/Regulator_malfunction |
The Underwater Offence (Turkish: Su Altı Taaruz), abbreviated SAT, is the special operations force of the Turkish Naval Forces. They are affiliated with the Naval Operation Directorate.
During wartime, these units are responsible for carrying out stealthy attacks, sabotage, and raids on enemy strategic facilities including those located under water, over water, on land, or in the air. They also target floating platforms. The SAT participates in coastal reconnaissance tasked with obtaining information on coastal areas before deploying forces and maintaining control over foreign ports and underwater areas.
== History ==
The first SAT course was conducted on 1962 in the city of Iskenderun, with its first trainees graduating in 1963. The original name of the SAT unit was Su Altı Komando (S.A.K.) ("Underwater Commando") and was bound to the Kurtarma ve Sualtı Komutanlığı (K.S.K.), or Rescue and Underwater Command.
In 1974 the SAT group command became bound to the Turkish Navy's General Command, and participated in the Turkish invasion of Cyprus later that year. They conducted the beach reconnaissance missions prior to the amphibious landing of the Turkish Armed Forces at Pentamili beach near Kyrnia (20 July 1974). Other publicised operations of SAT commandos are as follows:
SAT commandos took part in the Imia crisis in 1996.
In 2012, the SAT participated in Operation Ocean Shield, organized by NATO against piracy and rescued 7 Yemeni seafarers.
== Mission ==
The SAT's main tasks are:
Surveillance on enemy structures, facilities, defense systems or strategically relevant buildings.
Covert sabotage against naval units and/or enemy structures.
Covert landing and infiltration.
Reconnaissance on behind-the-beaches being considered for amphibious landing operations.
Determining secure landing paths.
Direct action during first wave of landing missions.
Counter-terrorism missions.
Close quarters combat.
== Training ==
To specialize in SAT, individuals must successfully complete the 50-week SAT (Marine Commando) course. The first phase of the course is eight weeks dedicated to physical and fitness development. Trainees who pass the rigorous physical and sea exams move on to the underwater phase, which lasts eight weeks. During this phase, they undergo frog-man training. After these phases are successfully completed, the land phase begins. In the land phase, it is called "hell week" after training on gaining a high level of land condition, swimming long distances in the water and getting on the boat, practicing VBSS, performing the task under pressure, getting rid of captivity, sea threats, long distance in the land, and finding targets. After intensive training, the land phase is completed. With these trainings, SAT specialists have the skills to sneak, sabotage and raid the enemy's coastal and floating targets. Then, the training mostly consists of tactical floating platforms and aircraft. SAT trainees will train for about 15 hours a day.
== Equipment ==
Underwater Offence Command specialists' equipment includes:
Handguns
SIG P226
Glock
Submachine Guns
CZ Scorpion Evo 3
H&K MP5A3
Assault Rifles
M4 carbine
Machine Guns
FN Minimi
M60
M134
Sniper Rifles
Barrett M82A1
Barrett M95
Remington XM2010
CheyTac Intervention
McMillan TAC-50
Rockets & Explosives
PSRL-1
RPG-7
M72 LAW
M203 grenade launcher
== Gallery ==
== References ==
== External links ==
Promotional/Training video of unit | Wikipedia/Underwater_Offence_(Turkish_Armed_Forces) |
The US Navy has used several decompression models from which their published decompression tables and authorized diving computer algorithms have been derived. The original C&R tables used a classic multiple independent parallel compartment model based on the work of John Scott Haldane in England in the early 20th century, using a critical ratio exponential ingassing and outgassing model. Later they were modified by O.D. Yarborough and published in 1937. A version developed by Des Granges was published in 1956. Further developments by M.W. Goodman and Robert D. Workman using a critical supersaturation approach to incorporate M-values, and expressed as an algorithm suitable for programming were published in 1965, and later again a significantly different model, the VVAL 18 exponential/linear model was developed by Edward D. Thalmann, using an exponential ingassing model and a combined exponential and linear outgassing model, which was further developed by Gerth and Doolette and published in Revision 6 of the US Navy Diving Manual as the 2008 tables.
Besides the air and heliox tables for open circuit bounce dives, the US Navy has published a variety of hyperbaric treatment schedules, decompression tables for open and closed circuit heliox and nitrox, tables incorporating surface decompression on oxygen, a system for modifying tables for use at high altitudes (Cross corrections), and saturation tables for various breathing gas mixtures. Many of these tables have been tested on human subjects, frequently with a result of symptomatic decompression sickness, and for this reason their test results are considered some of the most reliable available.
US Navy tables have generally been freely available for use by the general public, and have often been modified to further reduce risk, as commercial and recreational divers do not always fit the physical requirements for military divers, may not have a recompression chamber on site to manage decompression sickness on those occasions when it does occur, and may prefer to operate at a lower risk than military personnel. Several recreational diving tables were originally based on US Navy diving tables.
== C&R tables ==
In 1912, Chief Gunner George D. Stillson of the United States Navy created a program to test and refine Haldane's tables. This program ultimately led to the first publication of the United States Navy Diving Manual and the establishment of a Navy Diving School in Newport, Rhode Island. Diver training programs were later cut at the end of World War I.
The first decompression tables produced for the U.S. Navy were developed by the Bureau of Construction and Repair and published in 1915, and were consequently known as the C&R tables. They were derived from a Haldanean model, with oxygen decompression, to depths up to 300 ft on air, and were successfully used to depths of slightly over 300 ft: 3–1
== 1937 tables ==
1916 - UN Navy established its Deep Sea Diving School in Newport, Rhode Island.
1924 - US Navy published first US Navy Diving Manual.
1927 – Naval School, Diving and Salvage was re-established at the Washington Navy Yard. At that time the United States moved their Navy Experimental Diving Unit (NEDU) to the same naval yard. In the following years, the Experimental Diving Unit developed the US Navy Air Decompression Tables which became the accepted world standard for diving with compressed air.
1930's – J.A. Hawkins, C.W. Schilling and R.A. Hansen conducted extensive experimental dives to determine allowable supersaturation ratios for different tissue compartments for Haldanean model.: 3–2
1935 – Albert R. Behnke et al. experimented with oxygen for recompression therapy.
1937 – US Navy 1937 tables developed by O.D. Yarborough were published.: 3–2
== 1939 Heliox tables ==
In 1939, after the recovery of USS Squalus, tables were published for surface supplied Heliox diving.: 1–17
== 1956 tables ==
1956 – US Navy Decompression Tables developed by M. Des Granges (1956) were published.
1971 – In the US, the Williams-Steiger Occupational Safety and Health Act of 1970 triggered investigation of the safety of US Navy tables in reaction to an attempt to legislate their use for commercial diving.
1976 – Edward Beckman published findings of a comparison of US Navy air tables with RNPL, Buhlmann and other tables and indicating that the US Navy tables for diving below 100 fsw which were reputed to produce unacceptable rates of decompression sickness for civilian applications, were significantly less conservative than the other models in the comparison.
== Recompression tables ==
Although recompression and slow decompression were the accepted treatment, there was not yet a standard for either the recompression pressure or the rate of decompression. This changed when the first standard table for recompression treatment with air was published in the US Navy Diving Manual in 1924. These tables were not entirely successful - there was a 50% relapse rate, and the treatment, though fairly effective for mild cases, was less effective in serious cases.
1943 100-foot Air Treatment Table: Used for treatment of decompression sickness where relief is obtained at or less than 66 fsw.
1943 150-foot Air Treatment Table: Used for treatment of decompression sickness where relief is obtained at or less than 116 fsw.
1943 200-foot Air Treatment Table: Used for treatment of decompression sickness where relief is obtained at or less than 166 fsw.
1943 250-foot Air Treatment Table: Used for treatment of decompression sickness where relief is obtained at or less than 216 fsw.
1943 300-foot Air Treatment Table: Used for treatment of decompression sickness where relief is obtained at or less than 266 fsw.
1944 Long Air Recompression Treatment Table: Used for treatment of moderate to severe decompression sickness when oxygen is not available or the patient cannot tolerate the elevated oxygen partial pressure.
1944 Long Air Recompression Treatment Table with Oxygen: Used for treatment of moderate to severe decompression sickness when oxygen is available.
1944 Short Air Recompression Treatment Table: Used for treatment of mild decompression sickness when oxygen is not available or the patient cannot tolerate the elevated oxygen partial pressure.
1944 Short Oxygen Recompression Treatment Table: Used for treatment of mild decompression sickness.
Treatment Table 1: Used for treatment of pain only decompression sickness.
Air Treatment Table 1a: Used for treatment of pain only decompression sickness.
Treatment Table 2: Used for treatment of pain-only decompression sickness.
Air Treatment Table 2a: Used for treatment of pain only decompression sickness when oxygen cannot be used.
Air Treatment Table 3: Used as a last resort when oxygen is not available.
Treatment Table 4: Used for treatment of serious symptoms when oxygen can be used and symptoms are not relieved within 30 minutes at 165 fsw (50 msw).
Treatment Table 5: Use for treatment of pain-only decompression sickness when oxygen can be used and symptoms are relieved within 10 minutes at 60 ft.
Treatment Table 5a: Used for treatment of gas embolism when oxygen can be used and symptoms are relieved within 15 minutes at 165 fsw (50 msw).
Treatment Table 6: Used for treatment of pain-only decompression sickness when oxygen can be used and symptoms are not relieved within 10 minutes at 60 fsw (18 msw).
Treatment Table 6a: Used for treatment of gas embolism when oxygen can be used and symptoms moderate to a major extent within 30 minutes at 165 ft.
Treatment Table 7: Used for treatment of non-responding severe gas embolism or life-threatening decompression sickness. It is used when loss of life may result from decompression from 60 fsw. It is not used to treat residual symptoms that do not improve at 60 fsw, or to treat residual pain.
Treatment Table 8: Used mainly for treating deep uncontrolled ascents when more than 60 minutes of decompression have been omitted.
Treatment Table 9: Used for hyperbaric oxygen treatment as prescribed by Diving Medical Officer for residual symptoms after treatment for AGE/DCS. Also used for cases of carbon monoxide or cyanide poisoning, and smoke inhalation.
Treatment Table for decompression sickness occurring on saturation dives: One version used for treatment of decompression sickness manifested as musculoskeletal pains only, during decompression from saturation. Other version used for treatment of serious decompression sickness resulting from upward excursion.
In 1965, M.W. Goodman and Robert D. Workman introduced recompression tables using oxygen to accelerate elimination of inert gas.
== Saturation tables ==
Once all the tissue compartments have reached saturation for a given pressure and breathing mixture, continued exposure will not increase the gas loading of the tissues. From this point onward the required decompression remains the same. If divers work and live at pressure for a long period, and are decompressed only at the end of the period, the risks associated with decompression are limited to this single exposure. This principle has led to the practice of saturation diving, and as there is only one decompression, and it is done in the relative safety and comfort of a saturation habitat, the decompression is done on a very conservative profile, minimising the risk of bubble formation, growth and the consequent injury to tissues. A consequence of these procedures is that saturation divers are more likely to suffer decompression sickness symptoms in the slowest tissues, whereas bounce divers are more likely to develop bubbles in faster tissues.
Decompression from a saturation dive is a slow process. The rate of decompression typically ranges between 3 and 6 fsw (0.9 and 1.8 msw) per hour. The US Navy Heliox saturation decompression rates require a partial pressure of oxygen to be maintained at between 0.44 and 0.48 atm when possible, but not to exceed 23% by volume, to restrict the risk of fire.
For practicality the decompression is done in increments of 1 fsw at a rate not exceeding 1 fsw per minute, followed by a stop, with the average complying with the table ascent rate. Decompression is done for 16 hours in 24, with the remaining 8 hours split into two rest periods. A further adaptation generally made to the schedule is to stop at 4 fsw for the time that it would theoretically take to complete the decompression at the specified rate, i.e. 80 minutes, and then complete the decompression to surface at 1 fsw per minute. This is done to avoid the possibility of losing the door seal at a low pressure differential and losing the last hour or so of slow decompression.
== U.S. Navy E-L algorithm and the 2008 tables ==
In 1983, Edward D. Thalmann published the E-L model for constant PO2 nitrox and heliox closed circuit rebreathers, in 1984 published U.S. Navy Exponential-Linear algorithm and tables for constant PO2 Nitrox closed circuit rebreather (CCR) applications, and in 1985 Thalmann extended use of the E-L model for constant PO2 heliox closed circuit rebreathers.
In 2007, Wayne Gerth and David J. Doolette published VVal 18 and VVal 18M parameter sets for tables and programs based on the Thalmann E-L algorithm, and produced an internally compatible set of decompression tables for open circuit and CCR on air and nitrox, including in water air/oxygen decompression and surface decompression on oxygen.
In 2008 the US Navy Diving Manual Revision 6 was published, which includes a version of the 2007 tables by Gerth & Doolette. The air decompression tables in Revision 6 of the U.S. Navy Diving Manual combine decompression tables for air diving with schedules for decompression on air, air and in-water oxygen, and surface decompression using oxygen. The tables were computed using version VVal-18M of the Thalmann exponential-linear decompression model.
=== VVAL 18 algorithm ===
The Thalmann Algorithm (VVAL 18) is a deterministic decompression model originally designed in 1980 to produce a decompression schedule for divers using the US Navy Mk15 rebreather. It was developed by Capt. Edward D. Thalmann, MD, USN, who did research into decompression theory at the Naval Medical Research Institute, Navy Experimental Diving Unit, State University of New York at Buffalo, and Duke University. The algorithm forms the basis for the US Navy mixed gas and standard air dive tables published in US Navy Diving Manual Revisions 6 and 7. This decompression model is also referred to as the Linear–Exponential model or the Exponential–Linear model.
== US Navy Diving Manual Revision 7 ==
As of January 2023 the currently approved decompression tables are listed in Revision 7 of the US Navy Diving Manual.
== US Navy dive computers ==
In 1984 the US Navy diving computer (UDC) which was based on a 9 tissue model by Edward D. Thalmann of the Naval Experimental Diving Unit (NEDU), Panama City. Divetronic AG completed the UDC development – as it had been started by the chief engineer Kirk Jennings of the Naval Ocean System Center, Hawaii, and Thalmann of the NEDU – by adapting the Deco Brain for US Navy warfare use and for their 9-tissue MK-15 mixed gas model under a research and development contract with the US Navy.
In 2001, the US Navy approved the use of Cochran NAVY decompression computer with the VVAL 18 Thalmann algorithm for Special Warfare operations.
As of 2023, Shearwater Research has supplied dive computers to the US Navy with an exponential/linear algorithm bases on the Thalman algorithm since Cochran Undersea Technology closed down after the death of the owner. This algorithm is not as of 2024 available to the general public on Shearwater computers, although the algorithm is freely available and known to be lower risk than the Buhlmann algorithm for mixed gas and constant set-point CCR diving at deeper depths, which is the primary market for Shearwater products.
== Validation ==
It is important that any theory be validated by carefully controlled testing procedures. As testing procedures and equipment become more sophisticated, researchers learn more about the effects of decompression on the body. Initial research focused on producing dives that were free of recognizable symptoms of decompression sickness (DCS). With the later use of Doppler ultrasound testing, it was realized that bubbles were forming within the body even on dives where no DCI signs or symptoms were encountered. This phenomenon has become known as "silent bubbles".
The presence of venous gas emboli is considered a low specificity predictor of decompression sickness, but their absence is recognised to be a sensitive indicator of low risk decompression, therefore the quantitative detection of VGE is thought to be useful as an indicator of decompression stress when comparing decompression strategies, or assessing the efficiency of procedures.
The US Navy 1956 tables were based on limits determined by external DCS signs and symptoms. Later researchers were able to improve on this work by adjusting the limitations based on Doppler testing. However the US Navy CCR tables based on the Thalmann algorithm also used only recognisable DCS symptoms as the test criteria. Since the testing procedures are lengthy and costly, and there are ethical limitations on experimental work on human subjects with injury as an endpoint, it is common practice for researchers to make initial validations of new models based on experimental results from earlier trials. This has some implications when comparing models.: Ch10
== Cross altitude corrections ==
At altitude, atmospheric pressure is lower than at sea level, so surfacing at the end of an altitude dive leads to a greater relative reduction in pressure and an increased risk of decompression sickness compared to the same dive profile at sea level. The dives are also typically carried out in freshwater at altitude so it has a lower density than seawater used for calculation of decompression tables. The amount of time the diver has spent acclimatising at altitude is also of concern as divers with gas loadings near those of sea level may also be at an increased risk. The US Navy recommends waiting 12 hours following arrival at altitude before performing the first dive. The tissue supersaturation following an ascent to altitude can also be accounted for by considering it to be residual nitrogen and allocating a residual nitrogen group when using tables with this facility.
The most common of the modifications to decompression tables at altitude are the "Cross Corrections" which use a ratio of atmospheric pressure and sea level to that of the altitude to provide a conservative equivalent sea level depth. The procedure is described in detail in the U.S. Navy Diving Manual
== See also ==
History of decompression research and development
== References == | Wikipedia/US_Navy_decompression_models_and_tables |
Pierre Petit is not to be confused with (Jean) Pierre Yves-Petit (1886–1969), another French photographer who usually operated under the name Yvon.
Pierre Lanith Petit (15 August 1832 – 16 February 1909) was a French photographer. He is sometimes credited as Pierre Lamy Petit.
== Work ==
Petit learned photography in Paris in the workshop of André-Adolphe-Eugène Disdéri (1819–1889) (together with 76 other employees). In 1858, he opened his own workshop in Paris with Antoine René Trinquart, later to be called La Photographie des Deux Mondes. This proved to be very successful and workshops were opened in Baden-Baden and Marseille (in partnership with Emile Cazalis).
In his lifetime he made thousands of photographs. In 1908 he handed over the business to his son.
Some highlights in Petit's career:
He was the official photographer of the International Exposition of 1867.
He went to New York City several times to report on the construction of the Statue of Liberty.
Petit made many photographs of the Siege of Paris (1870–71).
In 1898, he made some attempts in underwater photography.
He exhibited many times at the Société française de photographie (SFP).
== Publications ==
Galerie des hommes de jour, a series of photographs of famous French people of the day, published in 1861
l’Episcopat français, clergé de Paris, a series of photographs of the clergy of Paris
== Museums ==
Museums that hold large collections of his photographs:
Musée Nicéphore-Niépce in Chalon-sur-Saône
Musée d'Orsay in Paris
National Library of France in Paris
National Portrait Gallery, London
== Photographs ==
=== Portraits ===
=== Others ===
== References ==
== External links ==
The Musée Nicéphore-Niépce website
Pierre Petit on the Luminous Lint website
Pierre Petit on the Getty Research Institute website
Pierre Petit on the J. Paul Getty Museum website
Websites showing photographs by Pierre Petit
Gallica, the BNF website
The Past to Present website
Pierre Petit on Flickr (from The Library of Nineteenth-Century Photography) | Wikipedia/Pierre_Petit_(photographer) |
The thermodynamic model was one of the first decompression models in which decompression is controlled by the volume of gas bubbles coming out of solution. In this model, pain only DCS is modelled by a single tissue which is diffusion-limited for gas uptake and bubble-formation during decompression causes "phase equilibration" of partial pressures between dissolved and free gases. The driving mechanism for gas elimination in this tissue is inherent unsaturation, also called partial pressure vacancy or the oxygen window, where oxygen metabolised is replaced by more soluble carbon dioxide. This model was used to explain the effectiveness of the Torres Straits Island pearl divers empirically developed decompression schedules, which used deeper decompression stops and less overall decompression time than the current naval decompression schedules. This trend to deeper decompression stops has become a feature of more recent decompression models.
== Concept ==
Brian A. Hills analysed the existing decompression hypotheses frequently referenced in the literature of the time, and identified three basic characteristics of comprehensive theoretical approaches to modeling decompression:
The number and composition of tissues involved;
A mechanism and controlling parameters for onset of identifiable symptoms;
A mathematical model for gas transport and distribution.
Hills found no evidence of discontinuity in the incidence of decompression symptoms for exposure/depth variations, which he interpreted as suggesting that either a single critical tissue or a continuous range of tissues are involved, and that correlation was not improved by assuming an infinite range of half times in a conventional exponential model. After later experimental work he concluded that the imminence of decompression sickness is more likely to be indicated by the quantity of gas separating from solution (the critical volume hypothesis) than its mere presence (as determined by a critical limit to supersaturation) and suggested that this implies that conventional (Haldanian) schedules are actually treating an asymptomatic gas phase in the tissues and not preventing the separation of gas from solution.
Efficient decompression will minimize the total ascent time while limiting the total accumulation of bubbles to an acceptable non-symptomatic critical value. The physics and physiology of bubble growth and elimination indicate that it is more efficient to eliminate bubbles while they are very small. Models which include bubble phase have produced decompression profiles with slower ascents and deeper initial decompression stops as a way of curtailing bubble growth and facilitating early elimination, in comparison with the models which consider only dissolved phase gas.
According to the thermodynamic model, the condition of optimum driving force for outgassing is satisfied when the ambient pressure is just sufficient to prevent phase separation (bubble formation). The fundamental difference of this approach is equating absolute ambient pressure with the total of the partial gas tensions in the tissue for each gas after decompression as the limiting point beyond which bubble formation is expected.
The model assumes that the natural unsaturation in the tissues due to metabolic reduction in oxygen partial pressure provides the buffer against bubble formation, and that the tissue may be safely decompressed provided that the reduction in ambient pressure does not exceed this unsaturation value. Clearly any method which increases the unsaturation would allow faster decompression, as the concentration gradient would be greater without risk of bubble formation.
The natural unsaturation, an effect variously known as the oxygen window, partial pressure vacancy and inherent unsaturation, increases with depth, so a larger ambient pressure differential is possible at greater depth, and reduces as the diver surfaces. This model leads to slower ascent rates and deeper first stops, but shorter shallow stops, as there is less bubble phase gas to be eliminated.
Natural unsaturation also increases with increase in partial pressure of oxygen in the breathing gas.
The thermodynamic model is based on the following assumptions:
Only one type of tissue is considered, which is the first type to present symptoms of decompression sickness. Other, non-symptomatic, tissues are disregarded as they do not present a problem.
The formation of bubble nuclei occurs randomly within the tissues, and at various levels of supersaturation.
Once a bubble nucleus has formed within a supersaturated tissue, dissolved gas in the tissue will diffuse through the bubble surface until equilibrium is reached between pressure in the bubble and concentration in the adjacent tissue.
Phase equilibration occurs within a few minutes.
Once bubbles have formed they have a tendency to coalesce, causing pressure on the tissues and nerves, which will eventually cause pain.
Once bubbles have formed, they are only eliminated by diffusion due to inherent unsaturation.
The requirement to maintain an ambient pressure high enough to prevent bubble growth leads to a significantly deeper first stop than the dissolved phase models which assume that bubbles do not form during asymptomatic decompression.
This model was a radical change from the traditional dissolved phase models. Hills was met with considerable skepticism and after several years of advocating two-phase models, eventually turned to other fields of research. Eventually, the work of other researchers provided enough impact to gain widespread acceptance for bubble models, and the value of Hills' research was recognised.
== Further development ==
The bubble models of decompression are a logical development from this model. The critical-volume criterion assumes that whenever the total volume of gas phase accumulated in the tissues exceeds a critical value, signs or symptoms of DCS will appear. This assumption is supported by doppler bubble detection surveys. The consequences of this approach depend strongly on the bubble formation and growth model used, primarily whether bubble formation is practicably avoidable during decompression.
This approach is used in decompression models which assume that during practical decompression profiles, there will be growth of stable microscopic bubble nuclei which always exist in aqueous media, including living tissues.
=== Varying Permeability Model ===
The Varying Permeability Model (VPM) is a decompression algorithm developed by D.E. Yount and others for use in professional and recreational diving. It was developed to model laboratory observations of bubble formation and growth in both inanimate and in vivo systems exposed to pressure. The VPM presumes that microscopic bubble nuclei always exist in water and tissues that contain water. Any nuclei larger than a specific "critical" size, which is related to the maximum dive depth will grow during decompression. The VPM aims to minimize the total volume of these growing bubbles by keeping the external pressure relatively large, and the inspired inert gas partial pressures low during decompression.
=== Reduced Gradient Bubble Model ===
The reduced gradient bubble model (RGBM) is a decompression algorithm developed by Dr Bruce Wienke. It is related to the Varying Permeability Model. but is conceptually different in that it rejects the gel-bubble model of the varying permeability model.
It is used in several dive computers, particularly those made by Suunto, Aqwary, Mares, HydroSpace Engineering, and Underwater Technologies Center. It is characterised by the following assumptions: blood flow (perfusion) provides a limit for tissue gas penetration by diffusion; an exponential distribution of sizes of bubble seeds is always present, with many more small seeds than large ones; bubbles are permeable to gas transfer across surface boundaries under all pressures; the haldanean tissue compartments range in half time from 1 to 720 minutes, depending on gas mixture.
== References == | Wikipedia/Thermodynamic_model_of_decompression |
Oceanography is a quarterly peer-reviewed scientific journal that publishes articles about ocean science and its applications. It is published by The Oceanography Society, a nonprofit professional society based in the United States.
In addition to its scientific articles, the journal also has a special section for news and information, society meeting reports, book reviews, and shorter editor-reviewed articles on public policy and education. One section, titled "Breaking Waves", is for short papers describing novel multidisciplinary approaches to oceanographic problems. The journal and all its back issues, dating to 1988, are available both in print and in full PDF format online in the journal website's archives. Oceanography is abstracted and indexed in the Science Citation Index Expanded. According to the Journal Citation Reports, the journal had an impact factor of 3.431 in 2019. In 2022, the journal had an h-index of 95.
Oceanography is a separate publication from The Journal of Oceanography, the journal of the Oceanographic Society of Japan.
== References ==
== External links ==
Official website | Wikipedia/Oceanography_(journal) |
Risk control, also known as hazard control, is a part of the risk management process in which methods for neutralising or reduction of identified risks are implemented. Controlled risks remain potential threats, but the probability of an associated incident or the consequences thereof have been significantly reduced.
Risk control logically follows after hazard identification and risk assessment.
The most effective method for controlling a risk is to eliminate the hazard, but this is not always reasonably practicable. There is a recognised hierarchy of hazard controls which is listed in a generally descending order of effectiveness and preference:
Elimination - the complete removal or avoidance of the hazard also removes the risk.
Substitution - A less hazardous or lower risk material, equipment or process may be available.
Isolation - If the hazard can be separated from the people or equipment at risk by barriers or demarcated areas. the risk is reduced.
Safeguards - Tools or equipment, can be modified by fitting guards, interlocks and similar engineering solutions.
Procedural methods – Safer ways to do something.
Personal protective equipment and clothing (PPE) is the last resort.
A combination of two or more of these methods may be most effective, or even necessary.
== References == | Wikipedia/Risk_control |
The Space Systems Laboratory (SSL) is part of the Aerospace Engineering Department and A. James Clark School of Engineering at the University of Maryland in College Park, Maryland. The Space Systems Laboratory is centered on the Neutral Buoyancy Research Facility, a 50-foot-diameter (15 m), 25-foot-deep (7.6 m) neutral buoyancy pool used to simulate the microgravity environment of space. The only such facility housed at a university, Maryland's neutral buoyancy tank is used for undergraduate and graduate research at the Space Systems Lab. Research in Space Systems emphasizes space robotics, human factors, applications of artificial intelligence and the underlying fundamentals of space simulation. There are currently five robots being tested, including Ranger, a four-armed satellite servicing robot, and SCAMP, a six-degree of freedom free-flying underwater camera platform. Ranger was funded by NASA starting in 1992, and was to be a technological demonstration of orbital satellite servicing. NASA was never able to manifest it for launch and the program was defunded circa 2006. For example, Ranger development work at the SSL continues, albeit at a slower pace; Ranger was used to demonstrate robotic servicing techniques for NASA's proposed robotic Hubble Servicing Mission.
== History ==
The Space Systems Lab was founded at MIT in 1976, by faculty members Renee Miller and J.W. Mar. Its early studies in space construction techniques led to the EASE (Experimental Assembly of Structures in EVA) flight experiment which flew on Space Shuttle mission STS-61-B in 1985.
In 1990, lab director Dr. Dave Akin moved the lab to the University of Maryland. The Neutral Buoyancy Research Facility, or NBRF, was completed in 1992. Current projects include the MX-2 suit, a simplified neutral buoyancy spacesuit for use in EVA research; Power Glove, a prototype motorized spacesuit glove which will help reduce astronaut hand fatigue; and TSUNAMI, an apparatus to test human neuromuscular adaptation in different gravitational fields and different simulations of weightlessness.
== Partners ==
Along with labs at Carnegie Mellon and Stanford, the SSL is part of the Institute for Dexterous Space Robotics.
== References ==
== See also ==
Neutral Buoyancy Laboratory – NASA astronaut training facility in Houston, Texas
SPHERES – Free-flying robotic system | Wikipedia/Space_Systems_Laboratory_(Maryland) |
Haldane's decompression model is a mathematical model for decompression to sea level atmospheric pressure of divers breathing compressed air at ambient pressure that was proposed in 1908 by the Scottish physiologist, John Scott Haldane (2 May 1860 – 14/15 March 1936), who was also famous for intrepid self-experimentation.
Haldane prepared the first recognized decompression table for the British Admiralty in 1908 based on extensive experiments on goats and other animals using a clinical endpoint of symptomatic decompression sickness. The model, commented as "a lasting contribution to the diving world", was published in the Journal of Hygiene.
Haldane observed that goats, saturated to depths of 165 feet (50 m) of sea water, did not develop decompression sickness (DCS) if subsequent decompression was limited to half the ambient pressure. Haldane constructed schedules which limited the critical supersaturation ratio to "2", in five hypothetical body tissue compartments characterized by their halftime. Halftime is also termed Half-life when linked to exponential processes such as radioactive decay. Haldane's five compartments (halftimes: 5, 10, 20, 40, 75 minutes) were used in decompression calculations and staged decompression procedures for fifty years.
Previous theories to Haldane worked on "uniform compression", as Paul Bert pointed in 1878 that very slow decompression could avoid the caisson disease, then Hermann von Schrötter proposed in 1895 the safe "uniform decompression" rate to be of "one atmosphere per 20 minutes". Haldane in 1907 worked on "staged decompression" – decompression using a specified relatively rapid ascent rate, interrupted by specified periods at constant depth – and proved it to be safer than "uniform decompression" at the rates then in use, and produced his decompression tables on that basis.
== Previous work ==
=== Paul Bert ===
Paul Bert (17 October 1833 – 11 November 1886) was a French physiologist who graduated at Paris as doctor of medicine in 1863, and doctor of science in 1866. He was appointed professor of physiology successively at Bordeaux (1866) and the Sorbonne (1869). Paul Bert was given the nickname of "Father of Aviation Medicine" after his work, La Pression barometrique (1878), a comprehensive investigation on the physiological effects of air-pressure, which pointed out that the symptoms of caisson disease could be avoided by means of very slow decompression. However, his work did not furnish data about safe decompression rates.
=== Schrötter ===
Anton Hermann Victor Thomas Schrötter (5 August 1870 – 6 January 1928), an Austrian physiologist and physician who was a native of Vienna, was a pioneer of aviation and hyperbaric medicine, and made important contributions in the study of decompression sickness. He studied medicine and natural sciences at the Universities of Vienna and Strasbourg, earning his medical degree in 1894, and during the following year receiving his doctorate of philosophy. He was active in many fields of medicine and physiology. His first interest from 1895 was the investigation and combating of caisson disease, and during his tenure in Nussdorf he studied the numerous diseases that have occurred and was looking for ways of treatment and prevention.
His published report in 1900 with Dr. Richard Heller and Dr. Wilhelm Mager, on air pressure disease is considered the basic German-language work of diving and hyperbaric medicine. Schrötter, Heller and Mager framed rules for safe decompression and believed that the decompression rate of one atmosphere (atm) per 20 minutes would be safe. Leonard Erskine Hill and Greenwood decompressed themselves without serious symptoms after exposure to 6 atm (610 kPa).
== Haldane's work ==
The Admiralty Committee needed to frame definite rules for safe decompression in the shortest possible time for deep diving, and hence, Haldane was commissioned in 1905 by the UK Royal Navy for this purpose, to design decompression tables for divers ascending from deep water.
In 1907 Haldane made a decompression chamber to help make deep-sea divers safer and produced the first decompression tables after extensive experiments with animals. In 1908 Haldane published the first recognized decompression table for the British Admiralty. His tables remained in use by the Royal Navy till 1955.
"The Prevention of Compressed Air Illness" was published in 1908 by Haldane, Boycott and Damant recommending staged decompression. These tables were accepted for use by the Royal Navy.
Haldane introduced the concept of half-times to model the uptake and release of nitrogen into the blood in different body tissues, and suggested five body tissue compartments with half times of 5, 10, 20, 40 and 75 minutes.
In his hypothesis, Haldane predicted that if the ascent rate does not allow the partial pressure of the inert gas (nitrogen) in each of the hypothetical tissues to exceed the environmental pressure by more than twice (2:1 ratio), then bubbles will not form in these tissues.
Basically this meant that one could ascend from a depth of 30 metres (100 ft) – an ambient pressure of 4 bars (60 psi) – to 10 metres (33 ft) (2 bars (29 psi)) or from 10 metres (33 ft) (2 bars (30 psi)) to the surface (1 bar (15 psi)) when saturated, without a decompression problem. To ensure this, a number of decompression stops were incorporated into the ascent tables.
The ascent rate and the fastest tissue in the model determine the time and depth of the first stop. Thereafter, the slower tissues determine when it is safe to ascend further.
=== Outline ===
Haldane ran his experiments on some animals, illustrating the difference between different kinds of animals such as goats, guinea-pigs, mice, rats, hens and rabbits, but his main work and results were done on goats and men.
Haldane stated in his paper: "In order to avoid the risk of bubbles being formed on decompression, it has hitherto been recommended that decompression should be slow and at as nearly a uniform rate throughout as possible. We must therefore carefully consider the process of desaturation of the body during slow and uniform decompression", hence the outline of his work is noted:
When humans or animals are placed in compressed air, the blood passing through lungs takes up an amount of gas in simple solution. This amount increases in proportion to the increase in partial pressure of each gas present in the alveolar air.
As regards to oxygen, the amount in simple solution in arterial blood will increase, but as soon as blood reaches body tissues, the extra dissolved oxygen will be used up so that venous blood will exhibit slight increase in partial pressure of oxygen.
As regards to carbon dioxide, the experiments of Haldane and Greenwood showed that partial pressure of CO2 in the alveolar air remains constant with the rise of atmospheric pressure, hence, there can be no increase in CO2 in blood during exposure to compressed air.
As regards to nitrogen, considerations should be taken for the saturation in body tissues.
The rate of solubility of nitrogen per unit mass of tissue, varies greatly in different parts of the body, hence, after a sudden rise in air pressure, varies correspondingly.
If the pressure is rapidly diminished to normal after exposure to saturation in compressed air, the venous blood will give off the whole of its excess of dissolved nitrogen during its passage to the lungs. If gas bubbles are formed in consequence of too rapid decompression, they will increase in size by diffusion into them, and thus cause blocking of small vessels. In order to avoid the risk of bubbles being formed during decompression, the decompression should be slow, and the rate of blood circulation can be increased considerably by muscular exertion.
When a diver goes down for a very short time, the time occupied in the descent and ascent is taken into account. During descent, the diver is being saturated with nitrogen, so he should descend as rapidly as practical. During ascent on the other hand, Haldane showed that at the end of decompression there is a dangerous excess of saturation in all parts of the body except those which half-saturated in less than about seven or eight minutes. The goats used for stage decompression experiments were subjected to uniform decompression in same time and exposure, and within thirty-six decompression trials, one died, two were paralyzed, one had indefinite general symptoms of severe character, and eleven other cases of "bends" occurred beside two doubtful cases.
Diving period:
For short diving periods of less than seven to eight minutes with no repetitive dive: Haldane's experiments on goats showed that sudden decompression in less than a minute after exposures up to four minutes at 75 psi (5.2 bar), equivalent to 42 metres (138 ft) of sea water, goats did not develop any symptoms, even when exposures were raised to six minutes in some cases. This coincides with reports at that time from the Mediterranean of skilled Greek divers, diving to 30 fathoms (55 m) who, should their gear become entangled on the bottom, will cut their air-pipe and line, and blow themselves up to the surface in less than a minute.
With dives exceeding a few minutes or brief repetitive dives: Hill and Greenwood compressed themselves to 91 psi (6.3 bar), equivalent to 53 metres (174 ft) of sea water, a very high pressure and risky experiment, and had bends after decompression. The saturation curves of their experiment for parts of the body were published in 1908.
Experiments continued on goats, and symptoms observed on goats were noted each time on appropriated schedule to record the presence of symptoms not the presence of bubbles:
Bends, the commonest symptom. The limb, most commonly the fore-leg.
Temporary paralysis, symptom to general deficiency of oxygen
Pain, continuous bleating
Permanent paralysis, usually immediately after decompression
Illness, impossible to identify any local symptoms, sometimes blind
Dyspnoea and death
Mechanical symptoms are not important, if goat suffered ear troubles during compression
Experiments on goats included:
staged decompression on different pressures, and different decompression times, and included also comparison with uniform decompression. Results showed that a certain minimum pressure is required to give symptoms on goats and that duration of exposure to high pressures with different decompression times had also an influence.
Experiments compared between different types of animals and their susceptibility to decompression symptoms, and compared influence of size between short and long exposures, and decompression time.
Experiments on blood mass and volume of goats showed apparently no relation to susceptibility.
Pathological observations on them post-mortem appearances of goats after decompression, showed practical importance in connection with the size of bubbles found in blood. Pathological changes underlying the chief symptoms were sufficiently noticed, except for bends. The exact cause of bends was not known.
=== Main results of Haldane’s work ===
This work is published in "The Prevention of Compressed-air Illness" book. Results are published in same book under "Summary" in pages 424 and 425. The main conclusions of his decompression model are:
In page 354, Haldane concluded: "It is clear that the rate of desaturation might be hastened by either (1) increasing the difference in nitrogen pressure between the venous blood and the air in the lungs, or (2) increasing the rate of blood circulation". So, in order to achieve faster desaturation, Haldane concluded that muscular exertion can considerably increase the rate of blood circulation, and thus "there should also be muscular exertion during decompression".
In summary, page 424, Haldane's fifth conclusion is: "Decompression is not safe if the pressure of nitrogen inside the body becomes much more than twice that of the atmospheric nitrogen". Haldane had placed goats in compression chambers under pressure for long hours, to ensure their tissues were fully saturated with nitrogen, then concluded after these experiments that "if absolute pressure is reduced by 50% it will not provoke DCI".
Haldane published his "Decompression Tables" Table I and Table II, on pages 442 and 443. For ease of use, convert feet to meters by multiplying by 0.3048, and from psi to bar by multiplying by 0.0689475729. These tables allow divers to ascend to half of their ambient absolute pressure and remain for a calculated decompression time before ascending further to half of the absolute pressure of the last stage. Haldane divided his schedules into Table I for "ordinary exposures" and Table II for "delay beyond the ordinary limits of time". Currently, when assessed, Table II decompression times were associated with great risk of decompression sickness.
Haldane divided body tissues into different categories, and measured the nitrogen desaturation in each. This led to fast tissues and slow tissues concept, where some tissues fill up with gas and empty it out rapidly; these are the fast tissues. On the other hand, slow tissues are slow filling up and slow emptying out. Haldane portrayed the logarithmic trend of these tissues to fill up and empty out.
== Further developments on Haldane's principles ==
The 2:1 ratio proposed by Haldane was found to be too conservative for fast tissues (short dives) and not conservative enough for slow tissues (long dives). The ratio also seemed to vary with depth. The ascent rates used on older tables were 18 metres per minute (59 ft/min), but newer tables now use 9 metres per minute (30 ft/min).
Haldane introduced decompression tables based on five tissue compartments with half times of 5, 10, 20, 40 and 75 minutes.
The US Navy refined Haldane's tables and introduced a model with nine tissues. They also introduced calculations for half-times starting from 5 minutes and reaching up to 240 minutes.
Professor Albert Bühlmann established decompression tables for diving in high altitude in mountain lakes. His model is based on Haldanian principles but his ZHL-16 tables considered 16 tissues with half-times up to 635 minutes and introduced factors that attempted to model the variation of supersaturation limit with depth.
== Haldane's related work and research ==
Haldane had many other related researches:
Established The Journal of Hygiene
Manufactured a decompression device to facilitate assistance to deep divers
Established decompression procedures for air diving to 200 feet or 65 meters for the Royal Navy in 1907, after many animal experiments
Described the Haldane effect, a property of hemoglobin
Proposed a formula to determine the coefficients of saturation of different tissues in the body, his equation is based on Henry's law:
T
N
2
=
T
0
+
(
T
f
−
T
0
)
(
1
−
(
1
/
2
)
t
/
t
0
)
{\displaystyle T_{N_{2}}=T_{0}+(T_{f}-T_{0})\left(1-(1/2)^{t/t_{0}}\right)}
where,
T: tension (pressure) of gas in tissues
T0: initial tension
TN2: current nitrogen tension
Tf: final tension
t0: compartment half-time
t: current time
== Contradicting work ==
Although Haldane's model remains the basis for modern decompression tables, Haldane's first decompression tables proved to be far from ideal. Haldane's equation is used by many dive tables and dive computers today, even though a growing number of decompression models contradict its assumptions such as the
Asymmetry of saturation phenomena of inert gases (uptake and elimination),
Desaturation according to Hempleman's memorandum and those of Thalmann, taking into account circulating bubbles, VPM, Reduced gradient bubble model.
== Figures and tables from "The Prevention of Compressed-air Illness" ==
== References == | Wikipedia/Haldane's_decompression_model |
Sewage treatment is a type of wastewater treatment which aims to remove contaminants from sewage to produce an effluent that is suitable to discharge to the surrounding environment or an intended reuse application, thereby preventing water pollution from raw sewage discharges. Sewage contains wastewater from households and businesses and possibly pre-treated industrial wastewater. There are a high number of sewage treatment processes to choose from. These can range from decentralized systems (including on-site treatment systems) to large centralized systems involving a network of pipes and pump stations (called sewerage) which convey the sewage to a treatment plant. For cities that have a combined sewer, the sewers will also carry urban runoff (stormwater) to the sewage treatment plant. Sewage treatment often involves two main stages, called primary and secondary treatment, while advanced treatment also incorporates a tertiary treatment stage with polishing processes and nutrient removal. Secondary treatment can reduce organic matter (measured as biological oxygen demand) from sewage, using aerobic or anaerobic biological processes. A so-called quaternary treatment step (sometimes referred to as advanced treatment) can also be added for the removal of organic micropollutants, such as pharmaceuticals. This has been implemented in full-scale for example in Sweden.
A large number of sewage treatment technologies have been developed, mostly using biological treatment processes. Design engineers and decision makers need to take into account technical and economical criteria of each alternative when choosing a suitable technology.: 215 Often, the main criteria for selection are: desired effluent quality, expected construction and operating costs, availability of land, energy requirements and sustainability aspects. In developing countries and in rural areas with low population densities, sewage is often treated by various on-site sanitation systems and not conveyed in sewers. These systems include septic tanks connected to drain fields, on-site sewage systems (OSS), vermifilter systems and many more. On the other hand, advanced and relatively expensive sewage treatment plants may include tertiary treatment with disinfection and possibly even a fourth treatment stage to remove micropollutants.
At the global level, an estimated 52% of sewage is treated. However, sewage treatment rates are highly unequal for different countries around the world. For example, while high-income countries treat approximately 74% of their sewage, developing countries treat an average of just 4.2%.
The treatment of sewage is part of the field of sanitation. Sanitation also includes the management of human waste and solid waste as well as stormwater (drainage) management. The term sewage treatment plant is often used interchangeably with the term wastewater treatment plant.
== Terminology ==
The term sewage treatment plant (STP) (or sewage treatment works) is nowadays often replaced with the term wastewater treatment plant (WWTP). Strictly speaking, the latter is a broader term that can also refer to industrial wastewater treatment.
The terms water recycling center or water reclamation plants are also in use as synonyms.
== Purposes and overview ==
The overall aim of treating sewage is to produce an effluent that can be discharged to the environment while causing as little water pollution as possible, or to produce an effluent that can be reused in a useful manner. This is achieved by removing contaminants from the sewage. It is a form of waste management.
With regards to biological treatment of sewage, the treatment objectives can include various degrees of the following: to transform or remove organic matter, nutrients (nitrogen and phosphorus), pathogenic organisms, and specific trace organic constituents (micropollutants).: 548
Some types of sewage treatment produce sewage sludge which can be treated before safe disposal or reuse. Under certain circumstances, the treated sewage sludge might be termed biosolids and can be used as a fertilizer.
== Sewage characteristics ==
== Collection ==
== Types of treatment processes ==
Sewage can be treated close to where the sewage is created, which may be called a decentralized system or even an on-site system (on-site sewage facility, septic tanks, etc.). Alternatively, sewage can be collected and transported by a network of pipes and pump stations to a municipal treatment plant. This is called a centralized system (see also sewerage and pipes and infrastructure).
A large number of sewage treatment technologies have been developed, mostly using biological treatment processes (see list of wastewater treatment technologies). Very broadly, they can be grouped into high tech (high cost) versus low tech (low cost) options, although some technologies might fall into either category. Other grouping classifications are intensive or mechanized systems (more compact, and frequently employing high tech options) versus extensive or natural or nature-based systems (usually using natural treatment processes and occupying larger areas) systems. This classification may be sometimes oversimplified, because a treatment plant may involve a combination of processes, and the interpretation of the concepts of high tech and low tech, intensive and extensive, mechanized and natural processes may vary from place to place.
=== Low tech, extensive or nature-based processes ===
Examples for more low-tech, often less expensive sewage treatment systems are shown below. They often use little or no energy. Some of these systems do not provide a high level of treatment, or only treat part of the sewage (for example only the toilet wastewater), or they only provide pre-treatment, like septic tanks. On the other hand, some systems are capable of providing a good performance, satisfactory for several applications. Many of these systems are based on natural treatment processes, requiring large areas, while others are more compact. In most cases, they are used in rural areas or in small to medium-sized communities.
For example, waste stabilization ponds are a low cost treatment option with practically no energy requirements but they require a lot of land.: 236 Due to their technical simplicity, most of the savings (compared with high tech systems) are in terms of operation and maintenance costs.: 220–243
Examples for systems that can provide full or partial treatment for toilet wastewater only:
Composting toilet (see also dry toilets in general)
Urine-diverting dry toilet
Vermifilter toilet
=== High tech, intensive or mechanized processes ===
Examples for more high-tech, intensive or mechanized, often relatively expensive sewage treatment systems are listed below. Some of them are energy intensive as well. Many of them provide a very high level of treatment. For example, broadly speaking, the activated sludge process achieves a high effluent quality but is relatively expensive and energy intensive.: 239
=== Disposal or treatment options ===
There are other process options which may be classified as disposal options, although they can also be understood as basic treatment options. These include: Application of sludge, irrigation, soak pit, leach field, fish pond, floating plant pond, water disposal/groundwater recharge, surface disposal and storage.: 138
The application of sewage to land is both: a type of treatment and a type of final disposal.: 189 It leads to groundwater recharge and/or to evapotranspiration. Land application include slow-rate systems, rapid infiltration, subsurface infiltration, overland flow. It is done by flooding, furrows, sprinkler and dripping. It is a treatment/disposal system that requires a large amount of land per person.
== Design aspects ==
=== Population equivalent ===
The per person organic matter load is a parameter used in the design of sewage treatment plants. This concept is known as population equivalent (PE). The base value used for PE can vary from one country to another. Commonly used definitions used worldwide are: 1 PE equates to 60 gram of BOD per person per day, and it also equals 200 liters of sewage per day. This concept is also used as a comparison parameter to express the strength of industrial wastewater compared to sewage.
=== Process selection ===
When choosing a suitable sewage treatment process, decision makers need to take into account technical and economical criteria.: 215 Therefore, each analysis is site-specific. A life cycle assessment (LCA) can be used, and criteria or weightings are attributed to the various aspects. This makes the final decision subjective to some extent.: 216 A range of publications exist to help with technology selection.: 221
In industrialized countries, the most important parameters in process selection are typically efficiency, reliability, and space requirements. In developing countries, they might be different and the focus might be more on construction and operating costs as well as process simplicity.: 218
Choosing the most suitable treatment process is complicated and requires expert inputs, often in the form of feasibility studies. This is because the main important factors to be considered when evaluating and selecting sewage treatment processes are numerous. They include: process applicability, applicable flow, acceptable flow variation, influent characteristics, inhibiting or refractory compounds, climatic aspects, process kinetics and reactor hydraulics, performance, treatment residuals, sludge processing, environmental constraints, requirements for chemical products, energy and other resources; requirements for personnel, operating and maintenance; ancillary processes, reliability, complexity, compatibility, area availability.: 219
With regards to environmental impacts of sewage treatment plants the following aspects are included in the selection process: Odors, vector attraction, sludge transportation, sanitary risks, air contamination, soil and subsoil contamination, surface water pollution or groundwater contamination, devaluation of nearby areas, inconvenience to the nearby population.: 220
=== Odor control ===
Odors emitted by sewage treatment are typically an indication of an anaerobic or septic condition. Early stages of processing will tend to produce foul-smelling gases, with hydrogen sulfide being most common in generating complaints. Large process plants in urban areas will often treat the odors with carbon reactors, a contact media with bio-slimes, small doses of chlorine, or circulating fluids to biologically capture and metabolize the noxious gases. Other methods of odor control exist, including addition of iron salts, hydrogen peroxide, calcium nitrate, etc. to manage hydrogen sulfide levels.
=== Energy requirements ===
The energy requirements vary with type of treatment process as well as sewage strength. For example, constructed wetlands and stabilization ponds have low energy requirements. In comparison, the activated sludge process has a high energy consumption because it includes an aeration step. Some sewage treatment plants produce biogas from their sewage sludge treatment process by using a process called anaerobic digestion. This process can produce enough energy to meet most of the energy needs of the sewage treatment plant itself.: 1505
For activated sludge treatment plants in the United States, around 30 percent of the annual operating costs is usually required for energy.: 1703 Most of this electricity is used for aeration, pumping systems and equipment for the dewatering and drying of sewage sludge. Advanced sewage treatment plants, e.g. for nutrient removal, require more energy than plants that only achieve primary or secondary treatment.: 1704
Small rural plants using trickling filters may operate with no net energy requirements, the whole process being driven by gravitational flow, including tipping bucket flow distribution and the desludging of settlement tanks to drying beds. This is usually only practical in hilly terrain and in areas where the treatment plant is relatively remote from housing because of the difficulty in managing odors.
=== Co-treatment of industrial effluent ===
In highly regulated developed countries, industrial wastewater usually receives at least pretreatment if not full treatment at the factories themselves to reduce the pollutant load, before discharge to the sewer. The pretreatment has the following two main aims: Firstly, to prevent toxic or inhibitory compounds entering the biological stage of the sewage treatment plant and reduce its efficiency. And secondly to avoid toxic compounds from accumulating in the produced sewage sludge which would reduce its beneficial reuse options. Some industrial wastewater may contain pollutants which cannot be removed by sewage treatment plants. Also, variable flow of industrial waste associated with production cycles may upset the population dynamics of biological treatment units.
=== Design aspects of secondary treatment processes ===
=== Non-sewered areas ===
Urban residents in many parts of the world rely on on-site sanitation systems without sewers, such as septic tanks and pit latrines, and fecal sludge management in these cities is an enormous challenge.
For sewage treatment the use of septic tanks and other on-site sewage facilities (OSSF) is widespread in some rural areas, for example serving up to 20 percent of the homes in the U.S.
== Available process steps ==
Sewage treatment often involves two main stages, called primary and secondary treatment, while advanced treatment also incorporates a tertiary treatment stage with polishing processes. Different types of sewage treatment may utilize some or all of the process steps listed below.
=== Preliminary treatment ===
Preliminary treatment (sometimes called pretreatment) removes coarse materials that can be easily collected from the raw sewage before they damage or clog the pumps and sewage lines of primary treatment clarifiers.
==== Screening ====
The influent in sewage water passes through a bar screen to remove all large objects like cans, rags, sticks, plastic packets, etc. carried in the sewage stream. This is most commonly done with an automated mechanically raked bar screen in modern plants serving large populations, while in smaller or less modern plants, a manually cleaned screen may be used. The raking action of a mechanical bar screen is typically paced according to the accumulation on the bar screens and/or flow rate. The solids are collected and later disposed in a landfill, or incinerated. Bar screens or mesh screens of varying sizes may be used to optimize solids removal. If gross solids are not removed, they become entrained in pipes and moving parts of the treatment plant, and can cause substantial damage and inefficiency in the process.: 9
==== Grit removal ====
Grit consists of sand, gravel, rocks, and other heavy materials. Preliminary treatment may include a sand or grit removal channel or chamber, where the velocity of the incoming sewage is reduced to allow the settlement of grit. Grit removal is necessary to (1) reduce formation of deposits in primary sedimentation tanks, aeration tanks, anaerobic digesters, pipes, channels, etc. (2) reduce the frequency of tank cleaning caused by excessive accumulation of grit; and (3) protect moving mechanical equipment from abrasion and accompanying abnormal wear. The removal of grit is essential for equipment with closely machined metal surfaces such as comminutors, fine screens, centrifuges, heat exchangers, and high pressure diaphragm pumps.
Grit chambers come in three types: horizontal grit chambers, aerated grit chambers, and vortex grit chambers. Vortex grit chambers include mechanically induced vortex, hydraulically induced vortex, and multi-tray vortex separators. Given that traditionally, grit removal systems have been designed to remove clean inorganic particles that are greater than 0.210 millimetres (0.0083 in), most of the finer grit passes through the grit removal flows under normal conditions. During periods of high flow deposited grit is resuspended and the quantity of grit reaching the treatment plant increases substantially.
==== Flow equalization ====
Equalization basins can be used to achieve flow equalization. This is especially useful for combined sewer systems which produce peak dry-weather flows or peak wet-weather flows that are much higher than the average flows.: 334 Such basins can improve the performance of the biological treatment processes and the secondary clarifiers.: 334
Disadvantages include the basins' capital cost and space requirements. Basins can also provide a place to temporarily hold, dilute and distribute batch discharges of toxic or high-strength wastewater which might otherwise inhibit biological secondary treatment (such was wastewater from portable toilets or fecal sludge that is brought to the sewage treatment plant in vacuum trucks). Flow equalization basins require variable discharge control, typically include provisions for bypass and cleaning, and may also include aerators and odor control.
==== Fat and grease removal ====
In some larger plants, fat and grease are removed by passing the sewage through a small tank where skimmers collect the fat floating on the surface. Air blowers in the base of the tank may also be used to help recover the fat as a froth. Many plants, however, use primary clarifiers with mechanical surface skimmers for fat and grease removal.
=== Primary treatment ===
Primary treatment is the "removal of a portion of the suspended solids and organic matter from the sewage".: 11 It consists of allowing sewage to pass slowly through a basin where heavy solids can settle to the bottom while oil, grease and lighter solids float to the surface and are skimmed off. These basins are called primary sedimentation tanks or primary clarifiers and typically have a hydraulic retention time (HRT) of 1.5 to 2.5 hours.: 398 The settled and floating materials are removed and the remaining liquid may be discharged or subjected to secondary treatment. Primary settling tanks are usually equipped with mechanically driven scrapers that continually drive the collected sludge towards a hopper in the base of the tank where it is pumped to sludge treatment facilities.: 9–11
Sewage treatment plants that are connected to a combined sewer system sometimes have a bypass arrangement after the primary treatment unit. This means that during very heavy rainfall events, the secondary and tertiary treatment systems can be bypassed to protect them from hydraulic overloading, and the mixture of sewage and storm-water receives primary treatment only.
Primary sedimentation tanks remove about 50–70% of the suspended solids, and 25–40% of the biological oxygen demand (BOD).: 396
=== Secondary treatment ===
The main processes involved in secondary sewage treatment are designed to remove as much of the solid material as possible. They use biological processes to digest and remove the remaining soluble material, especially the organic fraction. This can be done with either suspended-growth or biofilm processes. The microorganisms that feed on the organic matter present in the sewage grow and multiply, constituting the biological solids, or biomass. These grow and group together in the form of flocs or biofilms and, in some specific processes, as granules. The biological floc or biofilm and remaining fine solids form a sludge which can be settled and separated. After separation, a liquid remains that is almost free of solids, and with a greatly reduced concentration of pollutants.
Secondary treatment can reduce organic matter (measured as biological oxygen demand) from sewage, using aerobic or anaerobic processes. The organisms involved in these processes are sensitive to the presence of toxic materials, although these are not expected to be present at high concentrations in typical municipal sewage.
=== Tertiary treatment ===
Advanced sewage treatment generally involves three main stages, called primary, secondary and tertiary treatment but may also include intermediate stages and final polishing processes. The purpose of tertiary treatment (also called advanced treatment) is to provide a final treatment stage to further improve the effluent quality before it is discharged to the receiving water body or reused. More than one tertiary treatment process may be used at any treatment plant. If disinfection is practiced, it is always the final process. It is also called effluent polishing. Tertiary treatment may include biological nutrient removal (alternatively, this can be classified as secondary treatment), disinfection and partly removal of micropollutants, such as environmental persistent pharmaceutical pollutants.
Tertiary treatment is sometimes defined as anything more than primary and secondary treatment in order to allow discharge into a highly sensitive or fragile ecosystem such as estuaries, low-flow rivers or coral reefs. Treated water is sometimes disinfected chemically or physically (for example, by lagoons and microfiltration) prior to discharge into a stream, river, bay, lagoon or wetland, or it can be used for the irrigation of a golf course, greenway or park. If it is sufficiently clean, it can also be used for groundwater recharge or agricultural purposes.
Sand filtration removes much of the residual suspended matter.: 22–23 Filtration over activated carbon, also called carbon adsorption, removes residual toxins.: 19 Micro filtration or synthetic membranes are used in membrane bioreactors and can also remove pathogens.: 854
Settlement and further biological improvement of treated sewage may be achieved through storage in large human-made ponds or lagoons. These lagoons are highly aerobic, and colonization by native macrophytes, especially reeds, is often encouraged.
=== Disinfection ===
Disinfection of treated sewage aims to kill pathogens (disease-causing microorganisms) prior to disposal. It is increasingly effective after more elements of the foregoing treatment sequence have been completed.: 359 The purpose of disinfection in the treatment of sewage is to substantially reduce the number of pathogens in the water to be discharged back into the environment or to be reused. The target level of reduction of biological contaminants like pathogens is often regulated by the presiding governmental authority. The effectiveness of disinfection depends on the quality of the water being treated (e.g. turbidity, pH, etc.), the type of disinfection being used, the disinfectant dosage (concentration and time), and other environmental variables. Water with high turbidity will be treated less successfully, since solid matter can shield organisms, especially from ultraviolet light or if contact times are low. Generally, short contact times, low doses and high flows all militate against effective disinfection. Common methods of disinfection include ozone, chlorine, ultraviolet light, or sodium hypochlorite.: 16 Monochloramine, which is used for drinking water, is not used in the treatment of sewage because of its persistence.
Chlorination remains the most common form of treated sewage disinfection in many countries due to its low cost and long-term history of effectiveness. One disadvantage is that chlorination of residual organic material can generate chlorinated-organic compounds that may be carcinogenic or harmful to the environment. Residual chlorine or chloramines may also be capable of chlorinating organic material in the natural aquatic environment. Further, because residual chlorine is toxic to aquatic species, the treated effluent must also be chemically dechlorinated, adding to the complexity and cost of treatment.
Ultraviolet (UV) light can be used instead of chlorine, iodine, or other chemicals. Because no chemicals are used, the treated water has no adverse effect on organisms that later consume it, as may be the case with other methods. UV radiation causes damage to the genetic structure of bacteria, viruses, and other pathogens, making them incapable of reproduction. The key disadvantages of UV disinfection are the need for frequent lamp maintenance and replacement and the need for a highly treated effluent to ensure that the target microorganisms are not shielded from the UV radiation (i.e., any solids present in the treated effluent may protect microorganisms from the UV light). In many countries, UV light is becoming the most common means of disinfection because of the concerns about the impacts of chlorine in chlorinating residual organics in the treated sewage and in chlorinating organics in the receiving water.
As with UV treatment, heat sterilization also does not add chemicals to the water being treated. However, unlike UV, heat can penetrate liquids that are not transparent. Heat disinfection can also penetrate solid materials within wastewater, sterilizing their contents. Thermal effluent decontamination systems provide low resource, low maintenance effluent decontamination once installed.
Ozone (O3) is generated by passing oxygen (O2) through a high voltage potential resulting in a third oxygen atom becoming attached and forming O3. Ozone is very unstable and reactive and oxidizes most organic material it comes in contact with, thereby destroying many pathogenic microorganisms. Ozone is considered to be safer than chlorine because, unlike chlorine which has to be stored on site (highly poisonous in the event of an accidental release), ozone is generated on-site as needed from the oxygen in the ambient air. Ozonation also produces fewer disinfection by-products than chlorination. A disadvantage of ozone disinfection is the high cost of the ozone generation equipment and the requirements for special operators. Ozone sewage treatment requires the use of an ozone generator, which decontaminates the water as ozone bubbles percolate through the tank.
Membranes can also be effective disinfectants, because they act as barriers, avoiding the passage of the microorganisms. As a result, the final effluent may be devoid of pathogenic organisms, depending on the type of membrane used. This principle is applied in membrane bioreactors.
=== Biological nutrient removal ===
Sewage may contain high levels of the nutrients nitrogen and phosphorus. Typical values for nutrient loads per person and nutrient concentrations in raw sewage in developing countries have been published as follows: 8 g/person/d for total nitrogen (45 mg/L), 4.5 g/person/d for ammonia-N (25 mg/L) and 1.0 g/person/d for total phosphorus (7 mg/L).: 57 The typical ranges for these values are: 6–10 g/person/d for total nitrogen (35–60 mg/L), 3.5–6 g/person/d for ammonia-N (20–35 mg/L) and 0.7–2.5 g/person/d for total phosphorus (4–15 mg/L).: 57
Excessive release to the environment can lead to nutrient pollution, which can manifest itself in eutrophication. This process can lead to algal blooms, a rapid growth, and later decay, in the population of algae. In addition to causing deoxygenation, some algal species produce toxins that contaminate drinking water supplies.
Ammonia nitrogen, in the form of free ammonia (NH3) is toxic to fish. Ammonia nitrogen, when converted to nitrite and further to nitrate in a water body, in the process of nitrification, is associated with the consumption of dissolved oxygen. Nitrite and nitrate may also have public health significance if concentrations are high in drinking water, because of a disease called metahemoglobinemia.: 42
Phosphorus removal is important as phosphorus is a limiting nutrient for algae growth in many fresh water systems. Therefore, an excess of phosphorus can lead to eutrophication. It is also particularly important for water reuse systems where high phosphorus concentrations may lead to fouling of downstream equipment such as reverse osmosis.
A range of treatment processes are available to remove nitrogen and phosphorus. Biological nutrient removal (BNR) is regarded by some as a type of secondary treatment process, and by others as a tertiary (or advanced) treatment process.
==== Nitrogen removal ====
Nitrogen is removed through the biological oxidation of nitrogen from ammonia to nitrate (nitrification), followed by denitrification, the reduction of nitrate to nitrogen gas. Nitrogen gas is released to the atmosphere and thus removed from the water.
Nitrification itself is a two-step aerobic process, each step facilitated by a different type of bacteria. The oxidation of ammonia (NH4+) to nitrite (NO2−) is most often facilitated by bacteria such as Nitrosomonas spp. (nitroso refers to the formation of a nitroso functional group). Nitrite oxidation to nitrate (NO3−), though traditionally believed to be facilitated by Nitrobacter spp. (nitro referring the formation of a nitro functional group), is now known to be facilitated in the environment predominantly by Nitrospira spp.
Denitrification requires anoxic conditions to encourage the appropriate biological communities to form. Anoxic conditions refers to a situation where oxygen is absent but nitrate is present. Denitrification is facilitated by a wide diversity of bacteria. The activated sludge process, sand filters, waste stabilization ponds, constructed wetlands and other processes can all be used to reduce nitrogen.: 17–18 Since denitrification is the reduction of nitrate to dinitrogen (molecular nitrogen) gas, an electron donor is needed. This can be, depending on the wastewater, organic matter (from the sewage itself), sulfide, or an added donor like methanol. The sludge in the anoxic tanks (denitrification tanks) must be mixed well (mixture of recirculated mixed liquor, return activated sludge, and raw influent) e.g. by using submersible mixers in order to achieve the desired denitrification.
Over time, different treatment configurations for activated sludge processes have evolved to achieve high levels of nitrogen removal. An initial scheme was called the Ludzack–Ettinger Process. It could not achieve a high level of denitrification.: 616 The Modified Ludzak–Ettinger Process (MLE) came later and was an improvement on the original concept. It recycles mixed liquor from the discharge end of the aeration tank to the head of the anoxic tank. This provides nitrate for the facultative bacteria.: 616
There are other process configurations, such as variations of the Bardenpho process.: 160 They might differ in the placement of anoxic tanks, e.g. before and after the aeration tanks.
==== Phosphorus removal ====
Studies of United States sewage in the late 1960s estimated mean per capita contributions of 500 grams (18 oz) in urine and feces, 1,000 grams (35 oz) in synthetic detergents, and lesser variable amounts used as corrosion and scale control chemicals in water supplies. Source control via alternative detergent formulations has subsequently reduced the largest contribution, but naturally the phosphorus content of urine and feces remained unchanged.
Phosphorus can be removed biologically in a process called enhanced biological phosphorus removal. In this process, specific bacteria, called polyphosphate-accumulating organisms (PAOs), are selectively enriched and accumulate large quantities of phosphorus within their cells (up to 20 percent of their mass).: 148–155
Phosphorus removal can also be achieved by chemical precipitation, usually with salts of iron (e.g. ferric chloride) or aluminum (e.g. alum), or lime.: 18 This may lead to a higher sludge production as hydroxides precipitate and the added chemicals can be expensive. Chemical phosphorus removal requires significantly smaller equipment footprint than biological removal, is easier to operate and is often more reliable than biological phosphorus removal. Another method for phosphorus removal is to use granular laterite or zeolite.
Some systems use both biological phosphorus removal and chemical phosphorus removal. The chemical phosphorus removal in those systems may be used as a backup system, for use when the biological phosphorus removal is not removing enough phosphorus, or may be used continuously. In either case, using both biological and chemical phosphorus removal has the advantage of not increasing sludge production as much as chemical phosphorus removal on its own, with the disadvantage of the increased initial cost associated with installing two different systems.
Once removed, phosphorus, in the form of a phosphate-rich sewage sludge, may be sent to landfill or used as fertilizer in admixture with other digested sewage sludges. In the latter case, the treated sewage sludge is also sometimes referred to as biosolids. 22% of the world's phosphorus needs could be satisfied by recycling residential wastewater.
=== Fourth treatment stage ===
Micropollutants such as pharmaceuticals, ingredients of household chemicals, chemicals used in small businesses or industries, environmental persistent pharmaceutical pollutants (EPPP) or pesticides may not be eliminated in the commonly used sewage treatment processes (primary, secondary and tertiary treatment) and therefore lead to water pollution. Although concentrations of those substances and their decomposition products are quite low, there is still a chance of harming aquatic organisms. For pharmaceuticals, the following substances have been identified as toxicologically relevant: substances with endocrine disrupting effects, genotoxic substances and substances that enhance the development of bacterial resistances. They mainly belong to the group of EPPP.
Techniques for elimination of micropollutants via a fourth treatment stage during sewage treatment are implemented in Germany, Switzerland, Sweden and the Netherlands and tests are ongoing in several other countries. In Switzerland it has been enshrined in law since 2016. Since 1 January 2025, there has been a recast of the Urban Waste Water Treatment Directive in the European Union. Due to the large number of amendments that have now been made, the directive was rewritten on November 27, 2024 as Directive (EU) 2024/3019, published in the EU Official Journal on December 12, and entered into force on January 1, 2025. The member states now have 31 months, i.e. until July 31, 2027, to adapt their national legislation to the new directive ("implementation of the directive").
The amendment stipulates that, in addition to stricter discharge values for nitrogen and phosphorus, persistent trace substances must at least be partially separated. The target, similar to Switzerland, is that 80% of 6 key substances out of 12 must be removed between discharge into the sewage treatment plant and discharge into the water body. At least 80% of the investments and operating costs for the fourth treatment stage will be passed on to the pharmaceutical and cosmetics industry according to the polluter pays principle in order to relieve the population financially and provide an incentive for the development of more environmentally friendly products. In addition, the municipal wastewater treatment sector is to be energy neutral by 2045 and the emission of microplastics and PFAS is to be monitored.
The implementation of the framework guidelines is staggered until 2045, depending on the size of the sewage treatment plant and its population equivalents (PE). Sewage treatment plants with over 150,000 PE have priority and should be adapted immediately, as a significant proportion of the pollution comes from them. The adjustments are staggered at national level in:
20% of the plants by 31 December 2033,
60% of the plants by 31 December 2039,
100% of the plants by 31 December 2045.
Wastewater treatment plants with 10,000 to 150,000 PE that discharge into coastal waters or sensitive waters are staggered at national level in:
10% of the plants by 31 December 2033,
30% of the plants by 31 December 2036,
60% of the plants by 31 December 2039,
100% of the plants by 31 December 2045.
The latter concerns waters with a low dilution ratio, waters from which drinking water is obtained and those that are coastal waters, or those used as bathing waters or used for mussel farming. Member States will be given the option not to apply fourth treatment in these areas if a risk assessment shows that there is no potential risk from micropollutants to human health and/or the environment.
Such process steps mainly consist of activated carbon filters that adsorb the micropollutants. The combination of advanced oxidation with ozone followed by granular activated carbon (GAC) has been suggested as a cost-effective treatment combination for pharmaceutical residues. For a full reduction of microplasts the combination of ultrafiltration followed by GAC has been suggested. Also the use of enzymes such as laccase secreted by fungi is under investigation. Microbial biofuel cells are investigated for their property to treat organic matter in sewage.
To reduce pharmaceuticals in water bodies, source control measures are also under investigation, such as innovations in drug development or more responsible handling of drugs. In the US, the National Take Back Initiative is a voluntary program with the general public, encouraging people to return excess or expired drugs, and avoid flushing them to the sewage system.
=== Sludge treatment and disposal ===
== Environmental impacts ==
Sewage treatment plants can have significant effects on the biotic status of receiving waters and can cause some water pollution, especially if the treatment process used is only basic. For example, for sewage treatment plants without nutrient removal, eutrophication of receiving water bodies can be a problem.
In 2024, The Royal Academy of Engineering released a study into the effects wastewater on public health in the United Kingdom. The study gained media attention, with comments from the UKs leading health professionals, including Sir Chris Whitty. Outlining 15 recommendations for various UK bodies to dramatically reduce public health risks by increasing the water quality in its waterways, such as rivers and lakes.
After the release of the report, The Guardian newspaper interviewed Whitty, who stated that improving water quality and sewage treatment should be a high level of importance and a "public health priority". He compared it to eradicating cholera in the 19th century in the country following improvements to the sewage treatment network. The study also identified that low water flows in rivers saw high concentration levels of sewage, as well as times of flooding or heavy rainfall. While heavy rainfall had always been associated with sewage overflows into streams and rivers, the British media went as far to warn parents of the dangers of paddling in shallow rivers during warm weather.
Whitty's comments came after the study revealed that the UK was experiencing a growth in the number of people that were using coastal and inland waters recreationally. This could be connected to a growing interest in activities such as open water swimming or other water sports. Despite this growth in recreation, poor water quality meant some were becoming unwell during events. Most notably, the 2024 Paris Olympics had to delay numerous swimming-focused events like the triathlon due to high levels of sewage in the River Seine.
== Reuse ==
=== Irrigation ===
Increasingly, people use treated or even untreated sewage for irrigation to produce crops. Cities provide lucrative markets for fresh produce, so are attractive to farmers. Because agriculture has to compete for increasingly scarce water resources with industry and municipal users, there is often no alternative for farmers but to use water polluted with sewage directly to water their crops. There can be significant health hazards related to using water loaded with pathogens in this way. The World Health Organization developed guidelines for safe use of wastewater in 2006. They advocate a 'multiple-barrier' approach to wastewater use, where farmers are encouraged to adopt various risk-reducing behaviors. These include ceasing irrigation a few days before harvesting to allow pathogens to die off in the sunlight, applying water carefully so it does not contaminate leaves likely to be eaten raw, cleaning vegetables with disinfectant or allowing fecal sludge used in farming to dry before being used as a human manure.
=== Reclaimed water ===
== Global situation ==
Before the 20th century in Europe, sewers usually discharged into a body of water such as a river, lake, or ocean. There was no treatment, so the breakdown of the human waste was left to the ecosystem. This could lead to satisfactory results if the assimilative capacity of the ecosystem is sufficient which is nowadays not often the case due to increasing population density.: 78
Today, the situation in urban areas of industrialized countries is usually that sewers route their contents to a sewage treatment plant rather than directly to a body of water. In many developing countries, however, the bulk of municipal and industrial wastewater is discharged to rivers and the ocean without any treatment or after preliminary treatment or primary treatment only. Doing so can lead to water pollution. Few reliable figures exist on the share of the wastewater collected in sewers that is being treated worldwide. A global estimate by UNDP and UN-Habitat in 2010 was that 90% of all wastewater generated is released into the environment untreated. A more recent study in 2021 estimated that globally, about 52% of sewage is treated. However, sewage treatment rates are highly unequal for different countries around the world. For example, while high-income countries treat approximately 74% of their sewage, developing countries treat an average of just 4.2%. As of 2022, without sufficient treatment, more than 80% of all wastewater generated globally is released into the environment. High-income nations treat, on average, 70% of the wastewater they produce, according to UN Water. Only 8% of wastewater produced in low-income nations receives any sort of treatment.
The Joint Monitoring Programme (JMP) for Water Supply and Sanitation by WHO and UNICEF report in 2021 that 82% of people with sewer connections are connected to sewage treatment plants providing at least secondary treatment.: 55 However, this value varies widely between regions. For example, in Europe, North America, Northern Africa and Western Asia, a total of 31 countries had universal (>99%) wastewater treatment. However, in Albania, Bermuda, North Macedonia and Serbia "less than 50% of sewered wastewater received secondary or better treatment" and in Algeria, Lebanon and Libya the value was less than 20% of sewered wastewater that was being treated. The report also found that "globally, 594 million people have sewer connections that don't receive sufficient treatment. Many more are connected to wastewater treatment plants that do not provide effective treatment or comply with effluent requirements.".: 55
=== Global targets ===
Sustainable Development Goal 6 has a Target 6.3 which is formulated as follows: "By 2030, improve water quality by reducing pollution, eliminating,dumping and minimizing release of hazardous chemicals and materials, halving the proportion of untreated wastewater and substantially increasing recycling and safe reuse globally." The corresponding Indicator 6.3.1 is the "proportion of wastewater safely treated". It is anticipated that wastewater production would rise by 24% by 2030 and by 51% by 2050.
Data in 2020 showed that there is still too much uncollected household wastewater: Only 66% of all household wastewater flows were collected at treatment facilities in 2020 (this is determined from data from 128 countries).: 17 Based on data from 42 countries in 2015, the report stated that "32 per cent of all wastewater flows generated from point sources received at least some treatment".: 17 For sewage that has indeed been collected at centralized sewage treatment plants, about 79% went on to be safely treated in 2020.: 18
== History ==
The history of sewage treatment had the following developments: It began with land application (sewage farms) in the 1840s in England, followed by chemical treatment and sedimentation of sewage in tanks, then biological treatment in the late 19th century, which led to the development of the activated sludge process starting in 1912.
== Regulations ==
In most countries, sewage collection and treatment are subject to local and national regulations and standards.
== By country ==
=== Overview ===
=== Europe ===
In the European Union, 0.8% of total energy consumption goes to wastewater treatment facilities. The European Union needs to make extra investments of €90 billion in the water and waste sector to meet its 2030 climate and energy goals.
In October 2021, British Members of Parliament voted to continue allowing untreated sewage from combined sewer overflows to be released into waterways.
=== Asia ===
==== India ====
The 'Delhi Jal Board' (DJB) is currently operating on the construction of the largest sewage treatment plant in India. It will be operational by the end of 2022 with an estimated capacity of 564 MLD. It is supposed to solve the existing situation wherein untreated sewage water is being discharged directly into the river 'Yamuna'.
==== Japan ====
=== Africa ===
==== Libya ====
=== Americas ===
==== United States ====
== See also ==
Decentralized wastewater system
List of largest wastewater treatment plants
List of water supply and sanitation by country
Organisms involved in water purification
Sanitary engineering
Waste disposal
== References ==
== External links ==
Water Environment Federation – Professional association focusing on municipal wastewater treatment | Wikipedia/Sewage_treatment |
Underwater videography is the branch of electronic underwater photography concerned with capturing underwater moving images as a recreational diving, scientific, commercial, documentary, or filmmaking activity. Although technological changes since 1909 have improved the ease of operation and quality of images, significant challenges in the form of protecting equipment from water, low light levels, and the usual hazards of diving must be addressed.
== History ==
In 1909, Albert Samama Chikly took the first underwater shot. In 1910, he filmed Tuna fishing in Tunisia under the patronage of Albert I, Prince of Monaco.
In 1940 Hans Hass completed Pirsch unter Wasser (i.e. Stalking under Water) which was published by the Universum Film AG, lasted originally only 16 minutes and was shown in theatres before the main movie, but would eventually be extended by additional filming done in the Adriatic Sea close to Dubrovnik. It premiered in Berlin in 1942.
Sesto Continente directed by Folco Quilici and released in 1954, was the first full-length, full-color underwater documentary. The Silent World is noted as one of the first films to use underwater cinematography to show the ocean depths in color. Its title derives from Jacques-Yves Cousteau's 1953 book The Silent World: A Story of Undersea Discovery and Adventure.
=== Submarine-based ===
The first successful video-recording from a non-military submarine was made in May 1969. The purpose of the recording was to document the inspection and condition of an offshore oil storage unit located in 130 feet (40 m) of water off the Louisiana coast. During the mid-1960s and early 1970s, there was widespread interest in the United States in the topic of oceanography. Several major firms built small research submarines to explore the oceans. The major subs were Deep Star 4000, designed by Jacques Cousteau and built by Westinghouse Electric Company; Aluminaut, the first aluminum sub which was built by and operated by Reynolds Aluminum; Beaver, built by and operated by Rockwell International; Star III, owned and operated by Scripps Institute of Oceanography; and DOWB (Deep Ocean Work Boat), built by and operated by General Motors.
As part of their operations all of these subs attempted video-recordings. None were successful prior to 1969. The problem preventing a successful recording was in the output of the DC to AC power converted. This problem was resolved by using a different type of power converter. This new approach was used on the Shelf Diver, owned and operated by Perry Submarine to obtain the successful video-recording of the inspection of Tenneco's Molly Brown 32,500 barrel oil storage unit. The success of this video-recording ignited an immediate interest in the oil field. Two months later the Shelf Diver was employed by Humble Oil and Refining Company to make a geological survey of the floor of the Gulf of Mexico.
== Limitations ==
The primary difficulty in underwater camera usage is sealing the camera from water at high pressure, while maintaining the ability to operate it. The diving mask also inhibits the ability to view the camera image and to see the monitoring screen clearly through the camera housing. Previously the size of the video camera was also a limiting factor, necessitating large housings to enclose the separate camera and record deck. This results in a larger volume which creates extra buoyancy requiring a corresponding use of heavy weight to keep the housing underwater (about 64 lbs. per cubic foot of displacement or 1.03 kilogram per litre in sea water or 63 lbs per cubic foot of displacement (1 kilogram per litre) in fresh water). Early video cameras also needed large batteries because of the high power consumption of the system. Current Lithium-ion batteries have long run times with relatively light weight and low volume.
Another problem is the lower level of light underwater. Early cameras had problems with low light levels, were grainy, and did not record much color underwater without auxiliary lighting. Large unwieldy lighting systems were problematic to early underwater videography. And last, underwater objects viewed from an airspace with a flat window, such as the eye inside a mask or the camera inside a housing, appear to be about 25% larger than they are. The photographer needs to move farther back to get the subject into the field of view. Unfortunately that puts more water between the lens and the subject resulting in less clarity and reduced color and light. This problem is solved by the use of dome ports. Dome ports allow for very close subject distances, decreasing the in-water light path and improving image brightness and color saturation.
== Modern improvements ==
Today, the small size of fully automatic camcorders with large view screens and long-life rechargeable batteries has reduced the housing size and made underwater videography an easy, fun activity for the diver. Low-cost wide-angle lens add-ons are available for many cameras and some can even be fitted outside the camera housing for versatile use. This lets the photographer get closer and make the subject clearer and also with fewer focusing and depth of field problems. Today cameras are more sensitive to low light conditions and make automatic color balancing adjustments. Nevertheless, deeper water videography still needs auxiliary light sources to bring out colors filtered out of sunlight by the distance it has travelled through water. The longest wavelengths of light are lost first (reds and yellows) leaving only a greenish or blue cast in deep water. Even a hand light will help show off some of the magnificent colors of a coral reef or other marine life if used during recording.
Modern underwater video lights are now relatively small, have run times of 45–60 minutes and output 600-8000 lumens. These LED lights are powered by Lithium-ion batteries and usually have a 5600K (daylight) color temperature.
== Video housings ==
Many modern underwater housing are pressure resistant up to about 330 feet (100M). Typical construction is from moulded polycarbonate plastic, or aluminum for more professional systems. They usually have quick release snaps, an o-ring seal, and through housings fittings for several camera controls. A few are generic in nature from several manufacturers (such as Ikelite), and may be adaptable to several camera sizes. Most housings, however, are specific to the size and controls of a particular camera (such as Amphibico) type and may be marketed by the camera manufacturer or an after-market company.
Housed video cameras now record in HD (1920X1080) with some cameras operating at 4K (3840 x 2160) resolutions. Recording media may be solid state Solid-state drives (SSD), SXS cards, professional flash media or SDHC/XC cards. Codecs include H.265, H.264, XAVC and others. Small "action" cameras such as the GoPro style cameras have taken diving by storm and create incredible images for relatively little cost, provided that there is sufficient light. These cameras often record on SDXC/HC or MicroSD cards. These cards should have data record rates of at least 45 MB/s (Ultra) or faster.
Occasionally housings might be advertised as "waterproof housings" rather than underwater housings. Waterproof housings are not intended for deep water use, but rather are splash protection housings for use around the pool, in rain, or to protect if dropped overboard. At the most they are for very shallow activities - usually not more than about 1 or 2 metres / 3 to 6 feet in depth. One manufacturer offers a plastic bag type housing with a watertight seal, and a glass port front. The flexible bag allows some modest camera control, but when taken deeper the air inside the bag compresses from the pressure and makes the controls nearly impossible to operate. These bags are usually limited to shallow snorkeling activities and damage to the bag may cause irreparable flooding damage.
== Still/video combinations ==
Most current digital still cameras are also capable of capturing professional quality video images. This is usually a variation of the MPEG video standard of digital imaging created as a streaming series of digital images, with some advanced compression techniques. Codecs include QuickTime Video, H.265, H.264, WMV or AVI files.
A dedicated video camera, on the other hand may also have a "still frame" or snapshot capability. This is a better choice if the first intent is to have high quality moving pictures and an occasional still picture. Camera capacity, based on videotapes, or even harddrive recording is usually at least 2 hours, and necessitates very little opening of the housing during the dive day. Check the Pixel quality (16 megapixels or above preferred) on the still camera capability if this is of interest. Ultra-high-definition television cameras (4K UHD), provide the best quality and image resolution.
The trend today is toward replaceable memory cards for recording, or internal hard-drives built into the camera. This provides maximum versatility, high recording time options, and few mechanical breakdown possibilities, not to mention minimizing problems with condensation affecting the recording (tape) media of previous generations. The subsequent files may be easily transferred to a computer and edited with low-cost software solutions (and a reasonably high performance computer and video card). The subsequent results may be transferred to a hard drive, CD, DVD, Blu-ray Disc or thumbdrive for easy distribution or archiving. Many videographers maintain their own YouTube or Vimeo channel for sharing and showcasing their work.
== Training and certification ==
Training and certification for recreational divers as hobbyist level underwater videographers is available through some recreational diver training agencies, but professional class underwater videography is demonstrated by the quality of the product, and there is no requirement for certification by a diver training agency. It is a work skill, not a diving skill.
== Risk ==
The usual hazards of underwater diving are generally not directly affected using video equipment, but the risk associated with these hazards may be increased by task loading. This generally reduces the available attention and situational awareness of the operator, and the additional encumbrance of large video equipment reduces the diver's ability to react swiftly and precisely to rectify problems before they become serious. These issues are generally mitigated by practice, and where appropriate an assistant may be useful. Diving with a skilled and attentive buddy can also reduce the risk of problems getting out of control, but this buddy must be dedicated to monitoring the videographer throughout the dive to be of value.
== References ==
== External links ==
"Deep-Sea Documentary". Fayetteville Observer.
"On Location - Blue World". Jonathan Bird's Blue World.
"Video Produced On "Mardi Gras" Shipwreck". Texas A&M Today. 13 October 2008.
"2 Hours Of High-Quality Underwater Videography From The Pacific Northwest" ScubaBC May 2025 | Wikipedia/Underwater_videography |
Seismic oceanography is a form of acoustic oceanography, in which sound waves are used to study the physical properties and dynamics of the ocean. It provides images of changes in the temperature and salinity of seawater. Unlike most oceanographic acoustic imaging methods, which use sound waves with frequencies greater than 10,000 Hz, seismic oceanography uses sound waves with frequencies lower than 500 Hz. Use of low-frequency sound means that seismic oceanography is unique in its ability to provide highly detailed images of oceanographic structure that span horizontal distances of hundreds of kilometres and which extend from the sea surface to the seabed. Since its inception in 2003, seismic oceanography has been used to image a wide variety of oceanographic phenomena, including fronts, eddies, thermohaline staircases, turbid layers and cold methane seeps. In addition to providing spectacular images, seismic oceanographic data have given quantitative insight into processes such as movement of internal waves and turbulent mixing of seawater.
== Method ==
=== Data acquisition ===
Seismic oceanography is based on marine seismic reflection profiling, in which a ship tows specialised equipment for generating underwater sound. This equipment is known as the acoustic source. The ship also tows one or more cables along which are arranged hundreds of hydrophones, which are instruments for recording underwater sound. These cables are referred to as streamers, and are between a few hundred metres and 10 km in length. Both the acoustic source and the streamers lie a few metres beneath the sea surface.
The acoustic source generates sound waves once every few seconds by releasing either compressed air or electrical charge into the sea. Most of these sound waves travel downwards towards the seabed, and a small fraction of the sound is reflected from boundaries at which the temperature or salinity of seawater changes (these boundaries are known as thermohaline boundaries). The hydrophones detect these reflected sound waves. As the ship moves forwards, the positions of the acoustic source and hydrophones change with respect to the reflecting boundaries. Over a period of 30 minutes or less, multiple different configurations of acoustic source and hydrophones sample the same point on a boundary.
=== Image creation ===
==== Idealised case ====
Seismic data record how the intensity of sound at each hydrophone changes with time. The time at which reflected sound arrives at a particular hydrophone depends on the horizontal distance between the hydrophone and the acoustic source, on the depth and shape of the reflecting boundary, and on the speed of sound in seawater. The depth and shape of the boundary and the local speed of sound, which can vary between approximately 1450 m/s and 1540 m/s, are initially unknown. By analysing records from multiple different configurations of acoustic source and hydrophones, the speed of sound can be estimated. Using this estimated speed, the boundary depth is determined under the assumption that the boundary is horizontal. The effects of reflection from boundaries that are not horizontal can be accounted for using methods which are collectively known as seismic migration. After migration, different records that sample the same point on a boundary are added together to increase the signal-to-noise ratio (this process is known as stacking). Migration and stacking are carried out at every depth and at every horizontal position to make a spatially accurate seismic image.
==== Complications ====
The intensity of sound recorded by hydrophones can change due to causes other than reflection of sound from thermohaline boundaries. For instance, the acoustic source produces some sound waves that travel horizontally along the streamer, rather than downwards towards the seabed. Aside from sound produced by the acoustic source, the hydrophones record background noise caused by natural processes such as breaking of wind waves at the ocean surface. These other, unwanted sounds are often much louder than sound reflected from thermohaline boundaries. Use of signal-processing filters quietens unwanted sounds and increases the signal-to-noise ratio of reflections from thermohaline boundaries.
=== Analysis ===
The key advantage of seismic oceanography is that it provides high-resolution (up to 10 m) images of oceanic structure, that can be combined with quantitative information about the ocean. The imagery can be used to identify the length, width, and height of oceanic structures across a range of scales. If the seismic data is also 3D, then the evolution of the structures over time can be analyzed too.
==== Inverting for temperature and salinity ====
Combined with its imagery, processed seismic data can be used to extract other quantitative information about the ocean. So far, seismic oceanography has been used to extract distributions of temperature, and salinity, and therefore density and other important properties. There is a range of approaches that can be used to extract this information. For example, Paramo and Holbrook (2005) extracted temperature gradients in the Norwegian Sea using the Amplitude Versus Offset methods. The distributions of physical properties were limited to one-dimension however. More recently, there has been a move toward two-dimensional technique. Cord Papenberg et al. (2010) presented high-resolution two-dimensional temperature and salinity distributions. These fields were derived using an iterative inversion that combines seismic and physical oceanographic data. Since then, more complex inversions have been presented that are based on Monte Carlo inversion techniques, amongst others.
==== Spectral analysis for vertical mixing rates ====
Aside from temperature and salinity distributions, seismic data of the ocean can also be used to extract mixing rates through spectral analysis. This process is based on the assumption that reflections, which show undulations at a number of scales, track the internal wave field. Therefore, the vertical displacement of these undulations can give a measure of the vertical mixing rates of the ocean. This technique was first developed using data from the Norwegian Sea and showed the enhancement of internal wave energy close to the continental slope. Since 2005, the techniques have been further developed, adapted, and automated so that any seismic section may be converted into a two-dimensional distribution of mixing rates
== References == | Wikipedia/Seismic_Oceanography |
The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one-dimensional flow in fluids or a one-dimensional deformation in solids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot.
The basic idea of the jump conditions is to consider what happens to a fluid when it undergoes a rapid change. Consider, for example, driving a piston into a tube filled with non-reacting gas. A disturbance is propagated through the fluid somewhat faster than the speed of sound. Because the disturbance propagates supersonically, it is a shock wave, and the fluid downstream of the shock has no advance information of it. In a frame of reference moving with the wave, atoms or molecules in front of the wave slam into the wave supersonically. On a microscopic level, they undergo collisions on the scale of the mean free path length until they come to rest in the post-shock flow (but moving in the frame of reference of the wave or of the tube). The bulk transfer of kinetic energy heats the post-shock flow. Because the mean free path length is assumed to be negligible in comparison to all other length scales in a hydrodynamic treatment, the shock front is essentially a hydrodynamic discontinuity. The jump conditions then establish the transition between the pre- and post-shock flow, based solely upon the conservation of mass, momentum, and energy. The conditions are correct even though the shock actually has a positive thickness. This non-reacting example of a shock wave also generalizes to reacting flows, where a combustion front (either a detonation or a deflagration) can be modeled as a discontinuity in a first approximation.
== Governing Equations ==
In a coordinate system that is moving with the discontinuity, the Rankine–Hugoniot conditions can be expressed as:
where m is the mass flow rate per unit area, ρ1 and ρ2 are the mass density of the fluid upstream and downstream of the wave, u1 and u2 are the fluid velocity upstream and downstream of the wave, p1 and p2 are the pressures in the two regions, and h1 and h2 are the specific (with the sense of per unit mass) enthalpies in the two regions. If in addition, the flow is reactive, then the species conservation equations demands that
ω
i
,
1
=
ω
i
,
2
=
0
,
i
=
1
,
2
,
3
,
…
,
N
,
Conservation of species
{\displaystyle \omega _{i,1}=\omega _{i,2}=0,\quad i=1,2,3,\dots ,N,\qquad {\text{Conservation of species}}}
to vanish both upstream and downstream of the discontinuity. Here,
ω
{\displaystyle \omega }
is the mass production rate of the i-th species of total N species involved in the reaction.
Combining conservation of mass and momentum gives us
p
2
−
p
1
1
/
ρ
2
−
1
/
ρ
1
=
−
m
2
{\displaystyle {\frac {p_{2}-p_{1}}{1/\rho _{2}-1/\rho _{1}}}=-m^{2}}
which defines a straight line known as the Michelson–Rayleigh line, named after the Russian physicist Vladimir A. Mikhelson (usually anglicized as Michelson) and Lord Rayleigh, that has a negative slope (since
m
2
{\displaystyle m^{2}}
is always positive) in the
p
−
ρ
−
1
{\displaystyle p-\rho ^{-1}}
plane. Using the Rankine–Hugoniot equations for the conservation of mass and momentum to eliminate u1 and u2, the equation for the conservation of energy can be expressed as the Hugoniot equation:
h
2
−
h
1
=
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
.
{\displaystyle h_{2}-h_{1}={\frac {1}{2}}\,\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)\,(p_{2}-p_{1}).}
The inverse of the density can also be expressed as the specific volume,
v
=
1
/
ρ
{\displaystyle v=1/\rho }
. Along with these, one has to specify the relation between the upstream and downstream equation of state
f
(
p
1
,
ρ
1
,
T
1
,
Y
i
,
1
)
=
f
(
p
2
,
ρ
2
,
T
2
,
Y
i
,
2
)
{\displaystyle f(p_{1},\rho _{1},T_{1},Y_{i,1})=f(p_{2},\rho _{2},T_{2},Y_{i,2})}
where
Y
i
{\displaystyle Y_{i}}
is the mass fraction of the species. Finally, the calorific equation of state
h
=
h
(
p
,
ρ
,
Y
i
)
{\displaystyle h=h(p,\rho ,Y_{i})}
is assumed to be known, i.e.,
h
(
p
1
,
ρ
1
,
Y
i
,
1
)
=
h
(
p
2
,
ρ
2
,
Y
i
,
2
)
.
{\displaystyle h(p_{1},\rho _{1},Y_{i,1})=h(p_{2},\rho _{2},Y_{i,2}).}
== Simplified Rankine–Hugoniot relations ==
Source:
The following assumptions are made in order to simplify the Rankine–Hugoniot equations. The mixture is assumed to obey the ideal gas law, so that relation between the downstream and upstream equation of state can be written as
p
2
ρ
2
T
2
=
p
1
ρ
1
T
1
=
R
W
¯
{\displaystyle {\frac {p_{2}}{\rho _{2}T_{2}}}={\frac {p_{1}}{\rho _{1}T_{1}}}={\frac {R}{\overline {W}}}}
where
R
{\displaystyle R}
is the universal gas constant and the mean molecular weight
W
¯
{\displaystyle {\overline {W}}}
is assumed to be constant (otherwise,
W
¯
{\displaystyle {\overline {W}}}
would depend on the mass fraction of the all species). If one assumes that the specific heat at constant pressure
c
p
{\displaystyle c_{p}}
is also constant across the wave, the change in enthalpies (calorific equation of state) can be simply written as
h
2
−
h
1
=
−
q
+
c
p
(
T
2
−
T
1
)
{\displaystyle h_{2}-h_{1}=-q+c_{p}(T_{2}-T_{1})}
where the first term in the above expression represents the amount of heat released per unit mass of the upstream mixture by the wave and the second term represents the sensible heating. Eliminating temperature using the equation of state and substituting the above expression for the change in enthalpies into the Hugoniot equation, one obtains an Hugoniot equation expressed only in terms of pressure and densities,
(
γ
γ
−
1
)
(
p
2
ρ
2
−
p
1
ρ
1
)
−
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
=
q
,
{\displaystyle \left({\frac {\gamma }{\gamma -1}}\right)\left({\frac {p_{2}}{\rho _{2}}}-{\frac {p_{1}}{\rho _{1}}}\right)-{\frac {1}{2}}\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)(p_{2}-p_{1})=q,}
where
γ
{\displaystyle \gamma }
is the specific heat ratio, which for ordinary room temperature air (298 KELVIN) = 1.40. An Hugoniot curve without heat release (
q
=
0
{\displaystyle q=0}
) is often called a "shock Hugoniot", or simply a(n) "Hugoniot". Along with the Rayleigh line equation, the above equation completely determines the state of the system. These two equations can be written compactly by introducing the following non-dimensional scales,
p
~
=
p
2
p
1
,
v
~
=
ρ
1
ρ
2
,
α
=
q
ρ
1
p
1
,
μ
=
m
2
p
1
ρ
1
.
{\displaystyle {\tilde {p}}={\frac {p_{2}}{p_{1}}},\quad {\tilde {v}}={\frac {\rho _{1}}{\rho _{2}}},\quad \alpha ={\frac {q\rho _{1}}{p_{1}}},\quad \mu ={\frac {m^{2}}{p_{1}\rho _{1}}}.}
The Rayleigh line equation and the Hugoniot equation then simplifies to
p
~
−
1
v
~
−
1
=
−
μ
p
~
=
[
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
]
−
v
~
[
(
γ
+
1
)
/
(
γ
−
1
)
]
v
~
−
1
.
{\displaystyle {\begin{aligned}{\frac {{\tilde {p}}-1}{{\tilde {v}}-1}}&=-\mu \\{\tilde {p}}&={\frac {[2\alpha +(\gamma +1)/(\gamma -1)]-{\tilde {v}}}{[(\gamma +1)/(\gamma -1)]{\tilde {v}}-1}}.\end{aligned}}}
Given the upstream conditions, the intersection of above two equations in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane determine the downstream conditions; in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane, the upstream condition correspond to the point
(
v
~
,
p
~
)
=
(
1
,
1
)
{\displaystyle ({\tilde {v}},{\tilde {p}})=(1,1)}
. If no heat release occurs, for example, shock waves without chemical reaction, then
α
=
0
{\displaystyle \alpha =0}
. The Hugoniot curves asymptote to the lines
v
~
=
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {v}}=(\gamma -1)/(\gamma +1)}
and
p
~
=
−
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {p}}=-(\gamma -1)/(\gamma +1)}
, which are depicted as dashed lines in the figure. As mentioned in the figure, only the white region bounded by these two asymptotes are allowed so that
μ
{\displaystyle \mu }
is positive. Shock waves and detonations correspond to the top-left white region wherein
p
~
>
1
{\displaystyle {\tilde {p}}>1}
and
v
~
<
1
{\displaystyle {\tilde {v}}<1}
, that is to say, the pressure increases and the specific volume decreases across the wave (the Chapman–Jouguet condition for detonation is where Rayleigh line is tangent to the Hugoniot curve). Deflagrations, on the other hand, correspond to the bottom-right white region wherein
p
~
<
1
{\displaystyle {\tilde {p}}<1}
and
v
~
>
1
{\displaystyle {\tilde {v}}>1}
, that is to say, the pressure decreases and the specific volume increases across the wave; the pressure decrease a flame is typically very small which is seldom considered when studying deflagrations.
For shock waves and detonations, the pressure increase across the wave can take any values between
0
≤
p
~
<
∞
{\displaystyle 0\leq {\tilde {p}}<\infty }
; the steeper the slope of the Rayleigh line, the stronger is the wave. On the contrary, here the specific volume ratio is restricted to the finite interval
(
γ
−
1
)
/
(
γ
+
1
)
≤
v
~
≤
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
{\displaystyle (\gamma -1)/(\gamma +1)\leq {\tilde {v}}\leq 2\alpha +(\gamma +1)/(\gamma -1)}
(the upper bound is derived for the case
p
~
→
0
{\displaystyle {\tilde {p}}\rightarrow 0}
because pressure cannot take negative values). If
γ
=
1.4
{\displaystyle \gamma =1.4}
(diatomic gas without the vibrational mode excitation), the interval is
1
/
6
≤
v
~
≤
2
α
+
6
{\displaystyle 1/6\leq {\tilde {v}}\leq 2\alpha +6}
, in other words, the shock wave can increase the density at most by a factor of 6. For monatomic gas,
γ
=
5
/
3
{\displaystyle \gamma =5/3}
, the allowed interval is
1
/
4
≤
v
~
≤
2
α
+
4
{\displaystyle 1/4\leq {\tilde {v}}\leq 2\alpha +4}
. For diatomic gases with vibrational mode excited, we have
γ
=
9
/
7
{\displaystyle \gamma =9/7}
leading to the interval
1
/
8
≤
v
~
≤
2
α
+
8
{\displaystyle 1/8\leq {\tilde {v}}\leq 2\alpha +8}
. In reality, the specific heat ratio is not constant in the shock wave due to molecular dissociation and ionization, but even in these cases, density ratio in general do not exceed a factor of about 11–13.
== Derivation from Euler equations ==
Consider gas in a one-dimensional container (e.g., a long thin tube). Assume that the fluid is inviscid (i.e., it shows no viscosity effects as for example friction with the tube walls). Furthermore, assume that there is no heat transfer by conduction or radiation and that gravitational acceleration can be neglected. Such a system can be described by the following system of conservation laws, known as the 1D Euler equations, that in conservation form is:
where
ρ
,
{\displaystyle \rho ,}
fluid mass density,
u
,
{\displaystyle u,}
fluid velocity,
e
,
{\displaystyle e,}
specific internal energy of the fluid,
p
,
{\displaystyle p,}
fluid pressure, and
E
t
=
ρ
e
+
ρ
1
2
u
2
,
{\displaystyle E^{t}=\rho e+\rho {\tfrac {1}{2}}u^{2},}
is the total energy density of the fluid, [J/m3], while e is its specific internal energy
Assume further that the gas is calorically ideal and that therefore a polytropic equation-of-state of the simple form
is valid, where
γ
{\displaystyle \gamma }
is the constant ratio of specific heats
c
p
/
c
v
{\displaystyle c_{p}/c_{v}}
. This quantity also appears as the polytropic exponent of the polytropic process described by
For an extensive list of compressible flow equations, etc., refer to NACA Report 1135 (1953).
Note: For a calorically ideal gas
γ
{\displaystyle \gamma }
is a constant and for a thermally ideal gas
γ
{\displaystyle \gamma }
is a function of temperature. In the latter case, the dependence of pressure on mass density and internal energy might differ from that given by equation (4).
=== The jump condition ===
Before proceeding further it is necessary to introduce the concept of a jump condition – a condition that holds at a discontinuity or abrupt change.
Consider a 1D situation where there is a jump in the scalar conserved physical quantity
w
{\displaystyle w}
, which is governed by integral conservation law
for any
x
1
{\displaystyle x_{1}}
,
x
2
{\displaystyle x_{2}}
,
x
1
<
x
2
{\displaystyle x_{1}<x_{2}}
, and, therefore, by partial differential equation
for smooth solutions.
Let the solution exhibit a jump (or shock) at
x
=
x
s
(
t
)
{\displaystyle x=x_{s}(t)}
, where
x
1
<
x
s
(
t
)
{\displaystyle x_{1}<x_{s}(t)}
and
x
s
(
t
)
<
x
2
{\displaystyle x_{s}(t)<x_{2}}
, then
The subscripts 1 and 2 indicate conditions just upstream and just downstream of the jump respectively, i.e.
w
1
=
lim
ϵ
→
0
+
w
(
x
s
−
ϵ
)
{\textstyle w_{1}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}-\epsilon \right)}
and
w
2
=
lim
ϵ
→
0
+
w
(
x
s
+
ϵ
)
{\textstyle w_{2}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}+\epsilon \right)}
.
∴
{\displaystyle \therefore }
is the therefore sign.
Note, to arrive at equation (8) we have used the fact that
d
x
1
/
d
t
=
0
{\displaystyle dx_{1}/dt=0}
and
d
x
2
/
d
t
=
0
{\displaystyle dx_{2}/dt=0}
.
Now, let
x
1
→
x
s
(
t
)
−
ϵ
{\displaystyle x_{1}\to x_{s}(t)-\epsilon }
and
x
2
→
x
s
(
t
)
+
ϵ
{\displaystyle x_{2}\to x_{s}(t)+\epsilon }
, when we have
∫
x
1
x
s
(
t
)
−
ϵ
w
t
d
x
→
0
{\textstyle \int _{x_{1}}^{x_{s}(t)-\epsilon }w_{t}\,dx\to 0}
and
∫
x
s
(
t
)
+
ϵ
x
2
w
t
d
x
→
0
{\textstyle \int _{x_{s}(t)+\epsilon }^{x_{2}}w_{t}\,dx\to 0}
, and in the limit
where we have defined
u
s
=
d
x
s
(
t
)
/
d
t
{\displaystyle u_{s}=dx_{s}(t)/dt}
(the system characteristic or shock speed), which by simple division is given by
Equation (9) represents the jump condition for conservation law (6). A shock situation arises in a system where its characteristics intersect, and under these conditions a requirement for a unique single-valued solution is that the solution should satisfy the admissibility condition or entropy condition. For physically real applications this means that the solution should satisfy the Lax entropy condition
where
f
′
(
w
1
)
{\displaystyle f'\left(w_{1}\right)}
and
f
′
(
w
2
)
{\displaystyle f'\left(w_{2}\right)}
represent characteristic speeds at upstream and downstream conditions respectively.
=== Shock condition ===
In the case of the hyperbolic conservation law (6), we have seen that the shock speed can be obtained by simple division. However, for the 1D Euler equations (1), (2) and (3), we have the vector state variable
[
ρ
ρ
u
E
]
T
{\displaystyle {\begin{bmatrix}\rho &\rho u&E\end{bmatrix}}^{\mathsf {T}}}
and the jump conditions become
Equations (12), (13) and (14) are known as the Rankine–Hugoniot conditions for the Euler equations and are derived by enforcing the conservation laws in integral form over a control volume that includes the shock. For this situation
u
s
{\displaystyle u_{s}}
cannot be obtained by simple division. However, it can be shown by transforming the problem to a moving co-ordinate system
(setting
u
s
′
:=
u
s
−
u
1
{\displaystyle u_{s}':=u_{s}-u_{1}}
,
u
1
′
:=
0
{\displaystyle u'_{1}:=0}
,
u
2
′
:=
u
2
−
u
1
{\displaystyle u'_{2}:=u_{2}-u_{1}}
to remove
u
1
{\displaystyle u_{1}}
) and some algebraic manipulation (involving the elimination of
u
2
′
{\displaystyle u'_{2}}
from the transformed equation (13) using the transformed equation (12)), that the shock speed is given by
where
c
1
=
γ
p
1
/
ρ
1
{\textstyle c_{1}={\sqrt {\gamma p_{1}/\rho _{1}}}}
is the speed of sound in the fluid at upstream conditions.
== Shock Hugoniot and Rayleigh line in solids ==
For shocks in solids, a closed form expression such as equation (15) cannot be derived from first principles. Instead, experimental observations indicate that a linear relation can be used instead (called the shock Hugoniot in the us-up plane) that has the form
where c0 is the bulk speed of sound in the material (in uniaxial compression), s is a parameter (the slope of the shock Hugoniot) obtained from fits to experimental data, and up = u2 is the particle velocity inside the compressed region behind the shock front.
The above relation, when combined with the Hugoniot equations for the conservation of mass and momentum, can be used to determine the shock Hugoniot in the p-v plane, where v is the specific volume (per unit mass):
Alternative equations of state, such as the Mie–Grüneisen equation of state may also be used instead of the above equation.
The shock Hugoniot describes the locus of all possible thermodynamic states a material can exist in behind a shock, projected onto a two dimensional state-state plane. It is therefore a set of equilibrium states and does not specifically represent the path through which a material undergoes transformation.
Weak shocks are isentropic and that the isentrope represents the path through which the material is loaded from the initial to final states by a compression wave with converging characteristics. In the case of weak shocks, the Hugoniot will therefore fall directly on the isentrope and can be used directly as the equivalent path. In the case of a strong shock we can no longer make that simplification directly. However, for engineering calculations, it is deemed that the isentrope is close enough to the Hugoniot that the same assumption can be made.
If the Hugoniot is approximately the loading path between states for an "equivalent" compression wave, then the jump conditions for the shock loading path can be determined by drawing a straight line between the initial and final states. This line is called the Rayleigh line and has the following equation:
=== Hugoniot elastic limit ===
Most solid materials undergo plastic deformations when subjected to strong shocks. The point on the shock Hugoniot at which a material transitions from a purely elastic state to an elastic-plastic state is called the Hugoniot elastic limit (HEL) and the pressure at which this transition takes place is denoted pHEL. Values of pHEL can range from 0.2 GPa to 20 GPa. Above the HEL, the material loses much of its shear strength and starts behaving like a fluid.
== Magnetohydrodynamics ==
Rankine–Hugoniot conditions in magnetohydrodynamics are interesting to consider since they are very relevant to astrophysical applications. Across the discontinuity the normal component
H
n
{\displaystyle H_{n}}
of the magnetic field
H
{\displaystyle \mathbf {H} }
and the tangential component
E
t
{\displaystyle \mathbf {E} _{t}}
of the electric field
E
=
−
u
×
H
/
c
{\displaystyle \mathbf {E} =-\mathbf {u} \times \mathbf {H} /c}
(infinite conductivity limit) must be continuous. We thus have
0
=
[
[
j
]
]
,
j
≡
ρ
u
n
conservation of mass
,
0
=
[
[
H
n
]
]
continuity of normal component of
H
,
{\displaystyle {\begin{aligned}0=[\![j]\!],\,\,j\equiv \rho u_{n}&\quad {\text{conservation of mass}},\\0=[\![H_{n}]\!]&\quad {\text{continuity of normal component of }}\mathbf {H} ,\end{aligned}}}
where
[
[
⋅
]
]
{\displaystyle [\![\cdot ]\!]}
is the difference between the values of any physical quantity on the two sides of the discontinuity. The remaining conditions are given by
j
2
[
[
1
/
ρ
]
]
+
[
[
p
]
]
+
[
[
H
t
2
]
]
/
8
π
=
0
conservation of normal momentum
,
j
[
[
u
t
]
]
=
H
n
[
[
H
t
]
]
/
4
π
conservation of tangential momentum
,
j
[
[
h
+
j
2
/
2
ρ
2
+
u
t
2
/
2
+
H
t
2
/
4
π
ρ
]
]
=
H
n
[
[
H
t
⋅
u
t
]
]
/
4
π
conservation of energy
,
H
n
[
[
u
t
]
]
=
j
[
[
H
t
/
ρ
]
]
continuity of tangential components of
E
.
{\displaystyle {\begin{aligned}j^{2}[\![1/\rho ]\!]+[\![p]\!]+[\![\mathbf {H} _{t}^{2}]\!]/8\pi =0&\quad {\text{conservation of normal momentum}},\\j[\![\mathbf {u} _{t}]\!]=H_{n}[\![\mathbf {H} _{t}]\!]/4\pi &\quad {\text{conservation of tangential momentum}},\\j[\![h+j^{2}/2\rho ^{2}+\mathbf {u} _{t}^{2}/2+\mathbf {H} _{t}^{2}/4\pi \rho ]\!]=H_{n}[\![\mathbf {H} _{t}\cdot \mathbf {u} _{t}]\!]/4\pi &\quad {\text{conservation of energy}},\\H_{n}[\![\mathbf {u} _{t}]\!]=j[\![\mathbf {H} _{t}/\rho ]\!]&\quad {\text{continuity of tangential components of }}\mathbf {E} .\end{aligned}}}
These conditions are general in the sense that they include contact discontinuities (
j
=
0
,
H
n
≠
0
,
[
[
u
]
]
=
[
[
p
]
]
=
[
[
H
]
]
=
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=0,\,H_{n}\neq 0,\,[\![\mathbf {u} ]\!]=[\![p]\!]=[\![\mathbf {H} ]\!]=0,\,[\![\rho ]\!]\neq 0}
) tangential discontinuities (
j
=
H
n
=
0
,
[
[
u
t
ρ
]
]
≠
0
,
[
[
H
t
]
]
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=H_{n}=0,\,[\![\mathbf {u} _{t}\rho ]\!]\neq 0,\,[\![\mathbf {H} _{t}]\!]\neq 0,\,[\![\rho ]\!]\neq 0}
), rotational or Alfvén discontinuities (
j
=
H
n
ρ
/
4
π
≠
0
,
[
[
ρ
]
]
=
[
[
u
n
]
]
=
[
[
p
]
]
=
[
[
H
t
]
]
=
0
{\textstyle j=H_{n}{\sqrt {\rho /4\pi }}\neq 0,\,[\![\rho ]\!]=[\![u_{n}]\!]=[\![p]\!]=[\![\mathbf {H} _{t}]\!]=0}
) and shock waves (
j
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j\neq 0,\,[\![\rho ]\!]\neq 0}
).
== See also ==
Euler equations (fluid dynamics)
Shock polar
Becker–Morduchow–Libby solution
Mie–Grüneisen equation of state
Engineering Acoustics Wikibook
Atmospheric focusing
== References == | Wikipedia/Rankine–Hugoniot_equation |
In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of general relativity. They have applications in high-energy astrophysics and numerical relativity, where they are commonly used for describing phenomena such as gamma-ray bursts, accretion phenomena, and neutron stars, often with the addition of a magnetic field. Note: for consistency with the literature, this article makes use of natural units, namely the speed of light
c
=
1
{\displaystyle c=1}
and the Einstein summation convention.
== Motivation ==
For most fluids observable on Earth, traditional fluid mechanics based on Newtonian mechanics is sufficient. However, as the fluid velocity approaches the speed of light or moves through strong gravitational fields, or the pressure approaches the energy density (
P
∼
ρ
{\displaystyle P\sim \rho }
), these equations are no longer valid. Such situations occur frequently in astrophysical applications. For example, gamma-ray bursts often feature speeds only
0.01
%
{\displaystyle 0.01\%}
less than the speed of light, and neutron stars feature gravitational fields that are more than
10
11
{\displaystyle 10^{11}}
times stronger than the Earth's. Under these extreme circumstances, only a relativistic treatment of fluids will suffice.
== Introduction ==
The equations of motion are contained in the continuity equation of the stress–energy tensor
T
μ
ν
{\displaystyle T^{\mu \nu }}
:
∇
μ
T
μ
ν
=
0
,
{\displaystyle \nabla _{\mu }T^{\mu \nu }=0,}
where
∇
μ
{\displaystyle \nabla _{\mu }}
is the covariant derivative. For a perfect fluid,
T
μ
ν
=
(
e
+
p
)
u
μ
u
ν
+
p
g
μ
ν
.
{\displaystyle T^{\mu \nu }\,=(e+p)u^{\mu }u^{\nu }+pg^{\mu \nu }.}
Here
e
{\displaystyle e}
is the total mass-energy density (including both rest mass and internal energy density) of the fluid,
p
{\displaystyle p}
is the fluid pressure,
u
μ
{\displaystyle u^{\mu }}
is the four-velocity of the fluid, and
g
μ
ν
{\displaystyle g^{\mu \nu }}
is the metric tensor. To the above equations, a statement of conservation is usually added, usually conservation of baryon number. If
n
{\displaystyle n}
is the number density of baryons this may be stated
∇
μ
(
n
u
μ
)
=
0.
{\displaystyle \nabla _{\mu }(nu^{\mu })=0.}
These equations reduce to the classical Euler equations if the fluid three-velocity is much less than the speed of light, the pressure is much less than the energy density, and the latter is dominated by the rest mass density. To close this system, an equation of state, such as an ideal gas or a Fermi gas, is also added.
== Equations of motion in flat space ==
In the case of flat space, that is
∇
μ
=
∂
μ
{\displaystyle \nabla _{\mu }=\partial _{\mu }}
and using a metric signature of
(
−
,
+
,
+
,
+
)
{\displaystyle (-,+,+,+)}
, the equations of motion are,
(
e
+
p
)
u
μ
∂
μ
u
ν
=
−
∂
ν
p
−
u
ν
u
μ
∂
μ
p
{\displaystyle \left(e+p\right)u^{\mu }\partial _{\mu }u^{\nu }=-\partial ^{\nu }p-u^{\nu }u^{\mu }\partial _{\mu }p}
Where
e
=
γ
ρ
c
2
+
ρ
ε
{\displaystyle e=\gamma \rho c^{2}+\rho \varepsilon }
is the energy density of the system, with
p
{\displaystyle p}
being the pressure, and
u
μ
=
γ
(
1
,
v
/
c
)
{\displaystyle u^{\mu }=\gamma (1,\mathbf {v} /{c})}
being the four-velocity of the system.
Expanding out the sums and equations, we have, (using
d
d
t
{\displaystyle {\frac {d}{dt}}}
as the material derivative)
(
e
+
p
)
γ
c
d
u
μ
d
t
=
−
∂
μ
p
−
γ
c
d
p
d
t
u
μ
{\displaystyle \left(e+p\right){\frac {\gamma }{c}}{\frac {du^{\mu }}{dt}}=-\partial ^{\mu }p-{\frac {\gamma }{c}}{\frac {dp}{dt}}u^{\mu }}
Then, picking
u
ν
=
u
i
=
γ
c
v
i
{\displaystyle u^{\nu }=u^{i}={\frac {\gamma }{c}}v_{i}}
to observe the behavior of the velocity itself, we see that the equations of motion become
(
e
+
p
)
γ
c
2
d
d
t
(
γ
v
i
)
=
−
∂
i
p
−
γ
2
c
2
d
p
d
t
v
i
{\displaystyle \left(e+p\right){\frac {\gamma }{c^{2}}}{\frac {d}{dt}}{\left(\gamma v_{i}\right)}=-\partial _{i}p-{\frac {\gamma ^{2}}{c^{2}}}{\frac {dp}{dt}}v_{i}}
Note that taking the non-relativistic limit, we have
1
c
2
(
e
+
p
)
=
γ
ρ
+
1
c
2
ρ
ε
+
1
c
2
p
≈
ρ
{\textstyle {\frac {1}{c^{2}}}\left(e+p\right)=\gamma \rho +{\frac {1}{c^{2}}}\rho \varepsilon +{\frac {1}{c^{2}}}p\approx \rho }
. This says that the energy of the fluid is dominated by its rest energy.
In this limit, we have
γ
→
1
{\displaystyle \gamma \to 1}
and
c
→
∞
{\displaystyle c\to \infty }
, and can see that we return the Euler Equation of
ρ
d
v
i
d
t
=
−
∂
i
p
{\displaystyle \rho {\frac {dv_{i}}{dt}}=-\partial _{i}p}
.
=== Derivation ===
In order to determine the equations of motion, we take advantage of the following spatial projection tensor condition:
∂
μ
T
μ
ν
+
u
α
u
ν
∂
μ
T
μ
α
=
0
{\displaystyle \partial _{\mu }T^{\mu \nu }+u_{\alpha }u^{\nu }\partial _{\mu }T^{\mu \alpha }=0}
We prove this by looking at
∂
μ
T
μ
ν
+
u
α
u
ν
∂
μ
T
μ
α
{\displaystyle \partial _{\mu }T^{\mu \nu }+u_{\alpha }u^{\nu }\partial _{\mu }T^{\mu \alpha }}
and then multiplying each side by
u
ν
{\displaystyle u_{\nu }}
. Upon doing this, and noting that
u
μ
u
μ
=
−
1
{\displaystyle u^{\mu }u_{\mu }=-1}
, we have
u
ν
∂
μ
T
μ
ν
−
u
α
∂
μ
T
μ
α
{\displaystyle u_{\nu }\partial _{\mu }T^{\mu \nu }-u_{\alpha }\partial _{\mu }T^{\mu \alpha }}
. Relabeling the indices
α
{\displaystyle \alpha }
as
ν
{\displaystyle \nu }
shows that the two completely cancel. This cancellation is the expected result of contracting a temporal tensor with a spatial tensor.
Now, when we note that
T
μ
ν
=
w
u
μ
u
ν
+
p
g
μ
ν
{\displaystyle T^{\mu \nu }=wu^{\mu }u^{\nu }+pg^{\mu \nu }}
where we have implicitly defined that
w
≡
e
+
p
{\displaystyle w\equiv e+p}
, we can calculate that
∂
μ
T
μ
ν
=
(
∂
μ
w
)
u
μ
u
ν
+
w
(
∂
μ
u
μ
)
u
ν
+
w
u
μ
∂
μ
u
ν
+
∂
ν
p
∂
μ
T
μ
α
=
(
∂
μ
w
)
u
μ
u
α
+
w
(
∂
μ
u
μ
)
u
α
+
w
u
μ
∂
μ
u
α
+
∂
α
p
{\displaystyle {\begin{aligned}\partial _{\mu }T^{\mu \nu }&=\left(\partial _{\mu }w\right)u^{\mu }u^{\nu }+w\left(\partial _{\mu }u^{\mu }\right)u^{\nu }+wu^{\mu }\partial _{\mu }u^{\nu }+\partial ^{\nu }p\\[1ex]\partial _{\mu }T^{\mu \alpha }&=\left(\partial _{\mu }w\right)u^{\mu }u^{\alpha }+w\left(\partial _{\mu }u^{\mu }\right)u^{\alpha }+wu^{\mu }\partial _{\mu }u^{\alpha }+\partial ^{\alpha }p\end{aligned}}}
and thus
u
ν
u
α
∂
μ
T
μ
α
=
(
∂
μ
w
)
u
μ
u
ν
u
α
u
α
+
w
(
∂
μ
u
μ
)
u
ν
u
α
u
α
+
w
u
μ
u
ν
u
α
∂
μ
u
α
+
u
ν
u
α
∂
α
p
{\displaystyle u^{\nu }u_{\alpha }\partial _{\mu }T^{\mu \alpha }=(\partial _{\mu }w)u^{\mu }u^{\nu }u^{\alpha }u_{\alpha }+w(\partial _{\mu }u^{\mu })u^{\nu }u^{\alpha }u_{\alpha }+wu^{\mu }u^{\nu }u_{\alpha }\partial _{\mu }u^{\alpha }+u^{\nu }u_{\alpha }\partial ^{\alpha }p}
Then, let's note the fact that
u
α
u
α
=
−
1
{\displaystyle u^{\alpha }u_{\alpha }=-1}
and
u
α
∂
ν
u
α
=
0
{\displaystyle u^{\alpha }\partial _{\nu }u_{\alpha }=0}
. Note that the second identity follows from the first. Under these simplifications, we find that
u
ν
u
α
∂
μ
T
μ
α
=
−
(
∂
μ
w
)
u
μ
u
ν
−
w
(
∂
μ
u
μ
)
u
ν
+
u
ν
u
α
∂
α
p
{\displaystyle u^{\nu }u_{\alpha }\partial _{\mu }T^{\mu \alpha }=-(\partial _{\mu }w)u^{\mu }u^{\nu }-w(\partial _{\mu }u^{\mu })u^{\nu }+u^{\nu }u^{\alpha }\partial _{\alpha }p}
and thus by
∂
μ
T
μ
ν
+
u
α
u
ν
∂
μ
T
μ
α
=
0
{\displaystyle \partial _{\mu }T^{\mu \nu }+u_{\alpha }u^{\nu }\partial _{\mu }T^{\mu \alpha }=0}
, we have
(
∂
μ
w
)
u
μ
u
ν
+
w
(
∂
μ
u
μ
)
u
ν
+
w
u
μ
∂
μ
u
ν
+
∂
ν
p
−
(
∂
μ
w
)
u
μ
u
ν
−
w
(
∂
μ
u
μ
)
u
ν
+
u
ν
u
α
∂
α
p
=
0
{\displaystyle (\partial _{\mu }w)u^{\mu }u^{\nu }+w(\partial _{\mu }u^{\mu })u^{\nu }+wu^{\mu }\partial _{\mu }u^{\nu }+\partial ^{\nu }p-(\partial _{\mu }w)u^{\mu }u^{\nu }-w(\partial _{\mu }u^{\mu })u^{\nu }+u^{\nu }u^{\alpha }\partial _{\alpha }p=0}
We have two cancellations, and are thus left with
(
e
+
p
)
u
μ
∂
μ
u
ν
=
−
∂
ν
p
−
u
ν
u
α
∂
α
p
{\displaystyle (e+p)u^{\mu }\partial _{\mu }u^{\nu }=-\partial ^{\nu }p-u^{\nu }u^{\alpha }\partial _{\alpha }p}
== See also ==
Relativistic heat conduction
Equation of state (cosmology)
== References == | Wikipedia/Relativistic_Euler_equations |
The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one-dimensional flow in fluids or a one-dimensional deformation in solids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot.
The basic idea of the jump conditions is to consider what happens to a fluid when it undergoes a rapid change. Consider, for example, driving a piston into a tube filled with non-reacting gas. A disturbance is propagated through the fluid somewhat faster than the speed of sound. Because the disturbance propagates supersonically, it is a shock wave, and the fluid downstream of the shock has no advance information of it. In a frame of reference moving with the wave, atoms or molecules in front of the wave slam into the wave supersonically. On a microscopic level, they undergo collisions on the scale of the mean free path length until they come to rest in the post-shock flow (but moving in the frame of reference of the wave or of the tube). The bulk transfer of kinetic energy heats the post-shock flow. Because the mean free path length is assumed to be negligible in comparison to all other length scales in a hydrodynamic treatment, the shock front is essentially a hydrodynamic discontinuity. The jump conditions then establish the transition between the pre- and post-shock flow, based solely upon the conservation of mass, momentum, and energy. The conditions are correct even though the shock actually has a positive thickness. This non-reacting example of a shock wave also generalizes to reacting flows, where a combustion front (either a detonation or a deflagration) can be modeled as a discontinuity in a first approximation.
== Governing Equations ==
In a coordinate system that is moving with the discontinuity, the Rankine–Hugoniot conditions can be expressed as:
where m is the mass flow rate per unit area, ρ1 and ρ2 are the mass density of the fluid upstream and downstream of the wave, u1 and u2 are the fluid velocity upstream and downstream of the wave, p1 and p2 are the pressures in the two regions, and h1 and h2 are the specific (with the sense of per unit mass) enthalpies in the two regions. If in addition, the flow is reactive, then the species conservation equations demands that
ω
i
,
1
=
ω
i
,
2
=
0
,
i
=
1
,
2
,
3
,
…
,
N
,
Conservation of species
{\displaystyle \omega _{i,1}=\omega _{i,2}=0,\quad i=1,2,3,\dots ,N,\qquad {\text{Conservation of species}}}
to vanish both upstream and downstream of the discontinuity. Here,
ω
{\displaystyle \omega }
is the mass production rate of the i-th species of total N species involved in the reaction.
Combining conservation of mass and momentum gives us
p
2
−
p
1
1
/
ρ
2
−
1
/
ρ
1
=
−
m
2
{\displaystyle {\frac {p_{2}-p_{1}}{1/\rho _{2}-1/\rho _{1}}}=-m^{2}}
which defines a straight line known as the Michelson–Rayleigh line, named after the Russian physicist Vladimir A. Mikhelson (usually anglicized as Michelson) and Lord Rayleigh, that has a negative slope (since
m
2
{\displaystyle m^{2}}
is always positive) in the
p
−
ρ
−
1
{\displaystyle p-\rho ^{-1}}
plane. Using the Rankine–Hugoniot equations for the conservation of mass and momentum to eliminate u1 and u2, the equation for the conservation of energy can be expressed as the Hugoniot equation:
h
2
−
h
1
=
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
.
{\displaystyle h_{2}-h_{1}={\frac {1}{2}}\,\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)\,(p_{2}-p_{1}).}
The inverse of the density can also be expressed as the specific volume,
v
=
1
/
ρ
{\displaystyle v=1/\rho }
. Along with these, one has to specify the relation between the upstream and downstream equation of state
f
(
p
1
,
ρ
1
,
T
1
,
Y
i
,
1
)
=
f
(
p
2
,
ρ
2
,
T
2
,
Y
i
,
2
)
{\displaystyle f(p_{1},\rho _{1},T_{1},Y_{i,1})=f(p_{2},\rho _{2},T_{2},Y_{i,2})}
where
Y
i
{\displaystyle Y_{i}}
is the mass fraction of the species. Finally, the calorific equation of state
h
=
h
(
p
,
ρ
,
Y
i
)
{\displaystyle h=h(p,\rho ,Y_{i})}
is assumed to be known, i.e.,
h
(
p
1
,
ρ
1
,
Y
i
,
1
)
=
h
(
p
2
,
ρ
2
,
Y
i
,
2
)
.
{\displaystyle h(p_{1},\rho _{1},Y_{i,1})=h(p_{2},\rho _{2},Y_{i,2}).}
== Simplified Rankine–Hugoniot relations ==
Source:
The following assumptions are made in order to simplify the Rankine–Hugoniot equations. The mixture is assumed to obey the ideal gas law, so that relation between the downstream and upstream equation of state can be written as
p
2
ρ
2
T
2
=
p
1
ρ
1
T
1
=
R
W
¯
{\displaystyle {\frac {p_{2}}{\rho _{2}T_{2}}}={\frac {p_{1}}{\rho _{1}T_{1}}}={\frac {R}{\overline {W}}}}
where
R
{\displaystyle R}
is the universal gas constant and the mean molecular weight
W
¯
{\displaystyle {\overline {W}}}
is assumed to be constant (otherwise,
W
¯
{\displaystyle {\overline {W}}}
would depend on the mass fraction of the all species). If one assumes that the specific heat at constant pressure
c
p
{\displaystyle c_{p}}
is also constant across the wave, the change in enthalpies (calorific equation of state) can be simply written as
h
2
−
h
1
=
−
q
+
c
p
(
T
2
−
T
1
)
{\displaystyle h_{2}-h_{1}=-q+c_{p}(T_{2}-T_{1})}
where the first term in the above expression represents the amount of heat released per unit mass of the upstream mixture by the wave and the second term represents the sensible heating. Eliminating temperature using the equation of state and substituting the above expression for the change in enthalpies into the Hugoniot equation, one obtains an Hugoniot equation expressed only in terms of pressure and densities,
(
γ
γ
−
1
)
(
p
2
ρ
2
−
p
1
ρ
1
)
−
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
=
q
,
{\displaystyle \left({\frac {\gamma }{\gamma -1}}\right)\left({\frac {p_{2}}{\rho _{2}}}-{\frac {p_{1}}{\rho _{1}}}\right)-{\frac {1}{2}}\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)(p_{2}-p_{1})=q,}
where
γ
{\displaystyle \gamma }
is the specific heat ratio, which for ordinary room temperature air (298 KELVIN) = 1.40. An Hugoniot curve without heat release (
q
=
0
{\displaystyle q=0}
) is often called a "shock Hugoniot", or simply a(n) "Hugoniot". Along with the Rayleigh line equation, the above equation completely determines the state of the system. These two equations can be written compactly by introducing the following non-dimensional scales,
p
~
=
p
2
p
1
,
v
~
=
ρ
1
ρ
2
,
α
=
q
ρ
1
p
1
,
μ
=
m
2
p
1
ρ
1
.
{\displaystyle {\tilde {p}}={\frac {p_{2}}{p_{1}}},\quad {\tilde {v}}={\frac {\rho _{1}}{\rho _{2}}},\quad \alpha ={\frac {q\rho _{1}}{p_{1}}},\quad \mu ={\frac {m^{2}}{p_{1}\rho _{1}}}.}
The Rayleigh line equation and the Hugoniot equation then simplifies to
p
~
−
1
v
~
−
1
=
−
μ
p
~
=
[
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
]
−
v
~
[
(
γ
+
1
)
/
(
γ
−
1
)
]
v
~
−
1
.
{\displaystyle {\begin{aligned}{\frac {{\tilde {p}}-1}{{\tilde {v}}-1}}&=-\mu \\{\tilde {p}}&={\frac {[2\alpha +(\gamma +1)/(\gamma -1)]-{\tilde {v}}}{[(\gamma +1)/(\gamma -1)]{\tilde {v}}-1}}.\end{aligned}}}
Given the upstream conditions, the intersection of above two equations in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane determine the downstream conditions; in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane, the upstream condition correspond to the point
(
v
~
,
p
~
)
=
(
1
,
1
)
{\displaystyle ({\tilde {v}},{\tilde {p}})=(1,1)}
. If no heat release occurs, for example, shock waves without chemical reaction, then
α
=
0
{\displaystyle \alpha =0}
. The Hugoniot curves asymptote to the lines
v
~
=
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {v}}=(\gamma -1)/(\gamma +1)}
and
p
~
=
−
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {p}}=-(\gamma -1)/(\gamma +1)}
, which are depicted as dashed lines in the figure. As mentioned in the figure, only the white region bounded by these two asymptotes are allowed so that
μ
{\displaystyle \mu }
is positive. Shock waves and detonations correspond to the top-left white region wherein
p
~
>
1
{\displaystyle {\tilde {p}}>1}
and
v
~
<
1
{\displaystyle {\tilde {v}}<1}
, that is to say, the pressure increases and the specific volume decreases across the wave (the Chapman–Jouguet condition for detonation is where Rayleigh line is tangent to the Hugoniot curve). Deflagrations, on the other hand, correspond to the bottom-right white region wherein
p
~
<
1
{\displaystyle {\tilde {p}}<1}
and
v
~
>
1
{\displaystyle {\tilde {v}}>1}
, that is to say, the pressure decreases and the specific volume increases across the wave; the pressure decrease a flame is typically very small which is seldom considered when studying deflagrations.
For shock waves and detonations, the pressure increase across the wave can take any values between
0
≤
p
~
<
∞
{\displaystyle 0\leq {\tilde {p}}<\infty }
; the steeper the slope of the Rayleigh line, the stronger is the wave. On the contrary, here the specific volume ratio is restricted to the finite interval
(
γ
−
1
)
/
(
γ
+
1
)
≤
v
~
≤
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
{\displaystyle (\gamma -1)/(\gamma +1)\leq {\tilde {v}}\leq 2\alpha +(\gamma +1)/(\gamma -1)}
(the upper bound is derived for the case
p
~
→
0
{\displaystyle {\tilde {p}}\rightarrow 0}
because pressure cannot take negative values). If
γ
=
1.4
{\displaystyle \gamma =1.4}
(diatomic gas without the vibrational mode excitation), the interval is
1
/
6
≤
v
~
≤
2
α
+
6
{\displaystyle 1/6\leq {\tilde {v}}\leq 2\alpha +6}
, in other words, the shock wave can increase the density at most by a factor of 6. For monatomic gas,
γ
=
5
/
3
{\displaystyle \gamma =5/3}
, the allowed interval is
1
/
4
≤
v
~
≤
2
α
+
4
{\displaystyle 1/4\leq {\tilde {v}}\leq 2\alpha +4}
. For diatomic gases with vibrational mode excited, we have
γ
=
9
/
7
{\displaystyle \gamma =9/7}
leading to the interval
1
/
8
≤
v
~
≤
2
α
+
8
{\displaystyle 1/8\leq {\tilde {v}}\leq 2\alpha +8}
. In reality, the specific heat ratio is not constant in the shock wave due to molecular dissociation and ionization, but even in these cases, density ratio in general do not exceed a factor of about 11–13.
== Derivation from Euler equations ==
Consider gas in a one-dimensional container (e.g., a long thin tube). Assume that the fluid is inviscid (i.e., it shows no viscosity effects as for example friction with the tube walls). Furthermore, assume that there is no heat transfer by conduction or radiation and that gravitational acceleration can be neglected. Such a system can be described by the following system of conservation laws, known as the 1D Euler equations, that in conservation form is:
where
ρ
,
{\displaystyle \rho ,}
fluid mass density,
u
,
{\displaystyle u,}
fluid velocity,
e
,
{\displaystyle e,}
specific internal energy of the fluid,
p
,
{\displaystyle p,}
fluid pressure, and
E
t
=
ρ
e
+
ρ
1
2
u
2
,
{\displaystyle E^{t}=\rho e+\rho {\tfrac {1}{2}}u^{2},}
is the total energy density of the fluid, [J/m3], while e is its specific internal energy
Assume further that the gas is calorically ideal and that therefore a polytropic equation-of-state of the simple form
is valid, where
γ
{\displaystyle \gamma }
is the constant ratio of specific heats
c
p
/
c
v
{\displaystyle c_{p}/c_{v}}
. This quantity also appears as the polytropic exponent of the polytropic process described by
For an extensive list of compressible flow equations, etc., refer to NACA Report 1135 (1953).
Note: For a calorically ideal gas
γ
{\displaystyle \gamma }
is a constant and for a thermally ideal gas
γ
{\displaystyle \gamma }
is a function of temperature. In the latter case, the dependence of pressure on mass density and internal energy might differ from that given by equation (4).
=== The jump condition ===
Before proceeding further it is necessary to introduce the concept of a jump condition – a condition that holds at a discontinuity or abrupt change.
Consider a 1D situation where there is a jump in the scalar conserved physical quantity
w
{\displaystyle w}
, which is governed by integral conservation law
for any
x
1
{\displaystyle x_{1}}
,
x
2
{\displaystyle x_{2}}
,
x
1
<
x
2
{\displaystyle x_{1}<x_{2}}
, and, therefore, by partial differential equation
for smooth solutions.
Let the solution exhibit a jump (or shock) at
x
=
x
s
(
t
)
{\displaystyle x=x_{s}(t)}
, where
x
1
<
x
s
(
t
)
{\displaystyle x_{1}<x_{s}(t)}
and
x
s
(
t
)
<
x
2
{\displaystyle x_{s}(t)<x_{2}}
, then
The subscripts 1 and 2 indicate conditions just upstream and just downstream of the jump respectively, i.e.
w
1
=
lim
ϵ
→
0
+
w
(
x
s
−
ϵ
)
{\textstyle w_{1}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}-\epsilon \right)}
and
w
2
=
lim
ϵ
→
0
+
w
(
x
s
+
ϵ
)
{\textstyle w_{2}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}+\epsilon \right)}
.
∴
{\displaystyle \therefore }
is the therefore sign.
Note, to arrive at equation (8) we have used the fact that
d
x
1
/
d
t
=
0
{\displaystyle dx_{1}/dt=0}
and
d
x
2
/
d
t
=
0
{\displaystyle dx_{2}/dt=0}
.
Now, let
x
1
→
x
s
(
t
)
−
ϵ
{\displaystyle x_{1}\to x_{s}(t)-\epsilon }
and
x
2
→
x
s
(
t
)
+
ϵ
{\displaystyle x_{2}\to x_{s}(t)+\epsilon }
, when we have
∫
x
1
x
s
(
t
)
−
ϵ
w
t
d
x
→
0
{\textstyle \int _{x_{1}}^{x_{s}(t)-\epsilon }w_{t}\,dx\to 0}
and
∫
x
s
(
t
)
+
ϵ
x
2
w
t
d
x
→
0
{\textstyle \int _{x_{s}(t)+\epsilon }^{x_{2}}w_{t}\,dx\to 0}
, and in the limit
where we have defined
u
s
=
d
x
s
(
t
)
/
d
t
{\displaystyle u_{s}=dx_{s}(t)/dt}
(the system characteristic or shock speed), which by simple division is given by
Equation (9) represents the jump condition for conservation law (6). A shock situation arises in a system where its characteristics intersect, and under these conditions a requirement for a unique single-valued solution is that the solution should satisfy the admissibility condition or entropy condition. For physically real applications this means that the solution should satisfy the Lax entropy condition
where
f
′
(
w
1
)
{\displaystyle f'\left(w_{1}\right)}
and
f
′
(
w
2
)
{\displaystyle f'\left(w_{2}\right)}
represent characteristic speeds at upstream and downstream conditions respectively.
=== Shock condition ===
In the case of the hyperbolic conservation law (6), we have seen that the shock speed can be obtained by simple division. However, for the 1D Euler equations (1), (2) and (3), we have the vector state variable
[
ρ
ρ
u
E
]
T
{\displaystyle {\begin{bmatrix}\rho &\rho u&E\end{bmatrix}}^{\mathsf {T}}}
and the jump conditions become
Equations (12), (13) and (14) are known as the Rankine–Hugoniot conditions for the Euler equations and are derived by enforcing the conservation laws in integral form over a control volume that includes the shock. For this situation
u
s
{\displaystyle u_{s}}
cannot be obtained by simple division. However, it can be shown by transforming the problem to a moving co-ordinate system
(setting
u
s
′
:=
u
s
−
u
1
{\displaystyle u_{s}':=u_{s}-u_{1}}
,
u
1
′
:=
0
{\displaystyle u'_{1}:=0}
,
u
2
′
:=
u
2
−
u
1
{\displaystyle u'_{2}:=u_{2}-u_{1}}
to remove
u
1
{\displaystyle u_{1}}
) and some algebraic manipulation (involving the elimination of
u
2
′
{\displaystyle u'_{2}}
from the transformed equation (13) using the transformed equation (12)), that the shock speed is given by
where
c
1
=
γ
p
1
/
ρ
1
{\textstyle c_{1}={\sqrt {\gamma p_{1}/\rho _{1}}}}
is the speed of sound in the fluid at upstream conditions.
== Shock Hugoniot and Rayleigh line in solids ==
For shocks in solids, a closed form expression such as equation (15) cannot be derived from first principles. Instead, experimental observations indicate that a linear relation can be used instead (called the shock Hugoniot in the us-up plane) that has the form
where c0 is the bulk speed of sound in the material (in uniaxial compression), s is a parameter (the slope of the shock Hugoniot) obtained from fits to experimental data, and up = u2 is the particle velocity inside the compressed region behind the shock front.
The above relation, when combined with the Hugoniot equations for the conservation of mass and momentum, can be used to determine the shock Hugoniot in the p-v plane, where v is the specific volume (per unit mass):
Alternative equations of state, such as the Mie–Grüneisen equation of state may also be used instead of the above equation.
The shock Hugoniot describes the locus of all possible thermodynamic states a material can exist in behind a shock, projected onto a two dimensional state-state plane. It is therefore a set of equilibrium states and does not specifically represent the path through which a material undergoes transformation.
Weak shocks are isentropic and that the isentrope represents the path through which the material is loaded from the initial to final states by a compression wave with converging characteristics. In the case of weak shocks, the Hugoniot will therefore fall directly on the isentrope and can be used directly as the equivalent path. In the case of a strong shock we can no longer make that simplification directly. However, for engineering calculations, it is deemed that the isentrope is close enough to the Hugoniot that the same assumption can be made.
If the Hugoniot is approximately the loading path between states for an "equivalent" compression wave, then the jump conditions for the shock loading path can be determined by drawing a straight line between the initial and final states. This line is called the Rayleigh line and has the following equation:
=== Hugoniot elastic limit ===
Most solid materials undergo plastic deformations when subjected to strong shocks. The point on the shock Hugoniot at which a material transitions from a purely elastic state to an elastic-plastic state is called the Hugoniot elastic limit (HEL) and the pressure at which this transition takes place is denoted pHEL. Values of pHEL can range from 0.2 GPa to 20 GPa. Above the HEL, the material loses much of its shear strength and starts behaving like a fluid.
== Magnetohydrodynamics ==
Rankine–Hugoniot conditions in magnetohydrodynamics are interesting to consider since they are very relevant to astrophysical applications. Across the discontinuity the normal component
H
n
{\displaystyle H_{n}}
of the magnetic field
H
{\displaystyle \mathbf {H} }
and the tangential component
E
t
{\displaystyle \mathbf {E} _{t}}
of the electric field
E
=
−
u
×
H
/
c
{\displaystyle \mathbf {E} =-\mathbf {u} \times \mathbf {H} /c}
(infinite conductivity limit) must be continuous. We thus have
0
=
[
[
j
]
]
,
j
≡
ρ
u
n
conservation of mass
,
0
=
[
[
H
n
]
]
continuity of normal component of
H
,
{\displaystyle {\begin{aligned}0=[\![j]\!],\,\,j\equiv \rho u_{n}&\quad {\text{conservation of mass}},\\0=[\![H_{n}]\!]&\quad {\text{continuity of normal component of }}\mathbf {H} ,\end{aligned}}}
where
[
[
⋅
]
]
{\displaystyle [\![\cdot ]\!]}
is the difference between the values of any physical quantity on the two sides of the discontinuity. The remaining conditions are given by
j
2
[
[
1
/
ρ
]
]
+
[
[
p
]
]
+
[
[
H
t
2
]
]
/
8
π
=
0
conservation of normal momentum
,
j
[
[
u
t
]
]
=
H
n
[
[
H
t
]
]
/
4
π
conservation of tangential momentum
,
j
[
[
h
+
j
2
/
2
ρ
2
+
u
t
2
/
2
+
H
t
2
/
4
π
ρ
]
]
=
H
n
[
[
H
t
⋅
u
t
]
]
/
4
π
conservation of energy
,
H
n
[
[
u
t
]
]
=
j
[
[
H
t
/
ρ
]
]
continuity of tangential components of
E
.
{\displaystyle {\begin{aligned}j^{2}[\![1/\rho ]\!]+[\![p]\!]+[\![\mathbf {H} _{t}^{2}]\!]/8\pi =0&\quad {\text{conservation of normal momentum}},\\j[\![\mathbf {u} _{t}]\!]=H_{n}[\![\mathbf {H} _{t}]\!]/4\pi &\quad {\text{conservation of tangential momentum}},\\j[\![h+j^{2}/2\rho ^{2}+\mathbf {u} _{t}^{2}/2+\mathbf {H} _{t}^{2}/4\pi \rho ]\!]=H_{n}[\![\mathbf {H} _{t}\cdot \mathbf {u} _{t}]\!]/4\pi &\quad {\text{conservation of energy}},\\H_{n}[\![\mathbf {u} _{t}]\!]=j[\![\mathbf {H} _{t}/\rho ]\!]&\quad {\text{continuity of tangential components of }}\mathbf {E} .\end{aligned}}}
These conditions are general in the sense that they include contact discontinuities (
j
=
0
,
H
n
≠
0
,
[
[
u
]
]
=
[
[
p
]
]
=
[
[
H
]
]
=
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=0,\,H_{n}\neq 0,\,[\![\mathbf {u} ]\!]=[\![p]\!]=[\![\mathbf {H} ]\!]=0,\,[\![\rho ]\!]\neq 0}
) tangential discontinuities (
j
=
H
n
=
0
,
[
[
u
t
ρ
]
]
≠
0
,
[
[
H
t
]
]
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=H_{n}=0,\,[\![\mathbf {u} _{t}\rho ]\!]\neq 0,\,[\![\mathbf {H} _{t}]\!]\neq 0,\,[\![\rho ]\!]\neq 0}
), rotational or Alfvén discontinuities (
j
=
H
n
ρ
/
4
π
≠
0
,
[
[
ρ
]
]
=
[
[
u
n
]
]
=
[
[
p
]
]
=
[
[
H
t
]
]
=
0
{\textstyle j=H_{n}{\sqrt {\rho /4\pi }}\neq 0,\,[\![\rho ]\!]=[\![u_{n}]\!]=[\![p]\!]=[\![\mathbf {H} _{t}]\!]=0}
) and shock waves (
j
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j\neq 0,\,[\![\rho ]\!]\neq 0}
).
== See also ==
Euler equations (fluid dynamics)
Shock polar
Becker–Morduchow–Libby solution
Mie–Grüneisen equation of state
Engineering Acoustics Wikibook
Atmospheric focusing
== References == | Wikipedia/Hugoniot_equation |
The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one-dimensional flow in fluids or a one-dimensional deformation in solids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot.
The basic idea of the jump conditions is to consider what happens to a fluid when it undergoes a rapid change. Consider, for example, driving a piston into a tube filled with non-reacting gas. A disturbance is propagated through the fluid somewhat faster than the speed of sound. Because the disturbance propagates supersonically, it is a shock wave, and the fluid downstream of the shock has no advance information of it. In a frame of reference moving with the wave, atoms or molecules in front of the wave slam into the wave supersonically. On a microscopic level, they undergo collisions on the scale of the mean free path length until they come to rest in the post-shock flow (but moving in the frame of reference of the wave or of the tube). The bulk transfer of kinetic energy heats the post-shock flow. Because the mean free path length is assumed to be negligible in comparison to all other length scales in a hydrodynamic treatment, the shock front is essentially a hydrodynamic discontinuity. The jump conditions then establish the transition between the pre- and post-shock flow, based solely upon the conservation of mass, momentum, and energy. The conditions are correct even though the shock actually has a positive thickness. This non-reacting example of a shock wave also generalizes to reacting flows, where a combustion front (either a detonation or a deflagration) can be modeled as a discontinuity in a first approximation.
== Governing Equations ==
In a coordinate system that is moving with the discontinuity, the Rankine–Hugoniot conditions can be expressed as:
where m is the mass flow rate per unit area, ρ1 and ρ2 are the mass density of the fluid upstream and downstream of the wave, u1 and u2 are the fluid velocity upstream and downstream of the wave, p1 and p2 are the pressures in the two regions, and h1 and h2 are the specific (with the sense of per unit mass) enthalpies in the two regions. If in addition, the flow is reactive, then the species conservation equations demands that
ω
i
,
1
=
ω
i
,
2
=
0
,
i
=
1
,
2
,
3
,
…
,
N
,
Conservation of species
{\displaystyle \omega _{i,1}=\omega _{i,2}=0,\quad i=1,2,3,\dots ,N,\qquad {\text{Conservation of species}}}
to vanish both upstream and downstream of the discontinuity. Here,
ω
{\displaystyle \omega }
is the mass production rate of the i-th species of total N species involved in the reaction.
Combining conservation of mass and momentum gives us
p
2
−
p
1
1
/
ρ
2
−
1
/
ρ
1
=
−
m
2
{\displaystyle {\frac {p_{2}-p_{1}}{1/\rho _{2}-1/\rho _{1}}}=-m^{2}}
which defines a straight line known as the Michelson–Rayleigh line, named after the Russian physicist Vladimir A. Mikhelson (usually anglicized as Michelson) and Lord Rayleigh, that has a negative slope (since
m
2
{\displaystyle m^{2}}
is always positive) in the
p
−
ρ
−
1
{\displaystyle p-\rho ^{-1}}
plane. Using the Rankine–Hugoniot equations for the conservation of mass and momentum to eliminate u1 and u2, the equation for the conservation of energy can be expressed as the Hugoniot equation:
h
2
−
h
1
=
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
.
{\displaystyle h_{2}-h_{1}={\frac {1}{2}}\,\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)\,(p_{2}-p_{1}).}
The inverse of the density can also be expressed as the specific volume,
v
=
1
/
ρ
{\displaystyle v=1/\rho }
. Along with these, one has to specify the relation between the upstream and downstream equation of state
f
(
p
1
,
ρ
1
,
T
1
,
Y
i
,
1
)
=
f
(
p
2
,
ρ
2
,
T
2
,
Y
i
,
2
)
{\displaystyle f(p_{1},\rho _{1},T_{1},Y_{i,1})=f(p_{2},\rho _{2},T_{2},Y_{i,2})}
where
Y
i
{\displaystyle Y_{i}}
is the mass fraction of the species. Finally, the calorific equation of state
h
=
h
(
p
,
ρ
,
Y
i
)
{\displaystyle h=h(p,\rho ,Y_{i})}
is assumed to be known, i.e.,
h
(
p
1
,
ρ
1
,
Y
i
,
1
)
=
h
(
p
2
,
ρ
2
,
Y
i
,
2
)
.
{\displaystyle h(p_{1},\rho _{1},Y_{i,1})=h(p_{2},\rho _{2},Y_{i,2}).}
== Simplified Rankine–Hugoniot relations ==
Source:
The following assumptions are made in order to simplify the Rankine–Hugoniot equations. The mixture is assumed to obey the ideal gas law, so that relation between the downstream and upstream equation of state can be written as
p
2
ρ
2
T
2
=
p
1
ρ
1
T
1
=
R
W
¯
{\displaystyle {\frac {p_{2}}{\rho _{2}T_{2}}}={\frac {p_{1}}{\rho _{1}T_{1}}}={\frac {R}{\overline {W}}}}
where
R
{\displaystyle R}
is the universal gas constant and the mean molecular weight
W
¯
{\displaystyle {\overline {W}}}
is assumed to be constant (otherwise,
W
¯
{\displaystyle {\overline {W}}}
would depend on the mass fraction of the all species). If one assumes that the specific heat at constant pressure
c
p
{\displaystyle c_{p}}
is also constant across the wave, the change in enthalpies (calorific equation of state) can be simply written as
h
2
−
h
1
=
−
q
+
c
p
(
T
2
−
T
1
)
{\displaystyle h_{2}-h_{1}=-q+c_{p}(T_{2}-T_{1})}
where the first term in the above expression represents the amount of heat released per unit mass of the upstream mixture by the wave and the second term represents the sensible heating. Eliminating temperature using the equation of state and substituting the above expression for the change in enthalpies into the Hugoniot equation, one obtains an Hugoniot equation expressed only in terms of pressure and densities,
(
γ
γ
−
1
)
(
p
2
ρ
2
−
p
1
ρ
1
)
−
1
2
(
1
ρ
2
+
1
ρ
1
)
(
p
2
−
p
1
)
=
q
,
{\displaystyle \left({\frac {\gamma }{\gamma -1}}\right)\left({\frac {p_{2}}{\rho _{2}}}-{\frac {p_{1}}{\rho _{1}}}\right)-{\frac {1}{2}}\left({\frac {1}{\rho _{2}}}+{\frac {1}{\rho _{1}}}\right)(p_{2}-p_{1})=q,}
where
γ
{\displaystyle \gamma }
is the specific heat ratio, which for ordinary room temperature air (298 KELVIN) = 1.40. An Hugoniot curve without heat release (
q
=
0
{\displaystyle q=0}
) is often called a "shock Hugoniot", or simply a(n) "Hugoniot". Along with the Rayleigh line equation, the above equation completely determines the state of the system. These two equations can be written compactly by introducing the following non-dimensional scales,
p
~
=
p
2
p
1
,
v
~
=
ρ
1
ρ
2
,
α
=
q
ρ
1
p
1
,
μ
=
m
2
p
1
ρ
1
.
{\displaystyle {\tilde {p}}={\frac {p_{2}}{p_{1}}},\quad {\tilde {v}}={\frac {\rho _{1}}{\rho _{2}}},\quad \alpha ={\frac {q\rho _{1}}{p_{1}}},\quad \mu ={\frac {m^{2}}{p_{1}\rho _{1}}}.}
The Rayleigh line equation and the Hugoniot equation then simplifies to
p
~
−
1
v
~
−
1
=
−
μ
p
~
=
[
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
]
−
v
~
[
(
γ
+
1
)
/
(
γ
−
1
)
]
v
~
−
1
.
{\displaystyle {\begin{aligned}{\frac {{\tilde {p}}-1}{{\tilde {v}}-1}}&=-\mu \\{\tilde {p}}&={\frac {[2\alpha +(\gamma +1)/(\gamma -1)]-{\tilde {v}}}{[(\gamma +1)/(\gamma -1)]{\tilde {v}}-1}}.\end{aligned}}}
Given the upstream conditions, the intersection of above two equations in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane determine the downstream conditions; in the
v
~
{\displaystyle {\tilde {v}}}
-
p
~
{\displaystyle {\tilde {p}}}
plane, the upstream condition correspond to the point
(
v
~
,
p
~
)
=
(
1
,
1
)
{\displaystyle ({\tilde {v}},{\tilde {p}})=(1,1)}
. If no heat release occurs, for example, shock waves without chemical reaction, then
α
=
0
{\displaystyle \alpha =0}
. The Hugoniot curves asymptote to the lines
v
~
=
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {v}}=(\gamma -1)/(\gamma +1)}
and
p
~
=
−
(
γ
−
1
)
/
(
γ
+
1
)
{\displaystyle {\tilde {p}}=-(\gamma -1)/(\gamma +1)}
, which are depicted as dashed lines in the figure. As mentioned in the figure, only the white region bounded by these two asymptotes are allowed so that
μ
{\displaystyle \mu }
is positive. Shock waves and detonations correspond to the top-left white region wherein
p
~
>
1
{\displaystyle {\tilde {p}}>1}
and
v
~
<
1
{\displaystyle {\tilde {v}}<1}
, that is to say, the pressure increases and the specific volume decreases across the wave (the Chapman–Jouguet condition for detonation is where Rayleigh line is tangent to the Hugoniot curve). Deflagrations, on the other hand, correspond to the bottom-right white region wherein
p
~
<
1
{\displaystyle {\tilde {p}}<1}
and
v
~
>
1
{\displaystyle {\tilde {v}}>1}
, that is to say, the pressure decreases and the specific volume increases across the wave; the pressure decrease a flame is typically very small which is seldom considered when studying deflagrations.
For shock waves and detonations, the pressure increase across the wave can take any values between
0
≤
p
~
<
∞
{\displaystyle 0\leq {\tilde {p}}<\infty }
; the steeper the slope of the Rayleigh line, the stronger is the wave. On the contrary, here the specific volume ratio is restricted to the finite interval
(
γ
−
1
)
/
(
γ
+
1
)
≤
v
~
≤
2
α
+
(
γ
+
1
)
/
(
γ
−
1
)
{\displaystyle (\gamma -1)/(\gamma +1)\leq {\tilde {v}}\leq 2\alpha +(\gamma +1)/(\gamma -1)}
(the upper bound is derived for the case
p
~
→
0
{\displaystyle {\tilde {p}}\rightarrow 0}
because pressure cannot take negative values). If
γ
=
1.4
{\displaystyle \gamma =1.4}
(diatomic gas without the vibrational mode excitation), the interval is
1
/
6
≤
v
~
≤
2
α
+
6
{\displaystyle 1/6\leq {\tilde {v}}\leq 2\alpha +6}
, in other words, the shock wave can increase the density at most by a factor of 6. For monatomic gas,
γ
=
5
/
3
{\displaystyle \gamma =5/3}
, the allowed interval is
1
/
4
≤
v
~
≤
2
α
+
4
{\displaystyle 1/4\leq {\tilde {v}}\leq 2\alpha +4}
. For diatomic gases with vibrational mode excited, we have
γ
=
9
/
7
{\displaystyle \gamma =9/7}
leading to the interval
1
/
8
≤
v
~
≤
2
α
+
8
{\displaystyle 1/8\leq {\tilde {v}}\leq 2\alpha +8}
. In reality, the specific heat ratio is not constant in the shock wave due to molecular dissociation and ionization, but even in these cases, density ratio in general do not exceed a factor of about 11–13.
== Derivation from Euler equations ==
Consider gas in a one-dimensional container (e.g., a long thin tube). Assume that the fluid is inviscid (i.e., it shows no viscosity effects as for example friction with the tube walls). Furthermore, assume that there is no heat transfer by conduction or radiation and that gravitational acceleration can be neglected. Such a system can be described by the following system of conservation laws, known as the 1D Euler equations, that in conservation form is:
where
ρ
,
{\displaystyle \rho ,}
fluid mass density,
u
,
{\displaystyle u,}
fluid velocity,
e
,
{\displaystyle e,}
specific internal energy of the fluid,
p
,
{\displaystyle p,}
fluid pressure, and
E
t
=
ρ
e
+
ρ
1
2
u
2
,
{\displaystyle E^{t}=\rho e+\rho {\tfrac {1}{2}}u^{2},}
is the total energy density of the fluid, [J/m3], while e is its specific internal energy
Assume further that the gas is calorically ideal and that therefore a polytropic equation-of-state of the simple form
is valid, where
γ
{\displaystyle \gamma }
is the constant ratio of specific heats
c
p
/
c
v
{\displaystyle c_{p}/c_{v}}
. This quantity also appears as the polytropic exponent of the polytropic process described by
For an extensive list of compressible flow equations, etc., refer to NACA Report 1135 (1953).
Note: For a calorically ideal gas
γ
{\displaystyle \gamma }
is a constant and for a thermally ideal gas
γ
{\displaystyle \gamma }
is a function of temperature. In the latter case, the dependence of pressure on mass density and internal energy might differ from that given by equation (4).
=== The jump condition ===
Before proceeding further it is necessary to introduce the concept of a jump condition – a condition that holds at a discontinuity or abrupt change.
Consider a 1D situation where there is a jump in the scalar conserved physical quantity
w
{\displaystyle w}
, which is governed by integral conservation law
for any
x
1
{\displaystyle x_{1}}
,
x
2
{\displaystyle x_{2}}
,
x
1
<
x
2
{\displaystyle x_{1}<x_{2}}
, and, therefore, by partial differential equation
for smooth solutions.
Let the solution exhibit a jump (or shock) at
x
=
x
s
(
t
)
{\displaystyle x=x_{s}(t)}
, where
x
1
<
x
s
(
t
)
{\displaystyle x_{1}<x_{s}(t)}
and
x
s
(
t
)
<
x
2
{\displaystyle x_{s}(t)<x_{2}}
, then
The subscripts 1 and 2 indicate conditions just upstream and just downstream of the jump respectively, i.e.
w
1
=
lim
ϵ
→
0
+
w
(
x
s
−
ϵ
)
{\textstyle w_{1}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}-\epsilon \right)}
and
w
2
=
lim
ϵ
→
0
+
w
(
x
s
+
ϵ
)
{\textstyle w_{2}=\lim _{\epsilon \to 0^{+}}w\left(x_{s}+\epsilon \right)}
.
∴
{\displaystyle \therefore }
is the therefore sign.
Note, to arrive at equation (8) we have used the fact that
d
x
1
/
d
t
=
0
{\displaystyle dx_{1}/dt=0}
and
d
x
2
/
d
t
=
0
{\displaystyle dx_{2}/dt=0}
.
Now, let
x
1
→
x
s
(
t
)
−
ϵ
{\displaystyle x_{1}\to x_{s}(t)-\epsilon }
and
x
2
→
x
s
(
t
)
+
ϵ
{\displaystyle x_{2}\to x_{s}(t)+\epsilon }
, when we have
∫
x
1
x
s
(
t
)
−
ϵ
w
t
d
x
→
0
{\textstyle \int _{x_{1}}^{x_{s}(t)-\epsilon }w_{t}\,dx\to 0}
and
∫
x
s
(
t
)
+
ϵ
x
2
w
t
d
x
→
0
{\textstyle \int _{x_{s}(t)+\epsilon }^{x_{2}}w_{t}\,dx\to 0}
, and in the limit
where we have defined
u
s
=
d
x
s
(
t
)
/
d
t
{\displaystyle u_{s}=dx_{s}(t)/dt}
(the system characteristic or shock speed), which by simple division is given by
Equation (9) represents the jump condition for conservation law (6). A shock situation arises in a system where its characteristics intersect, and under these conditions a requirement for a unique single-valued solution is that the solution should satisfy the admissibility condition or entropy condition. For physically real applications this means that the solution should satisfy the Lax entropy condition
where
f
′
(
w
1
)
{\displaystyle f'\left(w_{1}\right)}
and
f
′
(
w
2
)
{\displaystyle f'\left(w_{2}\right)}
represent characteristic speeds at upstream and downstream conditions respectively.
=== Shock condition ===
In the case of the hyperbolic conservation law (6), we have seen that the shock speed can be obtained by simple division. However, for the 1D Euler equations (1), (2) and (3), we have the vector state variable
[
ρ
ρ
u
E
]
T
{\displaystyle {\begin{bmatrix}\rho &\rho u&E\end{bmatrix}}^{\mathsf {T}}}
and the jump conditions become
Equations (12), (13) and (14) are known as the Rankine–Hugoniot conditions for the Euler equations and are derived by enforcing the conservation laws in integral form over a control volume that includes the shock. For this situation
u
s
{\displaystyle u_{s}}
cannot be obtained by simple division. However, it can be shown by transforming the problem to a moving co-ordinate system
(setting
u
s
′
:=
u
s
−
u
1
{\displaystyle u_{s}':=u_{s}-u_{1}}
,
u
1
′
:=
0
{\displaystyle u'_{1}:=0}
,
u
2
′
:=
u
2
−
u
1
{\displaystyle u'_{2}:=u_{2}-u_{1}}
to remove
u
1
{\displaystyle u_{1}}
) and some algebraic manipulation (involving the elimination of
u
2
′
{\displaystyle u'_{2}}
from the transformed equation (13) using the transformed equation (12)), that the shock speed is given by
where
c
1
=
γ
p
1
/
ρ
1
{\textstyle c_{1}={\sqrt {\gamma p_{1}/\rho _{1}}}}
is the speed of sound in the fluid at upstream conditions.
== Shock Hugoniot and Rayleigh line in solids ==
For shocks in solids, a closed form expression such as equation (15) cannot be derived from first principles. Instead, experimental observations indicate that a linear relation can be used instead (called the shock Hugoniot in the us-up plane) that has the form
where c0 is the bulk speed of sound in the material (in uniaxial compression), s is a parameter (the slope of the shock Hugoniot) obtained from fits to experimental data, and up = u2 is the particle velocity inside the compressed region behind the shock front.
The above relation, when combined with the Hugoniot equations for the conservation of mass and momentum, can be used to determine the shock Hugoniot in the p-v plane, where v is the specific volume (per unit mass):
Alternative equations of state, such as the Mie–Grüneisen equation of state may also be used instead of the above equation.
The shock Hugoniot describes the locus of all possible thermodynamic states a material can exist in behind a shock, projected onto a two dimensional state-state plane. It is therefore a set of equilibrium states and does not specifically represent the path through which a material undergoes transformation.
Weak shocks are isentropic and that the isentrope represents the path through which the material is loaded from the initial to final states by a compression wave with converging characteristics. In the case of weak shocks, the Hugoniot will therefore fall directly on the isentrope and can be used directly as the equivalent path. In the case of a strong shock we can no longer make that simplification directly. However, for engineering calculations, it is deemed that the isentrope is close enough to the Hugoniot that the same assumption can be made.
If the Hugoniot is approximately the loading path between states for an "equivalent" compression wave, then the jump conditions for the shock loading path can be determined by drawing a straight line between the initial and final states. This line is called the Rayleigh line and has the following equation:
=== Hugoniot elastic limit ===
Most solid materials undergo plastic deformations when subjected to strong shocks. The point on the shock Hugoniot at which a material transitions from a purely elastic state to an elastic-plastic state is called the Hugoniot elastic limit (HEL) and the pressure at which this transition takes place is denoted pHEL. Values of pHEL can range from 0.2 GPa to 20 GPa. Above the HEL, the material loses much of its shear strength and starts behaving like a fluid.
== Magnetohydrodynamics ==
Rankine–Hugoniot conditions in magnetohydrodynamics are interesting to consider since they are very relevant to astrophysical applications. Across the discontinuity the normal component
H
n
{\displaystyle H_{n}}
of the magnetic field
H
{\displaystyle \mathbf {H} }
and the tangential component
E
t
{\displaystyle \mathbf {E} _{t}}
of the electric field
E
=
−
u
×
H
/
c
{\displaystyle \mathbf {E} =-\mathbf {u} \times \mathbf {H} /c}
(infinite conductivity limit) must be continuous. We thus have
0
=
[
[
j
]
]
,
j
≡
ρ
u
n
conservation of mass
,
0
=
[
[
H
n
]
]
continuity of normal component of
H
,
{\displaystyle {\begin{aligned}0=[\![j]\!],\,\,j\equiv \rho u_{n}&\quad {\text{conservation of mass}},\\0=[\![H_{n}]\!]&\quad {\text{continuity of normal component of }}\mathbf {H} ,\end{aligned}}}
where
[
[
⋅
]
]
{\displaystyle [\![\cdot ]\!]}
is the difference between the values of any physical quantity on the two sides of the discontinuity. The remaining conditions are given by
j
2
[
[
1
/
ρ
]
]
+
[
[
p
]
]
+
[
[
H
t
2
]
]
/
8
π
=
0
conservation of normal momentum
,
j
[
[
u
t
]
]
=
H
n
[
[
H
t
]
]
/
4
π
conservation of tangential momentum
,
j
[
[
h
+
j
2
/
2
ρ
2
+
u
t
2
/
2
+
H
t
2
/
4
π
ρ
]
]
=
H
n
[
[
H
t
⋅
u
t
]
]
/
4
π
conservation of energy
,
H
n
[
[
u
t
]
]
=
j
[
[
H
t
/
ρ
]
]
continuity of tangential components of
E
.
{\displaystyle {\begin{aligned}j^{2}[\![1/\rho ]\!]+[\![p]\!]+[\![\mathbf {H} _{t}^{2}]\!]/8\pi =0&\quad {\text{conservation of normal momentum}},\\j[\![\mathbf {u} _{t}]\!]=H_{n}[\![\mathbf {H} _{t}]\!]/4\pi &\quad {\text{conservation of tangential momentum}},\\j[\![h+j^{2}/2\rho ^{2}+\mathbf {u} _{t}^{2}/2+\mathbf {H} _{t}^{2}/4\pi \rho ]\!]=H_{n}[\![\mathbf {H} _{t}\cdot \mathbf {u} _{t}]\!]/4\pi &\quad {\text{conservation of energy}},\\H_{n}[\![\mathbf {u} _{t}]\!]=j[\![\mathbf {H} _{t}/\rho ]\!]&\quad {\text{continuity of tangential components of }}\mathbf {E} .\end{aligned}}}
These conditions are general in the sense that they include contact discontinuities (
j
=
0
,
H
n
≠
0
,
[
[
u
]
]
=
[
[
p
]
]
=
[
[
H
]
]
=
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=0,\,H_{n}\neq 0,\,[\![\mathbf {u} ]\!]=[\![p]\!]=[\![\mathbf {H} ]\!]=0,\,[\![\rho ]\!]\neq 0}
) tangential discontinuities (
j
=
H
n
=
0
,
[
[
u
t
ρ
]
]
≠
0
,
[
[
H
t
]
]
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j=H_{n}=0,\,[\![\mathbf {u} _{t}\rho ]\!]\neq 0,\,[\![\mathbf {H} _{t}]\!]\neq 0,\,[\![\rho ]\!]\neq 0}
), rotational or Alfvén discontinuities (
j
=
H
n
ρ
/
4
π
≠
0
,
[
[
ρ
]
]
=
[
[
u
n
]
]
=
[
[
p
]
]
=
[
[
H
t
]
]
=
0
{\textstyle j=H_{n}{\sqrt {\rho /4\pi }}\neq 0,\,[\![\rho ]\!]=[\![u_{n}]\!]=[\![p]\!]=[\![\mathbf {H} _{t}]\!]=0}
) and shock waves (
j
≠
0
,
[
[
ρ
]
]
≠
0
{\displaystyle j\neq 0,\,[\![\rho ]\!]\neq 0}
).
== See also ==
Euler equations (fluid dynamics)
Shock polar
Becker–Morduchow–Libby solution
Mie–Grüneisen equation of state
Engineering Acoustics Wikibook
Atmospheric focusing
== References == | Wikipedia/Rankine–Hugoniot_equations |
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field
u
(
x
,
t
)
{\displaystyle u(x,t)}
and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context)
ν
{\displaystyle \nu }
, the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system:
∂
u
∂
t
+
u
∂
u
∂
x
=
ν
∂
2
u
∂
x
2
.
{\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=\nu {\frac {\partial ^{2}u}{\partial x^{2}}}.}
The term
u
∂
u
/
∂
x
{\displaystyle u\partial u/\partial x}
can also be rewritten as
∂
(
u
2
/
2
)
/
∂
x
{\displaystyle \partial (u^{2}/2)/\partial x}
. When the diffusion term is absent (i.e.
ν
=
0
{\displaystyle \nu =0}
), Burgers' equation becomes the inviscid Burgers' equation:
∂
u
∂
t
+
u
∂
u
∂
x
=
0
,
{\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=0,}
which is a prototype for conservation equations that can develop discontinuities (shock waves).
The reason for the formation of sharp gradients for small values of
ν
{\displaystyle \nu }
becomes intuitively clear when one examines the left-hand side of the equation. The term
∂
/
∂
t
+
u
∂
/
∂
x
{\displaystyle \partial /\partial t+u\partial /\partial x}
is evidently a wave operator describing a wave propagating in the positive
x
{\displaystyle x}
-direction with a speed
u
{\displaystyle u}
. Since the wave speed is
u
{\displaystyle u}
, regions exhibiting large values of
u
{\displaystyle u}
will be propagated rightwards quicker than regions exhibiting smaller values of
u
{\displaystyle u}
; in other words, if
u
{\displaystyle u}
is decreasing in the
x
{\displaystyle x}
-direction, initially, then larger
u
{\displaystyle u}
's that lie in the backside will catch up with smaller
u
{\displaystyle u}
's on the front side. The role of the right-side diffusive term is essentially to stop the gradient becoming infinite.
== Inviscid Burgers' equation ==
The inviscid Burgers' equation is a conservation equation, more generally a first order quasilinear hyperbolic equation. The solution to the equation and along with the initial condition
∂
u
∂
t
+
u
∂
u
∂
x
=
0
,
u
(
x
,
0
)
=
f
(
x
)
{\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=0,\quad u(x,0)=f(x)}
can be constructed by the method of characteristics. Let
t
{\displaystyle t}
be the parameter characterising any given characteristics in the
x
{\displaystyle x}
-
t
{\displaystyle t}
plane, then the characteristic equations are given by
d
x
d
t
=
u
,
d
u
d
t
=
0.
{\displaystyle {\frac {dx}{dt}}=u,\quad {\frac {du}{dt}}=0.}
Integration of the second equation tells us that
u
{\displaystyle u}
is constant along the characteristic and integration of the first equation shows that the characteristics are straight lines, i.e.,
u
=
c
,
x
=
u
t
+
ξ
{\displaystyle u=c,\quad x=ut+\xi }
where
ξ
{\displaystyle \xi }
is the point (or parameter) on the x-axis (t = 0) of the x-t plane from which the characteristic curve is drawn. Since
u
{\displaystyle u}
at
x
{\displaystyle x}
-axis is known from the initial condition and the fact that
u
{\displaystyle u}
is unchanged as we move along the characteristic emanating from each point
x
=
ξ
{\displaystyle x=\xi }
, we write
u
=
c
=
f
(
ξ
)
{\displaystyle u=c=f(\xi )}
on each characteristic. Therefore, the family of trajectories of characteristics parametrized by
ξ
{\displaystyle \xi }
is
x
=
f
(
ξ
)
t
+
ξ
.
{\displaystyle x=f(\xi )t+\xi .}
Thus, the solution is given by
u
(
x
,
t
)
=
f
(
ξ
)
=
f
(
x
−
u
t
)
,
ξ
=
x
−
f
(
ξ
)
t
.
{\displaystyle u(x,t)=f(\xi )=f(x-ut),\quad \xi =x-f(\xi )t.}
This is an implicit relation that determines the solution of the inviscid Burgers' equation provided characteristics don't intersect. If the characteristics do intersect, then a classical solution to the PDE does not exist and leads to the formation of a shock wave. Whether characteristics can intersect or not depends on the initial condition. In fact, the breaking time before a shock wave can be formed is given by
t
b
=
−
1
inf
x
(
f
′
(
x
)
)
.
{\displaystyle t_{b}={\frac {-1}{\inf _{x}\left(f^{\prime }(x)\right)}}.}
=== Complete integral of the inviscid Burgers' equation ===
The implicit solution described above containing an arbitrary function
f
{\displaystyle f}
is called the general integral. However, the inviscid Burgers' equation, being a first-order partial differential equation, also has a complete integral which contains two arbitrary constants (for the two independent variables). Subrahmanyan Chandrasekhar provided the complete integral in 1943, which is given by
u
(
x
,
t
)
=
a
x
+
b
a
t
+
1
.
{\displaystyle u(x,t)={\frac {ax+b}{at+1}}.}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are arbitrary constants. The complete integral satisfies a linear initial condition, i.e.,
f
(
x
)
=
a
x
+
b
{\displaystyle f(x)=ax+b}
. One can also construct the general integral using the above complete integral.
== Viscous Burgers' equation ==
The viscous Burgers' equation can be converted to a linear equation by the Cole–Hopf transformation,
u
(
x
,
t
)
=
−
2
ν
∂
∂
x
ln
φ
(
x
,
t
)
,
{\displaystyle u(x,t)=-2\nu {\frac {\partial }{\partial x}}\ln \varphi (x,t),}
which turns it into the equation
2
ν
∂
∂
x
[
1
φ
(
∂
φ
∂
t
−
ν
∂
2
φ
∂
x
2
)
]
=
0
,
{\displaystyle 2\nu {\frac {\partial }{\partial x}}\left[{\frac {1}{\varphi }}\left({\frac {\partial \varphi }{\partial t}}-\nu {\frac {\partial ^{2}\varphi }{\partial x^{2}}}\right)\right]=0,}
which can be integrated with respect to
x
{\displaystyle x}
to obtain
∂
φ
∂
t
−
ν
∂
2
φ
∂
x
2
=
φ
d
f
(
t
)
d
t
,
{\displaystyle {\frac {\partial \varphi }{\partial t}}-\nu {\frac {\partial ^{2}\varphi }{\partial x^{2}}}=\varphi {\frac {df(t)}{dt}},}
where
d
f
/
d
t
{\displaystyle df/dt}
is an arbitrary function of time. Introducing the transformation
φ
→
φ
e
f
{\displaystyle \varphi \to \varphi e^{f}}
(which does not affect the function
u
(
x
,
t
)
{\displaystyle u(x,t)}
), the required equation reduces to that of the heat equation
∂
φ
∂
t
=
ν
∂
2
φ
∂
x
2
.
{\displaystyle {\frac {\partial \varphi }{\partial t}}=\nu {\frac {\partial ^{2}\varphi }{\partial x^{2}}}.}
The diffusion equation can be solved. That is, if
φ
(
x
,
0
)
=
φ
0
(
x
)
{\displaystyle \varphi (x,0)=\varphi _{0}(x)}
, then
φ
(
x
,
t
)
=
1
4
π
ν
t
∫
−
∞
∞
φ
0
(
x
′
)
exp
[
−
(
x
−
x
′
)
2
4
ν
t
]
d
x
′
.
{\displaystyle \varphi (x,t)={\frac {1}{\sqrt {4\pi \nu t}}}\int _{-\infty }^{\infty }\varphi _{0}(x')\exp \left[-{\frac {(x-x')^{2}}{4\nu t}}\right]dx'.}
The initial function
φ
0
(
x
)
{\displaystyle \varphi _{0}(x)}
is related to the initial function
u
(
x
,
0
)
=
f
(
x
)
{\displaystyle u(x,0)=f(x)}
by
ln
φ
0
(
x
)
=
−
1
2
ν
∫
0
x
f
(
x
′
)
d
x
′
,
{\displaystyle \ln \varphi _{0}(x)=-{\frac {1}{2\nu }}\int _{0}^{x}f(x')dx',}
where the lower limit is chosen arbitrarily. Inverting the Cole–Hopf transformation, we have
u
(
x
,
t
)
=
−
2
ν
∂
∂
x
ln
{
1
4
π
ν
t
∫
−
∞
∞
exp
[
−
(
x
−
x
′
)
2
4
ν
t
−
1
2
ν
∫
0
x
′
f
(
x
″
)
d
x
″
]
d
x
′
}
{\displaystyle u(x,t)=-2\nu {\frac {\partial }{\partial x}}\ln \left\{{\frac {1}{\sqrt {4\pi \nu t}}}\int _{-\infty }^{\infty }\exp \left[-{\frac {(x-x')^{2}}{4\nu t}}-{\frac {1}{2\nu }}\int _{0}^{x'}f(x'')dx''\right]dx'\right\}}
which simplifies, by getting rid of the time-dependent prefactor in the argument of the logarithm, to
u
(
x
,
t
)
=
−
2
ν
∂
∂
x
ln
{
∫
−
∞
∞
exp
[
−
(
x
−
x
′
)
2
4
ν
t
−
1
2
ν
∫
0
x
′
f
(
x
″
)
d
x
″
]
d
x
′
}
.
{\displaystyle u(x,t)=-2\nu {\frac {\partial }{\partial x}}\ln \left\{\int _{-\infty }^{\infty }\exp \left[-{\frac {(x-x')^{2}}{4\nu t}}-{\frac {1}{2\nu }}\int _{0}^{x'}f(x'')dx''\right]dx'\right\}.}
This solution is derived from the solution of the heat equation for
φ
{\displaystyle \varphi }
that decays to zero as
x
→
±
∞
{\displaystyle x\to \pm \infty }
; other solutions for
u
{\displaystyle u}
can be obtained starting from solutions of
φ
{\displaystyle \varphi }
that satisfies different boundary conditions.
== Some explicit solutions of the viscous Burgers' equation ==
Explicit expressions for the viscous Burgers' equation are available. Some of the physically relevant solutions are given below:
=== Steadily propagating traveling wave ===
If
u
(
x
,
0
)
=
f
(
x
)
{\displaystyle u(x,0)=f(x)}
is such that
f
(
−
∞
)
=
f
+
{\displaystyle f(-\infty )=f^{+}}
and
f
(
+
∞
)
=
f
−
{\displaystyle f(+\infty )=f^{-}}
and
f
′
(
x
)
<
0
{\displaystyle f'(x)<0}
, then we have a traveling-wave solution (with a constant speed
c
=
(
f
+
+
f
−
)
/
2
{\displaystyle c=(f^{+}+f^{-})/2}
) given by
u
(
x
,
t
)
=
c
−
f
+
−
f
−
2
tanh
[
f
+
−
f
−
4
ν
(
x
−
c
t
)
]
.
{\displaystyle u(x,t)=c-{\frac {f^{+}-f^{-}}{2}}\tanh \left[{\frac {f^{+}-f^{-}}{4\nu }}(x-ct)\right].}
This solution, that was originally derived by Harry Bateman in 1915, is used to describe the variation of pressure across a weak shock wave. When
f
+
=
2
{\displaystyle f^{+}=2}
and
f
−
=
0
{\displaystyle f^{-}=0}
this simplifies to
u
(
x
,
t
)
=
2
1
+
e
x
−
t
ν
{\displaystyle u(x,t)={\frac {2}{1+e^{\frac {x-t}{\nu }}}}}
with
c
=
1
{\displaystyle c=1}
.
=== Delta function as an initial condition ===
If
u
(
x
,
0
)
=
2
ν
R
e
δ
(
x
)
{\displaystyle u(x,0)=2\nu Re\delta (x)}
, where
R
e
{\displaystyle Re}
(say, the Reynolds number) is a constant, then we have
u
(
x
,
t
)
=
ν
π
t
[
(
e
R
e
−
1
)
e
−
x
2
/
4
ν
t
1
+
(
e
R
e
−
1
)
e
r
f
c
(
x
/
4
ν
t
)
/
2
]
.
{\displaystyle u(x,t)={\sqrt {\frac {\nu }{\pi t}}}\left[{\frac {(e^{Re}-1)e^{-x^{2}/4\nu t}}{1+(e^{Re}-1)\mathrm {erfc} (x/{\sqrt {4\nu t}})/2}}\right].}
In the limit
R
e
→
0
{\displaystyle Re\to 0}
, the limiting behaviour is a diffusional spreading of a source and therefore is given by
u
(
x
,
t
)
=
2
ν
R
e
4
π
ν
t
exp
(
−
x
2
4
ν
t
)
.
{\displaystyle u(x,t)={\frac {2\nu Re}{\sqrt {4\pi \nu t}}}\exp \left(-{\frac {x^{2}}{4\nu t}}\right).}
On the other hand, In the limit
R
e
→
∞
{\displaystyle Re\to \infty }
, the solution approaches that of the aforementioned Chandrasekhar's shock-wave solution of the inviscid Burgers' equation and is given by
u
(
x
,
t
)
=
{
x
t
,
0
<
x
<
2
ν
R
e
t
,
0
,
otherwise
.
{\displaystyle u(x,t)={\begin{cases}{\frac {x}{t}},\quad 0<x<{\sqrt {2\nu Re\,t}},\\0,\quad {\text{otherwise}}.\end{cases}}}
The shock wave location and its speed are given by
x
=
2
ν
R
e
t
{\displaystyle x={\sqrt {2\nu Re\,t}}}
and
ν
R
e
/
t
.
{\displaystyle {\sqrt {\nu Re/t}}.}
=== N-wave solution ===
The N-wave solution comprises a compression wave followed by a rarafaction wave. A solution of this type is given by
u
(
x
,
t
)
=
x
t
[
1
+
1
e
R
e
0
−
1
t
t
0
exp
(
−
R
e
(
t
)
x
2
4
ν
R
e
0
t
)
]
−
1
{\displaystyle u(x,t)={\frac {x}{t}}\left[1+{\frac {1}{e^{Re_{0}-1}}}{\sqrt {\frac {t}{t_{0}}}}\exp \left(-{\frac {Re(t)x^{2}}{4\nu Re_{0}t}}\right)\right]^{-1}}
where
R
e
0
{\displaystyle Re_{0}}
may be regarded as an initial Reynolds number at time
t
=
t
0
{\displaystyle t=t_{0}}
and
R
e
(
t
)
=
(
1
/
2
ν
)
∫
0
∞
u
d
x
=
ln
(
1
+
τ
/
t
)
{\displaystyle Re(t)=(1/2\nu )\int _{0}^{\infty }udx=\ln(1+{\sqrt {\tau /t}})}
with
τ
=
t
0
e
R
e
0
−
1
{\displaystyle \tau =t_{0}{\sqrt {e^{Re_{0}}-1}}}
, may be regarded as the time-varying Reynold number.
== Other forms ==
=== Multi-dimensional Burgers' equation ===
In two or more dimensions, the Burgers' equation becomes
∂
u
∂
t
+
u
⋅
∇
u
=
ν
∇
2
u
.
{\displaystyle {\frac {\partial u}{\partial t}}+u\cdot \nabla u=\nu \nabla ^{2}u.}
One can also extend the equation for the vector field
u
{\displaystyle \mathbf {u} }
, as in
∂
u
∂
t
+
u
⋅
∇
u
=
ν
∇
2
u
.
{\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}+\mathbf {u} \cdot \nabla \mathbf {u} =\nu \nabla ^{2}\mathbf {u} .}
=== Generalized Burgers' equation ===
The generalized Burgers' equation extends the quasilinear convective to more generalized form, i.e.,
∂
u
∂
t
+
c
(
u
)
∂
u
∂
x
=
ν
∂
2
u
∂
x
2
.
{\displaystyle {\frac {\partial u}{\partial t}}+c(u){\frac {\partial u}{\partial x}}=\nu {\frac {\partial ^{2}u}{\partial x^{2}}}.}
where
c
(
u
)
{\displaystyle c(u)}
is any arbitrary function of u. The inviscid
ν
=
0
{\displaystyle \nu =0}
equation is still a quasilinear hyperbolic equation for
c
(
u
)
>
0
{\displaystyle c(u)>0}
and its solution can be constructed using method of characteristics as before.
=== Stochastic Burgers' equation ===
Added space-time noise
η
(
x
,
t
)
=
W
˙
(
x
,
t
)
{\displaystyle \eta (x,t)={\dot {W}}(x,t)}
, where
W
{\displaystyle W}
is an
L
2
(
R
)
{\displaystyle L^{2}(\mathbb {R} )}
Wiener process, forms a stochastic Burgers' equation
∂
u
∂
t
+
u
∂
u
∂
x
=
ν
∂
2
u
∂
x
2
−
λ
∂
η
∂
x
.
{\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=\nu {\frac {\partial ^{2}u}{\partial x^{2}}}-\lambda {\frac {\partial \eta }{\partial x}}.}
This stochastic PDE is the one-dimensional version of Kardar–Parisi–Zhang equation in a field
h
(
x
,
t
)
{\displaystyle h(x,t)}
upon substituting
u
(
x
,
t
)
=
−
λ
∂
h
/
∂
x
{\displaystyle u(x,t)=-\lambda \partial h/\partial x}
.
== See also ==
Chaplygin's equation
Conservation equation
Euler–Tricomi equation
Fokker–Planck equation
KdV-Burgers equation
== References ==
== External links ==
Burgers' Equation at EqWorld: The World of Mathematical Equations.
Burgers' Equation at NEQwiki, the nonlinear equations encyclopedia. | Wikipedia/Burgers_equation |
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all.
A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume.
From Noether's theorem, every differentiable symmetry leads to a local conservation law. Other conserved quantities can exist as well.
== Conservation laws as fundamental laws of nature ==
Conservation laws are fundamental to our understanding of the physical world, in that they describe which processes can or cannot occur in nature. For example, the conservation law of energy states that the total quantity of energy in an isolated system does not change, though it may change form. In general, the total quantity of the property governed by that law remains unchanged during physical processes. With respect to classical physics, conservation laws include conservation of energy, mass (or matter), linear momentum, angular momentum, and electric charge. With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle. With respect to symmetries and invariance principles, three special conservation laws have been described, associated with inversion or reversal of space, time, and charge.
Conservation laws are considered to be fundamental laws of nature, with broad application in physics, as well as in other fields such as chemistry, biology, geology, and engineering.
Most conservation laws are exact, or absolute, in the sense that they apply to all possible processes. Some conservation laws are partial, in that they hold for some processes but not for others.
One particularly important result concerning local conservation laws is Noether's theorem, which states that there is a one-to-one correspondence between each one of them and a differentiable symmetry of the Universe. For example, the local conservation of energy follows from the uniformity of time and the local conservation of angular momentum arises from the isotropy of space, i.e. because there is no preferred direction of space. Notably, there is no conservation law associated with time-reversal, although more complex conservation laws combining time-reversal with other symmetries are known.
== Exact laws ==
A partial listing of physical conservation equations due to symmetry that are said to be exact laws, or more precisely have never been proven to be violated:
Another exact symmetry is CPT symmetry, the simultaneous inversion of space and time coordinates, together with swapping all particles with their antiparticles; however being a discrete symmetry Noether's theorem does not apply to it. Accordingly, the conserved quantity, CPT parity, can usually not be meaningfully calculated or determined.
== Approximate laws ==
There are also approximate conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions.
Conservation of (macroscopic) mechanical energy (approximately true for processes close to free of dissipative forces like friction)
Conservation of (rest) mass (approximately true for nonrelativistic speeds)
Conservation of baryon number (See chiral anomaly and sphaleron)
Conservation of lepton number (In the Standard Model)
Conservation of flavor (violated by the weak interaction)
Conservation of strangeness (violated by the weak interaction)
Conservation of space-parity (violated by the weak interaction)
Conservation of charge-parity (violated by the weak interaction)
Conservation of time-parity (violated by the weak interaction)
Conservation of CP parity (violated by the weak interaction); by the CPT theorem, this is equivalent to conservation of time-parity.
== Global and local conservation laws ==
The total amount of some conserved quantity in the universe could remain unchanged if an equal amount were to appear at one point A and simultaneously disappear from another separate point B. For example, an amount of energy could appear on Earth without changing the total amount in the Universe if the same amount of energy were to disappear from some other region of the Universe. This weak form of "global" conservation is really not a conservation law because it is not Lorentz invariant, so phenomena like the above do not occur in nature. Due to special relativity, if the appearance of the energy at A and disappearance of the energy at B are simultaneous in one inertial reference frame, they will not be simultaneous in other inertial reference frames moving with respect to the first. In a moving frame one will occur before the other; either the energy at A will appear before or after the energy at B disappears. In both cases, during the interval energy will not be conserved.
A stronger form of conservation law requires that, for the amount of a conserved quantity at a point to change, there must be a flow, or flux of the quantity into or out of the point. For example, the amount of electric charge at a point is never found to change without an electric current into or out of the point that carries the difference in charge. Since it only involves continuous local changes, this stronger type of conservation law is Lorentz invariant; a quantity conserved in one reference frame is conserved in all moving reference frames. This is called a local conservation law. Local conservation also implies global conservation; that the total amount of the conserved quantity in the Universe remains constant. All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a continuity equation, which states that the change in the quantity in a volume is equal to the total net "flux" of the quantity through the surface of the volume. The following sections discuss continuity equations in general.
== Differential forms ==
In continuum mechanics, the most general form of an exact conservation law is given by a continuity equation. For example, conservation of electric charge q is
∂
ρ
∂
t
=
−
∇
⋅
j
{\displaystyle {\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {j} \,}
where ∇⋅ is the divergence operator, ρ is the density of q (amount per unit volume), j is the flux of q (amount crossing a unit area in unit time), and t is time.
If we assume that the motion u of the charge is a continuous function of position and time, then
j
=
ρ
u
∂
ρ
∂
t
=
−
∇
⋅
(
ρ
u
)
.
{\displaystyle {\begin{aligned}\mathbf {j} &=\rho \mathbf {u} \\{\frac {\partial \rho }{\partial t}}&=-\nabla \cdot (\rho \mathbf {u} )\,.\end{aligned}}}
In one space dimension this can be put into the form of a homogeneous first-order quasilinear hyperbolic equation:: 43
y
t
+
A
(
y
)
y
x
=
0
{\displaystyle y_{t}+A(y)y_{x}=0}
where the dependent variable y is called the density of a conserved quantity, and A(y) is called the current Jacobian, and the subscript notation for partial derivatives has been employed. The more general inhomogeneous case:
y
t
+
A
(
y
)
y
x
=
s
{\displaystyle y_{t}+A(y)y_{x}=s}
is not a conservation equation but the general kind of balance equation describing a dissipative system. The dependent variable y is called a nonconserved quantity, and the inhomogeneous term s(y,x,t) is the-source, or dissipation. For example, balance equations of this kind are the momentum and energy Navier-Stokes equations, or the entropy balance for a general isolated system.
In the one-dimensional space a conservation equation is a first-order quasilinear hyperbolic equation that can be put into the advection form:
y
t
+
a
(
y
)
y
x
=
0
{\displaystyle y_{t}+a(y)y_{x}=0}
where the dependent variable y(x,t) is called the density of the conserved (scalar) quantity, and a(y) is called the current coefficient, usually corresponding to the partial derivative in the conserved quantity of a current density of the conserved quantity j(y):: 43
a
(
y
)
=
j
y
(
y
)
{\displaystyle a(y)=j_{y}(y)}
In this case since the chain rule applies:
j
x
=
j
y
(
y
)
y
x
=
a
(
y
)
y
x
{\displaystyle j_{x}=j_{y}(y)y_{x}=a(y)y_{x}}
the conservation equation can be put into the current density form:
y
t
+
j
x
(
y
)
=
0
{\displaystyle y_{t}+j_{x}(y)=0}
In a space with more than one dimension the former definition can be extended to an equation that can be put into the form:
y
t
+
a
(
y
)
⋅
∇
y
=
0
{\displaystyle y_{t}+\mathbf {a} (y)\cdot \nabla y=0}
where the conserved quantity is y(r,t), ⋅ denotes the scalar product, ∇ is the nabla operator, here indicating a gradient, and a(y) is a vector of current coefficients, analogously corresponding to the divergence of a vector current density associated to the conserved quantity j(y):
y
t
+
∇
⋅
j
(
y
)
=
0
{\displaystyle y_{t}+\nabla \cdot \mathbf {j} (y)=0}
This is the case for the continuity equation:
ρ
t
+
∇
⋅
(
ρ
u
)
=
0
{\displaystyle \rho _{t}+\nabla \cdot (\rho \mathbf {u} )=0}
Here the conserved quantity is the mass, with density ρ(r,t) and current density ρu, identical to the momentum density, while u(r, t) is the flow velocity.
In the general case a conservation equation can be also a system of this kind of equations (a vector equation) in the form:: 43
y
t
+
A
(
y
)
⋅
∇
y
=
0
{\displaystyle \mathbf {y} _{t}+\mathbf {A} (\mathbf {y} )\cdot \nabla \mathbf {y} =\mathbf {0} }
where y is called the conserved (vector) quantity, ∇y is its gradient, 0 is the zero vector, and A(y) is called the Jacobian of the current density. In fact as in the former scalar case, also in the vector case A(y) usually corresponding to the Jacobian of a current density matrix J(y):
A
(
y
)
=
J
y
(
y
)
{\displaystyle \mathbf {A} (\mathbf {y} )=\mathbf {J} _{\mathbf {y} }(\mathbf {y} )}
and the conservation equation can be put into the form:
y
t
+
∇
⋅
J
(
y
)
=
0
{\displaystyle \mathbf {y} _{t}+\nabla \cdot \mathbf {J} (\mathbf {y} )=\mathbf {0} }
For example, this the case for Euler equations (fluid dynamics). In the simple incompressible case they are:
∇
⋅
u
=
0
,
∂
u
∂
t
+
u
⋅
∇
u
+
∇
s
=
0
,
{\displaystyle \nabla \cdot \mathbf {u} =0\,,\qquad {\frac {\partial \mathbf {u} }{\partial t}}+\mathbf {u} \cdot \nabla \mathbf {u} +\nabla s=\mathbf {0} ,}
where:
u is the flow velocity vector, with components in a N-dimensional space u1, u2, ..., uN,
s is the specific pressure (pressure per unit density) giving the source term,
It can be shown that the conserved (vector) quantity and the current density matrix for these equations are respectively:
y
=
(
1
u
)
;
J
=
(
u
u
⊗
u
+
s
I
)
;
{\displaystyle {\mathbf {y} }={\begin{pmatrix}1\\\mathbf {u} \end{pmatrix}};\qquad {\mathbf {J} }={\begin{pmatrix}\mathbf {u} \\\mathbf {u} \otimes \mathbf {u} +s\mathbf {I} \end{pmatrix}};\qquad }
where
⊗
{\displaystyle \otimes }
denotes the outer product.
== Integral and weak forms ==
Conservation equations can usually also be expressed in integral form: the advantage of the latter is substantially that it requires less smoothness of the solution, which paves the way to weak form, extending the class of admissible solutions to include discontinuous solutions.: 62–63 By integrating in any space-time domain the current density form in 1-D space:
y
t
+
j
x
(
y
)
=
0
{\displaystyle y_{t}+j_{x}(y)=0}
and by using Green's theorem, the integral form is:
∫
−
∞
∞
y
d
x
+
∫
0
∞
j
(
y
)
d
t
=
0
{\displaystyle \int _{-\infty }^{\infty }y\,dx+\int _{0}^{\infty }j(y)\,dt=0}
In a similar fashion, for the scalar multidimensional space, the integral form is:
∮
[
y
d
N
r
+
j
(
y
)
d
t
]
=
0
{\displaystyle \oint \left[y\,d^{N}r+j(y)\,dt\right]=0}
where the line integration is performed along the boundary of the domain, in an anticlockwise manner.: 62–63
Moreover, by defining a test function φ(r,t) continuously differentiable both in time and space with compact support, the weak form can be obtained pivoting on the initial condition. In 1-D space it is:
∫
0
∞
∫
−
∞
∞
ϕ
t
y
+
ϕ
x
j
(
y
)
d
x
d
t
=
−
∫
−
∞
∞
ϕ
(
x
,
0
)
y
(
x
,
0
)
d
x
{\displaystyle \int _{0}^{\infty }\int _{-\infty }^{\infty }\phi _{t}y+\phi _{x}j(y)\,dx\,dt=-\int _{-\infty }^{\infty }\phi (x,0)y(x,0)\,dx}
In the weak form all the partial derivatives of the density and current density have been passed on to the test function, which with the former hypothesis is sufficiently smooth to admit these derivatives.: 62–63
== See also ==
Invariant (physics)
Momentum
Cauchy momentum equation
Energy
Conservation of energy and the First law of thermodynamics
Conservative system
Conserved quantity
Some kinds of helicity are conserved in dissipationless limit: hydrodynamical helicity, magnetic helicity, cross-helicity.
Principle of mutability
Conservation law of the Stress–energy tensor
Riemann invariant
Philosophy of physics
Totalitarian principle
Convection–diffusion equation
Uniformity of nature
=== Examples and applications ===
Advection
Mass conservation, or Continuity equation
Charge conservation
Euler equations (fluid dynamics)
inviscid Burgers equation
Kinematic wave
Conservation of energy
Traffic flow
== Notes ==
== References ==
Philipson, Schuster, Modeling by Nonlinear Differential Equations: Dissipative and Conservative Processes, World Scientific Publishing Company 2009.
Victor J. Stenger, 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Buffalo NY: Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.
E. Godlewski and P.A. Raviart, Hyperbolic systems of conservation laws, Ellipses, 1991.
== External links ==
Media related to Conservation laws at Wikimedia Commons
Conservation Laws – Ch. 11–15 in an online textbook | Wikipedia/Conservation_equation |
The Jeans equations are a set of partial differential equations that describe the motion of a collection of stars in a gravitational field. The Jeans equations relate the second-order velocity moments to the density and potential of a stellar system for systems without collision. They are analogous to the Euler equations for fluid flow and may be derived from the collisionless Boltzmann equation. The Jeans equations can come in a variety of different forms, depending on the structure of what is being modelled. Most utilization of these equations has been found in simulations with large number of gravitationally bound objects.
== History ==
The Jeans equations were originally derived by James Clerk Maxwell. However, they were first applied to astronomy by James Jeans in 1915 while working on stellar hydrodynamics. Since then, multiple solutions to the equations have been calculated analytically and numerically. Some notable solutions include a spherically symmetric solution, derived by James Binney in 1983 and axisymmetric solutions found in 1995 by Richard Arnold.
== Mathematics ==
=== Derivation from Boltzmann equation ===
The collisionless Boltzmann equation, also called the Vlasov Equation is a special form of Liouville' equation and is given by:
∂
f
∂
t
+
v
∂
f
∂
r
−
∂
Φ
∂
r
∂
f
∂
v
=
0
{\displaystyle {\partial f \over \partial t}+v{\partial f \over \partial r}-{\partial \Phi \over \partial r}{\partial f \over \partial v}=0}
Or in vector form:
∂
f
∂
t
+
v
→
⋅
∇
→
f
−
∇
→
Φ
⋅
∂
f
∂
v
→
=
0
{\displaystyle {\partial f \over \partial t}+{\vec {v}}\cdot {\vec {\nabla }}f-{\vec {\nabla }}\Phi \cdot {\partial f \over \partial {\vec {v}}}=0}
Combining the Vlasov equation with the Poisson equation for gravity:
∇
2
ϕ
=
4
π
G
ρ
.
{\displaystyle \nabla ^{2}\phi =4\pi G\rho .}
gives the Jeans equations.
More explicitly, If n=n(x,t) is the density of stars in space, as a function of position x = (x1,x2,x3) and time t, v = (v1,v2,v3) is the velocity, and Φ = Φ(x,t) is the gravitational potential, the Jeans equations may be written as:
∂
n
∂
t
+
∑
i
∂
(
n
⟨
v
i
⟩
)
∂
x
i
=
0
,
{\displaystyle {\frac {\partial n}{\partial t}}+\sum _{i}{\frac {\partial (n\langle {v_{i}}\rangle )}{\partial x_{i}}}=0,}
∂
(
n
⟨
v
j
⟩
)
∂
t
+
n
∂
Φ
∂
x
j
+
∑
i
∂
(
n
⟨
v
i
v
j
⟩
)
∂
x
i
=
0
(
j
=
1
,
2
,
3.
)
{\displaystyle {\frac {\partial (n\langle {v_{j}}\rangle )}{\partial t}}+n{\frac {\partial \Phi }{\partial x_{j}}}+\sum _{i}{\frac {\partial (n\langle {v_{i}v_{j}}\rangle )}{\partial x_{i}}}=0\qquad (j=1,2,3.)}
Here, the ⟨...⟩ notation means an average at a given point and time (x,t), so that, for example,
⟨
v
1
⟩
{\displaystyle \langle {v_{1}}\rangle }
is the average of component 1 of the velocity of the stars at a given point and time. The second set of equations may alternately be written as
n
∂
⟨
v
j
⟩
∂
t
+
∑
i
n
⟨
v
i
⟩
∂
⟨
v
j
⟩
∂
x
i
=
−
n
∂
Φ
∂
x
j
−
∑
i
∂
(
n
σ
i
j
2
)
∂
x
i
(
j
=
1
,
2
,
3.
)
{\displaystyle n{\frac {\partial \langle {v_{j}}\rangle }{\partial t}}+\sum _{i}n\langle {v_{i}}\rangle {\frac {\partial {\langle {v_{j}}\rangle }}{\partial x_{i}}}=-n{\frac {\partial \Phi }{\partial x_{j}}}-\sum _{i}{\frac {\partial (n\sigma _{ij}^{2})}{\partial x_{i}}}\qquad (j=1,2,3.)}
where the spatial part of the stress–energy tensor is defined as:
σ
i
j
2
=
⟨
v
i
v
j
⟩
−
⟨
v
i
⟩
⟨
v
j
⟩
{\displaystyle \sigma _{ij}^{2}=\langle {v_{i}v_{j}}\rangle -\langle {v_{i}}\rangle \langle {v_{j}}\rangle }
and measures the velocity dispersion in components i and j at a given point.
Some given assumptions regarding these equations include:
The flow in phase space must conserve mass
The density around a given star remains the same, or is incompressible
Notice that the Jeans equations contain 9 unknowns (3 average velocities and 6 stress tensor terms), but only 3 equations. This means that Jeans equations are not closed. To solve different systems, various assumptions are made about the stress tensor.
=== Spherical Jeans equations ===
One fundamental usage of Jean's equation is in spherical gravitational bodies. In spherical coordinates, the equations are:
∂
ρ
⟨
v
r
⟩
∂
t
+
∂
ρ
⟨
v
r
2
⟩
∂
r
+
ρ
r
[
2
⟨
v
r
2
⟩
−
⟨
v
θ
2
⟩
−
⟨
v
ϕ
2
⟩
]
+
ρ
∂
Φ
∂
r
=
0
{\displaystyle {\partial \rho \langle v_{r}\rangle \over \partial t}+{\partial \rho \langle v_{r}^{2}\rangle \over \partial r}+{\rho \over r}[2\langle v_{r}^{2}\rangle -\langle v_{\theta }^{2}\rangle -\langle v_{\phi }^{2}\rangle ]+\rho {\partial \Phi \over \partial r}=0}
∂
ρ
⟨
v
θ
⟩
∂
t
+
∂
ρ
⟨
v
r
v
θ
⟩
∂
r
+
ρ
r
[
3
⟨
v
r
v
θ
⟩
+
(
⟨
v
θ
2
⟩
−
⟨
v
ϕ
2
⟩
)
cot
(
θ
)
]
=
0
{\displaystyle {\partial \rho \langle v_{\theta }\rangle \over \partial t}+{\partial \rho \langle v_{r}v_{\theta }\rangle \over \partial r}+{\rho \over r}[3\langle v_{r}v_{\theta }\rangle +(\langle v_{\theta }^{2}\rangle -\langle v_{\phi }^{2}\rangle )\cot(\theta )]=0}
∂
ρ
⟨
v
ϕ
⟩
∂
t
+
∂
ρ
⟨
v
r
v
ϕ
⟩
∂
r
+
ρ
r
[
3
⟨
v
r
v
ϕ
⟩
+
2
⟨
v
θ
v
ϕ
⟩
cot
(
θ
)
]
=
0
{\displaystyle {\partial \rho \langle v_{\phi }\rangle \over \partial t}+{\partial \rho \langle v_{r}v_{\phi }\rangle \over \partial r}+{\rho \over r}[3\langle v_{r}v_{\phi }\rangle +2\langle v_{\theta }v_{\phi }\rangle \cot(\theta )]=0}
Using the stress tensor with the assumption that it is diagonal and
σ
θ
2
=
σ
ϕ
2
{\displaystyle \sigma _{\theta }^{2}=\sigma _{\phi }^{2}}
, can reduce these equations to a single simplified equation:
∂
(
ρ
σ
r
2
)
∂
r
+
2
ρ
r
[
σ
r
2
−
σ
θ
2
]
+
ρ
∂
Φ
∂
r
=
0
{\displaystyle {\partial (\rho \sigma _{r}^{2}) \over \partial r}+{2\rho \over r}[\sigma _{r}^{2}-\sigma _{\theta }^{2}]+\rho {\partial \Phi \over \partial r}=0}
Again, there are two unknown functions (
σ
r
2
(
r
)
{\displaystyle \sigma _{r}^{2}(r)}
and
σ
θ
2
(
r
)
{\displaystyle \sigma _{\theta }^{2}(r)}
) that require assumptions for the equation to be solved.
== Applications ==
Jeans equation have found great utility in N-body simulation gravitational research. The scale of these simulations can range in size from just our solar system to the entire universe. Using measurements of stellar number density and various kinematic values, parameters within the Jeans equations can be estimated. This allows for various analyses to be made through the lens of Jeans equations. This is particularly useful when simulating dark matter halo distributions, due to its isothermal, non-interactive behavior. Searches for structure in galaxy formation, dark matter formation, and universe formation can have observations supplemented with simulations using Jeans equations.
=== Milky Way dark matter halo ===
An example of such an analysis is given by the constraints that can be placed on the dark matter halo within the Milky Way. Using Sloan Digital Sky Survey measurements of our Galaxy, researchers were able to simulate the dark matter halo distribution using Jeans equations. By comparing measured values with Jeans equation simulation results, they confirmed the need for extra dark matter and placed limits on its ellipsoid size. They estimated the ratio of minor to major axis of this halo to be 0.47
±
{\displaystyle \pm }
0.14. This method has been applied to many other galactic halos and have produced similar results regarding dark matter halo topology.
=== Simulation limitations ===
The limiting factor of these simulations however, has been the data required to approximate stress tensor parameter values that dictate the Jeans equations behavior. Additionally, some constraints can be placed on Jeans equation simulations in order to produce reliable results Some of these limitations include a wavelength resolution requirement, variable gravitational softening, and a minimum vertical structure particle resolution.
== See also ==
Jeans's theorem
== References == | Wikipedia/Jeans_equations |
In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is:
(
U
−
c
)
(
φ
″
−
k
2
φ
)
−
U
″
φ
=
0
,
{\displaystyle (U-c)(\varphi ''-k^{2}\varphi )-U''\varphi =0,}
with
U
(
z
)
{\displaystyle U(z)}
the flow velocity of the steady base flow whose stability is to be studied and
z
{\displaystyle z}
is the cross-stream direction (i.e. perpendicular to the flow direction). Further
φ
(
z
)
{\displaystyle \varphi (z)}
is the complex valued amplitude of the infinitesimal streamfunction perturbations applied to the base flow,
k
{\displaystyle k}
is the wavenumber of the perturbations and
c
{\displaystyle c}
is the phase speed with which the perturbations propagate in the flow direction. The prime denotes differentiation with respect to
z
.
{\displaystyle z.}
== Background ==
The equation is named after Lord Rayleigh, who introduced it in 1880. The Orr–Sommerfeld equation – introduced later, for the study of stability of parallel viscous flow – reduces to Rayleigh's equation when the viscosity is zero.
Rayleigh's equation, together with appropriate boundary conditions, most often poses an eigenvalue problem. For given (real-valued) wavenumber
k
{\displaystyle k}
and mean flow velocity
U
(
z
)
,
{\displaystyle U(z),}
the eigenvalues are the phase speeds
c
,
{\displaystyle c,}
and the eigenfunctions are the associated streamfunction amplitudes
φ
(
z
)
.
{\displaystyle \varphi (z).}
In general, the eigenvalues form a continuous spectrum. In certain cases there may further be a discrete spectrum of complex conjugate pairs of
c
.
{\displaystyle c.}
Since the wavenumber
k
{\displaystyle k}
occurs only as a square
k
2
{\displaystyle k^{2}}
in Rayleigh's equation, a solution (i.e.
φ
(
z
)
{\displaystyle \varphi (z)}
and
c
{\displaystyle c}
) for wavenumber
+
k
{\displaystyle +k}
is also a solution for the wavenumber
−
k
.
{\displaystyle -k.}
Rayleigh's equation only concerns two-dimensional perturbations to the flow. From Squire's theorem it follows that the two-dimensional perturbations are less stable than three-dimensional perturbations.
If a real-valued phase speed
c
{\displaystyle c}
is in between the minimum and maximum of
U
(
z
)
,
{\displaystyle U(z),}
the problem has so-called critical layers near
z
=
z
c
r
i
t
{\displaystyle z=z_{\mathrm {crit} }}
where
U
(
z
c
r
i
t
)
=
c
.
{\displaystyle U(z_{\mathrm {crit} })=c.}
At the critical layers Rayleigh's equation becomes singular. These were first being studied by Lord Kelvin, also in 1880. His solution gives rise to a so-called cat's eye pattern of streamlines near the critical layer, when observed in a frame of reference moving with the phase speed
c
.
{\displaystyle c.}
== Derivation ==
Consider a parallel shear flow
U
(
z
)
{\displaystyle U(z)}
in the
x
{\displaystyle x}
direction, which varies only in the cross-flow direction
z
.
{\displaystyle z.}
The stability of the flow is studied by adding small perturbations to the flow velocity
u
(
x
,
z
,
t
)
{\displaystyle u(x,z,t)}
and
w
(
x
,
z
,
t
)
{\displaystyle w(x,z,t)}
in the
x
{\displaystyle x}
and
z
{\displaystyle z}
directions, respectively. The flow is described using the incompressible Euler equations, which become after linearization – using velocity components
U
(
z
)
+
u
(
x
,
z
,
t
)
{\displaystyle U(z)+u(x,z,t)}
and
w
(
x
,
z
,
t
)
:
{\displaystyle w(x,z,t):}
∂
t
u
+
U
∂
x
u
+
w
U
′
=
−
1
ρ
∂
x
p
,
∂
t
w
+
U
∂
x
w
=
−
1
ρ
∂
z
p
and
∂
x
u
+
∂
z
w
=
0
,
{\displaystyle {\begin{aligned}&\partial _{t}u+U\,\partial _{x}u+w\,U'=-{\frac {1}{\rho }}\partial _{x}p,\\&\partial _{t}w+U\,\partial _{x}w=-{\frac {1}{\rho }}\partial _{z}p\qquad {\text{and}}\\&\partial _{x}u+\partial _{z}w=0,\end{aligned}}}
with
∂
t
{\displaystyle \partial _{t}}
the partial derivative operator with respect to time, and similarly
∂
x
{\displaystyle \partial _{x}}
and
∂
z
{\displaystyle \partial _{z}}
with respect to
x
{\displaystyle x}
and
z
.
{\displaystyle z.}
The pressure fluctuations
p
(
x
,
z
,
t
)
{\displaystyle p(x,z,t)}
ensure that the continuity equation
∂
x
u
+
∂
z
w
=
0
{\displaystyle \partial _{x}u+\partial _{z}w=0}
is fulfilled. The fluid density is denoted as
ρ
{\displaystyle \rho }
and is a constant in the present analysis. The prime
U
′
{\displaystyle U'}
denotes differentiation of
U
(
z
)
{\displaystyle U(z)}
with respect to its argument
z
.
{\displaystyle z.}
The flow oscillations
u
{\displaystyle u}
and
w
{\displaystyle w}
are described using a streamfunction
ψ
(
x
,
z
,
t
)
,
{\displaystyle \psi (x,z,t),}
ensuring that the continuity equation is satisfied:
u
=
+
∂
z
ψ
and
w
=
−
∂
x
ψ
.
{\displaystyle u=+\partial _{z}\psi \quad {\text{ and }}\quad w=-\partial _{x}\psi .}
Taking the
z
{\displaystyle z}
- and
x
{\displaystyle x}
-derivatives of the
x
{\displaystyle x}
- and
z
{\displaystyle z}
-momentum equation, and thereafter subtracting the two equations, the pressure
p
{\displaystyle p}
can be eliminated:
∂
t
(
∂
x
2
ψ
+
∂
z
2
ψ
)
+
U
∂
x
(
∂
x
2
ψ
+
∂
z
2
ψ
)
−
U
″
∂
x
ψ
=
0
,
{\displaystyle \partial _{t}\left(\partial _{x}^{2}\psi +\partial _{z}^{2}\psi \right)+U\,\partial _{x}\left(\partial _{x}^{2}\psi +\partial _{z}^{2}\psi \right)-U''\,\partial _{x}\psi =0,}
which is essentially the vorticity transport equation,
∂
x
2
ψ
+
∂
z
2
ψ
{\displaystyle \partial _{x}^{2}\psi +\partial _{z}^{2}\psi }
being (minus) the vorticity.
Next, sinusoidal fluctuations are considered:
ψ
(
x
,
z
,
t
)
=
ℜ
{
φ
(
z
)
exp
(
i
k
(
x
−
c
t
)
)
}
,
{\displaystyle \psi (x,z,t)=\Re \left\{\varphi (z)\,\exp(ik(x-ct))\right\},}
with
φ
(
z
)
{\displaystyle \varphi (z)}
the complex-valued amplitude of the streamfunction oscillations, while
i
{\displaystyle i}
is the imaginary unit (
i
2
=
−
1
{\displaystyle i^{2}=-1}
) and
ℜ
{
⋅
}
{\displaystyle \Re \left\{\cdot \right\}}
denotes the real part of the expression between the brackets. Using this in the vorticity transport equation, Rayleigh's equation is obtained.
The boundary conditions for flat impermeable walls follow from the fact that the streamfunction is a constant at them. So at impermeable walls the streamfunction oscillations are zero, i.e.
φ
=
0.
{\displaystyle \varphi =0.}
For unbounded flows the common boundary conditions are that
lim
z
→
±
∞
φ
(
z
)
=
0.
{\displaystyle \lim _{z\to \pm \infty }\varphi (z)=0.}
== Notes ==
== References == | Wikipedia/Rayleigh_equation |
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change and information systems including the transmission of information in telecommunication.
Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible.
The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names thermodynamic function and heat-potential. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as transformation-content, in German Verwandlungsinhalt, and later coined the term entropy from a Greek word for transformation.
Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behaviour, in form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, which has become one of the defining universal constants for the modern International System of Units.
== History ==
In his 1803 paper Fundamental Principles of Equilibrium and Movement, the French mathematician Lazare Carnot proposed that in any machine, the accelerations and shocks of the moving parts represent losses of moment of activity; in any natural process there exists an inherent tendency towards the dissipation of useful energy. In 1824, building on that work, Lazare's son, Sadi Carnot, published Reflections on the Motive Power of Fire, which posited that in all heat-engines, whenever "caloric" (what is now known as heat) falls through a temperature difference, work or motive power can be produced from the actions of its fall from a hot to cold body. He used an analogy with how water falls in a water wheel. That was an early insight into the second law of thermodynamics. Carnot based his views of heat partially on the early 18th-century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on the contemporary views of Count Rumford, who showed in 1789 that heat could be created by friction, as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete engine cycle, "no change occurs in the condition of the working body".
The first law of thermodynamics, deduced from the heat-friction experiments of James Joule in 1843, expresses the concept of energy and its conservation in all processes; the first law, however, is unsuitable to separately quantify the effects of friction and dissipation.
In the 1850s and 1860s, German physicist Rudolf Clausius objected to the supposition that no change occurs in the working body, and gave that change a mathematical interpretation, by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction. He described his observations as a dissipative use of energy, resulting in a transformation-content (Verwandlungsinhalt in German), of a thermodynamic system or working body of chemical species during a change of state. That was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Clausius discovered that the non-usable energy increases as steam proceeds from inlet to exhaust in a steam engine. From the prefix en-, as in 'energy', and from the Greek word τροπή [tropē], which is translated in an established lexicon as turning or change and that he rendered in German as Verwandlung, a word often translated into English as transformation, in 1865 Clausius coined the name of that property as entropy. The word was adopted into the English language in 1868.
Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, and James Clerk Maxwell gave entropy a statistical basis. In 1877, Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy as proportional to the natural logarithm of the number of microstates such a gas could occupy. The proportionality constant in this definition, called the Boltzmann constant, has become one of the defining universal constants for the modern International System of Units (SI). Henceforth, the essential problem in statistical thermodynamics has been to determine the distribution of a given amount of energy E over N identical systems. Constantin Carathéodory, a Greek mathematician, linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability.
== Etymology ==
In 1865, Clausius named the concept of "the differential of a quantity which depends on the configuration of the system", entropy (Entropie) after the Greek word for 'transformation'. He gave "transformational content" (Verwandlungsinhalt) as a synonym, paralleling his "thermal and ergonal content" (Wärme- und Werkinhalt) as the name of U, but preferring the term entropy as a close parallel of the word energy, as he found the concepts nearly "analogous in their physical significance". This term was formed by replacing the root of ἔργον ('ergon', 'work') by that of τροπή ('tropy', 'transformation').
In more detail, Clausius explained his choice of "entropy" as a name as follows:
I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, therefore, to call S the entropy of a body, after the Greek word "transformation". I have designedly coined the word entropy to be similar to energy, for these two quantities are so analogous in their physical significance, that an analogy of denominations seems to me helpful.
Leon Cooper added that in this way "he succeeded in coining a word that meant the same thing to everybody: nothing".
== Definitions and descriptions ==
The concept of entropy is described by two principal approaches, the macroscopic perspective of classical thermodynamics, and the microscopic description central to statistical mechanics. The classical approach defines entropy in terms of macroscopically measurable physical properties, such as bulk mass, volume, pressure, and temperature. The statistical definition of entropy defines it in terms of the statistics of the motions of the microscopic constituents of a system — modelled at first classically, e.g. Newtonian particles constituting a gas, and later quantum-mechanically (photons, phonons, spins, etc.). The two approaches form a consistent, unified view of the same phenomenon as expressed in the second law of thermodynamics, which has found universal applicability to physical processes.
=== State variables and functions of state ===
Many thermodynamic properties are defined by physical variables that define a state of thermodynamic equilibrium, which essentially are state variables. State variables depend only on the equilibrium condition, not on the path evolution to that state. State variables can be functions of state, also called state functions, in a sense that one state variable is a mathematical function of other state variables. Often, if some properties of a system are determined, they are sufficient to determine the state of the system and thus other properties' values. For example, temperature and pressure of a given quantity of gas determine its state, and thus also its volume via the ideal gas law. A system composed of a pure substance of a single phase at a particular uniform temperature and pressure is determined, and is thus a particular state, and has a particular volume. The fact that entropy is a function of state makes it useful. In the Carnot cycle, the working fluid returns to the same state that it had at the start of the cycle, hence the change or line integral of any state function, such as entropy, over this reversible cycle is zero.
=== Reversible process ===
The entropy change
d
S
{\textstyle \mathrm {d} S}
of a system can be well-defined as a small portion of heat
δ
Q
r
e
v
{\textstyle \delta Q_{\mathsf {rev}}}
transferred from the surroundings to the system during a reversible process divided by the temperature
T
{\textstyle T}
of the system during this heat transfer:
d
S
=
δ
Q
r
e
v
T
{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
The reversible process is quasistatic (i.e., it occurs without any dissipation, deviating only infinitesimally from the thermodynamic equilibrium), and it may conserve total entropy. For example, in the Carnot cycle, while the heat flow from a hot reservoir to a cold reservoir represents the increase in the entropy in a cold reservoir, the work output, if reversibly and perfectly stored, represents the decrease in the entropy which could be used to operate the heat engine in reverse, returning to the initial state; thus the total entropy change may still be zero at all times if the entire process is reversible.
In contrast, an irreversible process increases the total entropy of the system and surroundings. Any process that happens quickly enough to deviate from the thermal equilibrium cannot be reversible; the total entropy increases, and the potential for maximum work to be done during the process is lost.
=== Carnot cycle ===
The concept of entropy arose from Rudolf Clausius's study of the Carnot cycle which is a thermodynamic cycle performed by a Carnot heat engine as a reversible heat engine. In a Carnot cycle, the heat
Q
H
{\textstyle Q_{\mathsf {H}}}
is transferred from a hot reservoir to a working gas at the constant temperature
T
H
{\textstyle T_{\mathsf {H}}}
during isothermal expansion stage and the heat
Q
C
{\textstyle Q_{\mathsf {C}}}
is transferred from a working gas to a cold reservoir at the constant temperature
T
C
{\textstyle T_{\mathsf {C}}}
during isothermal compression stage. According to Carnot's theorem, a heat engine with two thermal reservoirs can produce a work
W
{\textstyle W}
if and only if there is a temperature difference between reservoirs. Originally, Carnot did not distinguish between heats
Q
H
{\textstyle Q_{\mathsf {H}}}
and
Q
C
{\textstyle Q_{\mathsf {C}}}
, as he assumed caloric theory to be valid and hence that the total heat in the system was conserved. But in fact, the magnitude of heat
Q
H
{\textstyle Q_{\mathsf {H}}}
is greater than the magnitude of heat
Q
C
{\textstyle Q_{\mathsf {C}}}
. Through the efforts of Clausius and Kelvin, the work
W
{\textstyle W}
done by a reversible heat engine was found to be the product of the Carnot efficiency (i.e., the efficiency of all reversible heat engines with the same pair of thermal reservoirs) and the heat
Q
H
{\textstyle Q_{\mathsf {H}}}
absorbed by a working body of the engine during isothermal expansion:
W
=
T
H
−
T
C
T
H
⋅
Q
H
=
(
1
−
T
C
T
H
)
Q
H
{\displaystyle W={\frac {T_{\mathsf {H}}-T_{\mathsf {C}}}{T_{\mathsf {H}}}}\cdot Q_{\mathsf {H}}=\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}}
To derive the Carnot efficiency Kelvin had to evaluate the ratio of the work output to the heat absorbed during the isothermal expansion with the help of the Carnot–Clapeyron equation, which contained an unknown function called the Carnot function. The possibility that the Carnot function could be the temperature as measured from a zero point of temperature was suggested by Joule in a letter to Kelvin. This allowed Kelvin to establish his absolute temperature scale.
It is known that a work
W
>
0
{\textstyle W>0}
produced by an engine over a cycle equals to a net heat
Q
Σ
=
|
Q
H
|
−
|
Q
C
|
{\textstyle Q_{\Sigma }=\left\vert Q_{\mathsf {H}}\right\vert -\left\vert Q_{\mathsf {C}}\right\vert }
absorbed over a cycle. Thus, with the sign convention for a heat
Q
{\textstyle Q}
transferred in a thermodynamic process (
Q
>
0
{\textstyle Q>0}
for an absorption and
Q
<
0
{\textstyle Q<0}
for a dissipation) we get:
W
−
Q
Σ
=
W
−
|
Q
H
|
+
|
Q
C
|
=
W
−
Q
H
−
Q
C
=
0
{\displaystyle W-Q_{\Sigma }=W-\left\vert Q_{\mathsf {H}}\right\vert +\left\vert Q_{\mathsf {C}}\right\vert =W-Q_{\mathsf {H}}-Q_{\mathsf {C}}=0}
Since this equality holds over an entire Carnot cycle, it gave Clausius the hint that at each stage of the cycle the difference between a work and a net heat would be conserved, rather than a net heat itself. Which means there exists a state function
U
{\textstyle U}
with a change of
d
U
=
δ
Q
−
d
W
{\textstyle \mathrm {d} U=\delta Q-\mathrm {d} W}
. It is called an internal energy and forms a central concept for the first law of thermodynamics.
Finally, comparison for both the representations of a work output in a Carnot cycle gives us:
|
Q
H
|
T
H
−
|
Q
C
|
T
C
=
Q
H
T
H
+
Q
C
T
C
=
0
{\displaystyle {\frac {\left\vert Q_{\mathsf {H}}\right\vert }{T_{\mathsf {H}}}}-{\frac {\left\vert Q_{\mathsf {C}}\right\vert }{T_{\mathsf {C}}}}={\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=0}
Similarly to the derivation of internal energy, this equality implies existence of a state function
S
{\textstyle S}
with a change of
d
S
=
δ
Q
/
T
{\textstyle \mathrm {d} S=\delta Q/T}
and which is conserved over an entire cycle. Clausius called this state function entropy.
In addition, the total change of entropy in both thermal reservoirs over Carnot cycle is zero too, since the inversion of a heat transfer direction means a sign inversion for the heat transferred during isothermal stages:
−
Q
H
T
H
−
Q
C
T
C
=
Δ
S
r
,
H
+
Δ
S
r
,
C
=
0
{\displaystyle -{\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}-{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=\Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}=0}
Here we denote the entropy change for a thermal reservoir by
Δ
S
r
,
i
=
−
Q
i
/
T
i
{\textstyle \Delta S_{{\mathsf {r}},i}=-Q_{i}/T_{i}}
, where
i
{\textstyle i}
is either
H
{\textstyle {\mathsf {H}}}
for a hot reservoir or
C
{\textstyle {\mathsf {C}}}
for a cold one.
If we consider a heat engine which is less effective than Carnot cycle (i.e., the work
W
{\textstyle W}
produced by this engine is less than the maximum predicted by Carnot's theorem), its work output is capped by Carnot efficiency as:
W
<
(
1
−
T
C
T
H
)
Q
H
{\displaystyle W<\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}}
Substitution of the work
W
{\textstyle W}
as the net heat into the inequality above gives us:
Q
H
T
H
+
Q
C
T
C
<
0
{\displaystyle {\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}<0}
or in terms of the entropy change
Δ
S
r
,
i
{\textstyle \Delta S_{{\mathsf {r}},i}}
:
Δ
S
r
,
H
+
Δ
S
r
,
C
>
0
{\displaystyle \Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}>0}
A Carnot cycle and an entropy as shown above prove to be useful in the study of any classical thermodynamic heat engine: other cycles, such as an Otto, Diesel or Brayton cycle, could be analysed from the same standpoint. Notably, any machine or cyclic process converting heat into work (i.e., heat engine) that is claimed to produce an efficiency greater than the one of Carnot is not viable — due to violation of the second law of thermodynamics.
For further analysis of sufficiently discrete systems, such as an assembly of particles, statistical thermodynamics must be used. Additionally, descriptions of devices operating near the limit of de Broglie waves, e.g. photovoltaic cells, have to be consistent with quantum statistics.
=== Classical thermodynamics ===
The thermodynamic definition of entropy was developed in the early 1850s by Rudolf Clausius and essentially describes how to measure the entropy of an isolated system in thermodynamic equilibrium with its parts. Clausius created the term entropy as an extensive thermodynamic variable that was shown to be useful in characterizing the Carnot cycle. Heat transfer in the isotherm steps (isothermal expansion and isothermal compression) of the Carnot cycle was found to be proportional to the temperature of a system (known as its absolute temperature). This relationship was expressed in an increment of entropy that is equal to incremental heat transfer divided by temperature. Entropy was found to vary in the thermodynamic cycle but eventually returned to the same value at the end of every cycle. Thus it was found to be a function of state, specifically a thermodynamic state of the system.
While Clausius based his definition on a reversible process, there are also irreversible processes that change entropy. Following the second law of thermodynamics, entropy of an isolated system always increases for irreversible processes. The difference between an isolated system and closed system is that energy may not flow to and from an isolated system, but energy flow to and from a closed system is possible. Nevertheless, for both closed and isolated systems, and indeed, also in open systems, irreversible thermodynamics processes may occur.
According to the Clausius equality, for a reversible cyclic thermodynamic process:
∮
δ
Q
r
e
v
T
=
0
{\displaystyle \oint {\frac {\delta Q_{\mathsf {rev}}}{T}}=0}
which means the line integral
∫
L
δ
Q
r
e
v
/
T
{\textstyle \int _{L}{\delta Q_{\mathsf {rev}}/T}}
is path-independent. Thus we can define a state function
S
{\textstyle S}
, called entropy:
d
S
=
δ
Q
r
e
v
T
{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
Therefore, thermodynamic entropy has the dimension of energy divided by temperature, and the unit joule per kelvin (J/K) in the International System of Units (SI).
To find the entropy difference between any two states of the system, the integral must be evaluated for some reversible path between the initial and final states. Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. However, the heat transferred to or from the surroundings is different as well as its entropy change.
We can calculate the change of entropy only by integrating the above formula. To obtain the absolute value of the entropy, we consider the third law of thermodynamics: perfect crystals at the absolute zero have an entropy
S
=
0
{\textstyle S=0}
.
From a macroscopic perspective, in classical thermodynamics the entropy is interpreted as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. In any process, where the system gives up
Δ
E
{\displaystyle \Delta E}
of energy to the surrounding at the temperature
T
{\textstyle T}
, its entropy falls by
Δ
S
{\textstyle \Delta S}
and at least
T
⋅
Δ
S
{\textstyle T\cdot \Delta S}
of that energy must be given up to the system's surroundings as a heat. Otherwise, this process cannot go forward. In classical thermodynamics, the entropy of a system is defined if and only if it is in a thermodynamic equilibrium (though a chemical equilibrium is not required: for example, the entropy of a mixture of two moles of hydrogen and one mole of oxygen in standard conditions is well-defined).
=== Statistical mechanics ===
The statistical definition was developed by Ludwig Boltzmann in the 1870s by analysing the statistical behaviour of the microscopic components of the system. Boltzmann showed that this definition of entropy was equivalent to the thermodynamic entropy to within a constant factor—known as the Boltzmann constant. In short, the thermodynamic definition of entropy provides the experimental verification of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature.
The interpretation of entropy in statistical mechanics is the measure of uncertainty, disorder, or mixedupness in the phrase of Gibbs, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the entropy measures the degree to which the probability of the system is spread out over different possible microstates. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and momentum of every molecule. The more such states are available to the system with appreciable probability, the greater the entropy. In statistical mechanics, entropy is a measure of the number of ways a system can be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (microstates) that could cause the observed macroscopic state (macrostate) of the system. The constant of proportionality is the Boltzmann constant.
The Boltzmann constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K−1) in the International System of Units (or kg⋅m2⋅s−2⋅K−1 in terms of base units). The entropy of a substance is usually given as an intensive property — either entropy per unit mass (SI unit: J⋅K−1⋅kg−1) or entropy per unit amount of substance (SI unit: J⋅K−1⋅mol−1).
Specifically, entropy is a logarithmic measure for the system with a number of states, each with a probability
p
i
{\textstyle p_{i}}
of being occupied (usually given by the Boltzmann distribution):
S
=
−
k
B
∑
i
p
i
ln
p
i
{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
where
k
B
{\textstyle k_{\mathsf {B}}}
is the Boltzmann constant and the summation is performed over all possible microstates of the system.
In case states are defined in a continuous manner, the summation is replaced by an integral over all possible states, or equivalently we can consider the expected value of the logarithm of the probability that a microstate is occupied:
S
=
−
k
B
⟨
ln
p
⟩
{\displaystyle S=-k_{\mathsf {B}}\left\langle \ln {p}\right\rangle }
This definition assumes the basis states to be picked in a way that there is no information on their relative phases. In a general case the expression is:
S
=
−
k
B
t
r
(
ρ
^
×
ln
ρ
^
)
{\displaystyle S=-k_{\mathsf {B}}\ \mathrm {tr} {\left({\hat {\rho }}\times \ln {\hat {\rho }}\right)}}
where
ρ
^
{\textstyle {\hat {\rho }}}
is a density matrix,
t
r
{\displaystyle \mathrm {tr} }
is a trace operator and
ln
{\displaystyle \ln }
is a matrix logarithm. The density matrix formalism is not required if the system is in thermal equilibrium so long as the basis states are chosen to be eigenstates of the Hamiltonian. For most practical purposes it can be taken as the fundamental definition of entropy since all other formulae for
S
{\textstyle S}
can be derived from it, but not vice versa.
In what has been called the fundamental postulate in statistical mechanics, among system microstates of the same energy (i.e., degenerate microstates) each microstate is assumed to be populated with equal probability
p
i
=
1
/
Ω
{\textstyle p_{i}=1/\Omega }
, where
Ω
{\textstyle \Omega }
is the number of microstates whose energy equals that of the system. Usually, this assumption is justified for an isolated system in a thermodynamic equilibrium. Then in case of an isolated system the previous formula reduces to:
S
=
k
B
ln
Ω
{\displaystyle S=k_{\mathsf {B}}\ln {\Omega }}
In thermodynamics, such a system is one with a fixed volume, number of molecules, and internal energy, called a microcanonical ensemble.
The most general interpretation of entropy is as a measure of the extent of uncertainty about a system. The equilibrium state of a system maximizes the entropy because it does not reflect all information about the initial conditions, except for the conserved variables. This uncertainty is not of the everyday subjective kind, but rather the uncertainty inherent to the experimental method and interpretative model.
The interpretative model has a central role in determining entropy. The qualifier "for a given set of macroscopic variables" above has deep implications when two observers use different sets of macroscopic variables. For example, consider observer A using variables
U
{\textstyle U}
,
V
{\textstyle V}
,
W
{\textstyle W}
and observer B using variables
U
{\textstyle U}
,
V
{\textstyle V}
,
W
{\textstyle W}
,
X
{\textstyle X}
. If observer B changes variable
X
{\textstyle X}
, then observer A will see a violation of the second law of thermodynamics, since he does not possess information about variable
X
{\textstyle X}
and its influence on the system. In other words, one must choose a complete set of macroscopic variables to describe the system, i.e. every independent parameter that may change during experiment.
Entropy can also be defined for any Markov processes with reversible dynamics and the detailed balance property.
In Boltzmann's 1896 Lectures on Gas Theory, he showed that this expression gives a measure of entropy for systems of atoms and molecules in the gas phase, thus providing a measure for the entropy of classical thermodynamics.
=== Entropy of a system ===
In a thermodynamic system, pressure and temperature tend to become uniform over time because the equilibrium state has higher probability (more possible combinations of microstates) than any other state. As an example, for a glass of ice water in air at room temperature, the difference in temperature between the warm room (the surroundings) and the cold glass of ice and water (the system and not part of the room) decreases as portions of the thermal energy from the warm surroundings spread to the cooler system of ice and water. Over time the temperature of the glass and its contents and the temperature of the room become equal. In other words, the entropy of the room has decreased as some of its energy has been dispersed to the ice and water, of which the entropy has increased.
However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the "universe" of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the thermodynamic system is a measure of how far the equalisation has progressed.
Thermodynamic entropy is a non-conserved state function that is of great importance in the sciences of physics and chemistry. Historically, the concept of entropy evolved to explain why some processes (permitted by conservation laws) occur spontaneously while their time reversals (also permitted by conservation laws) do not; systems tend to progress in the direction of increasing entropy. For isolated systems, entropy never decreases. This fact has several important consequences in science: first, it prohibits "perpetual motion" machines; and second, it implies the arrow of entropy has the same direction as the arrow of time. Increases in the total entropy of system and surroundings correspond to irreversible changes, because some energy is expended as waste heat, limiting the amount of work a system can do.
Unlike many other functions of state, entropy cannot be directly observed but must be calculated. Absolute standard molar entropy of a substance can be calculated from the measured temperature dependence of its heat capacity. The molar entropy of ions is obtained as a difference in entropy from a reference state defined as zero entropy. The second law of thermodynamics states that the entropy of an isolated system must increase or remain constant. Therefore, entropy is not a conserved quantity: for example, in an isolated system with non-uniform temperature, heat might irreversibly flow and the temperature become more uniform such that entropy increases. Chemical reactions cause changes in entropy and system entropy, in conjunction with enthalpy, plays an important role in determining in which direction a chemical reaction spontaneously proceeds.
One dictionary definition of entropy is that it is "a measure of thermal energy per unit temperature that is not available for useful work" in a cyclic process. For instance, a substance at uniform temperature is at maximum entropy and cannot drive a heat engine. A substance at non-uniform temperature is at a lower entropy (than if the heat distribution is allowed to even out) and some of the thermal energy can drive a heat engine.
A special case of entropy increase, the entropy of mixing, occurs when two or more different substances are mixed. If the substances are at the same temperature and pressure, there is no net exchange of heat or work – the entropy change is entirely due to the mixing of the different substances. At a statistical mechanical level, this results due to the change in available volume per particle with mixing.
=== Equivalence of definitions ===
Proofs of equivalence between the entropy in statistical mechanics — the Gibbs entropy formula:
S
=
−
k
B
∑
i
p
i
ln
p
i
{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
and the entropy in classical thermodynamics:
d
S
=
δ
Q
r
e
v
T
{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
together with the fundamental thermodynamic relation are known for the microcanonical ensemble, the canonical ensemble, the grand canonical ensemble, and the isothermal–isobaric ensemble. These proofs are based on the probability density of microstates of the generalised Boltzmann distribution and the identification of the thermodynamic internal energy as the ensemble average
U
=
⟨
E
i
⟩
{\textstyle U=\left\langle E_{i}\right\rangle }
. Thermodynamic relations are then employed to derive the well-known Gibbs entropy formula. However, the equivalence between the Gibbs entropy formula and the thermodynamic definition of entropy is not a fundamental thermodynamic relation but rather a consequence of the form of the generalized Boltzmann distribution.
Furthermore, it has been shown that the definitions of entropy in statistical mechanics is the only entropy that is equivalent to the classical thermodynamics entropy under the following postulates:
== Second law of thermodynamics ==
The second law of thermodynamics requires that, in general, the total entropy of any system does not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system tends not to decrease. It follows that heat cannot flow from a colder body to a hotter body without the application of work to the colder body. Secondly, it is impossible for any device operating on a cycle to produce net work from a single temperature reservoir; the production of net work requires flow of heat from a hotter reservoir to a colder reservoir, or a single expanding reservoir undergoing adiabatic cooling, which performs adiabatic work. As a result, there is no possibility of a perpetual motion machine. It follows that a reduction in the increase of entropy in a specified process, such as a chemical reaction, means that it is energetically more efficient.
It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. An air conditioner, for example, may cool the air in a room, thus reducing the entropy of the air of that system. The heat expelled from the room (the system), which the air conditioner transports and discharges to the outside air, always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air of that system. Thus, the total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.
In mechanics, the second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work. The entropy change of a system at temperature
T
{\textstyle T}
absorbing an infinitesimal amount of heat
δ
q
{\textstyle \delta q}
in a reversible way, is given by
δ
q
/
T
{\textstyle \delta q/T}
. More explicitly, an energy
T
R
S
{\textstyle T_{R}S}
is not available to do useful work, where
T
R
{\textstyle T_{R}}
is the temperature of the coldest accessible reservoir or heat sink external to the system. For further discussion, see Exergy.
Statistical mechanics demonstrates that entropy is governed by probability, thus allowing for a decrease in disorder even in an isolated system. Although this is possible, such an event has a small probability of occurring, making it unlikely.
The applicability of a second law of thermodynamics is limited to systems in or sufficiently near equilibrium state, so that they have defined entropy. Some inhomogeneous systems out of thermodynamic equilibrium still satisfy the hypothesis of local thermodynamic equilibrium, so that entropy density is locally defined as an intensive quantity. For such systems, there may apply a principle of maximum time rate of entropy production. It states that such a system may evolve to a steady state that maximises its time rate of entropy production. This does not mean that such a system is necessarily always in a condition of maximum time rate of entropy production; it means that it may evolve to such a steady state.
== Applications ==
=== The fundamental thermodynamic relation ===
The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy
U
{\textstyle U}
to changes in the entropy and the external parameters. This relation is known as the fundamental thermodynamic relation. If external pressure
p
{\textstyle p}
bears on the volume
V
{\textstyle V}
as the only external parameter, this relation is:
d
U
=
T
d
S
−
p
d
V
{\displaystyle \mathrm {d} U=T\ \mathrm {d} S-p\ \mathrm {d} V}
Since both internal energy and entropy are monotonic functions of temperature
T
{\textstyle T}
, implying that the internal energy is fixed when one specifies the entropy and the volume, this relation is valid even if the change from one state of thermal equilibrium to another with infinitesimally larger entropy and volume happens in a non-quasistatic way (so during this change the system may be very far out of thermal equilibrium and then the whole-system entropy, pressure, and temperature may not exist).
The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system. Important examples are the Maxwell relations and the relations between heat capacities.
=== Entropy in chemical thermodynamics ===
Thermodynamic entropy is central in chemical thermodynamics, enabling changes to be quantified and the outcome of reactions predicted. The second law of thermodynamics states that entropy in an isolated system — the combination of a subsystem under study and its surroundings — increases during all spontaneous chemical and physical processes. The Clausius equation introduces the measurement of entropy change which describes the direction and quantifies the magnitude of simple changes such as heat transfer between systems — always from hotter body to cooler one spontaneously.
Thermodynamic entropy is an extensive property, meaning that it scales with the size or extent of a system. In many processes it is useful to specify the entropy as an intensive property independent of the size, as a specific entropy characteristic of the type of system studied. Specific entropy may be expressed relative to a unit of mass, typically the kilogram (unit: J⋅kg−1⋅K−1). Alternatively, in chemistry, it is also referred to one mole of substance, in which case it is called the molar entropy with a unit of J⋅mol−1⋅K−1.
Thus, when one mole of substance at about 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of
q
r
e
v
/
T
{\textstyle q_{\mathsf {rev}}/T}
constitute each element's or compound's standard molar entropy, an indicator of the amount of energy stored by a substance at 298 K. Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture.
Entropy is equally essential in predicting the extent and direction of complex chemical reactions. For such applications,
Δ
S
{\textstyle \Delta S}
must be incorporated in an expression that includes both the system and its surroundings:
Δ
S
u
n
i
v
e
r
s
e
=
Δ
S
s
u
r
r
o
u
n
d
i
n
g
s
+
Δ
S
s
y
s
t
e
m
{\displaystyle \Delta S_{\mathsf {universe}}=\Delta S_{\mathsf {surroundings}}+\Delta S_{\mathsf {system}}}
Via additional steps this expression becomes the equation of Gibbs free energy change
Δ
G
{\textstyle \Delta G}
for reactants and products in the system at the constant pressure and temperature
T
{\textstyle T}
:
Δ
G
=
Δ
H
−
T
Δ
S
{\displaystyle \Delta G=\Delta H-T\ \Delta S}
where
Δ
H
{\textstyle \Delta H}
is the enthalpy change and
Δ
S
{\textstyle \Delta S}
is the entropy change.
The spontaneity of a chemical or physical process is governed by the Gibbs free energy change (ΔG), as defined by the equation ΔG = ΔH − TΔS, where ΔH represents the enthalpy change, ΔS the entropy change, and T the temperature in Kelvin. A negative ΔG indicates a thermodynamically favorable (spontaneous) process, while a positive ΔG denotes a non-spontaneous one. When both ΔH and ΔS are positive (endothermic, entropy-increasing), the reaction becomes spontaneous at sufficiently high temperatures, as the TΔS term dominates. Conversely, if both ΔH and ΔS are negative (exothermic, entropy-decreasing), spontaneity occurs only at low temperatures, where the enthalpy term prevails. Reactions with ΔH < 0 and ΔS > 0 (exothermic and entropy-increasing) are spontaneous at all temperatures, while those with ΔH > 0 and ΔS < 0 (endothermic and entropy-decreasing) are non-spontaneous regardless of temperature. These principles underscore the interplay between energy exchange, disorder, and temperature in determining the direction of natural processes, from phase transitions to biochemical reactions.
=== World's technological capacity to store and communicate entropic information ===
A 2011 study in Science estimated the world's technological capacity to store and communicate optimally compressed information normalised on the most effective compression algorithms available in the year 2007, therefore estimating the entropy of the technologically available sources. The author's estimate that humankind's technological capacity to store information grew from 2.6 (entropically compressed) exabytes in 1986 to 295 (entropically compressed) exabytes in 2007. The world's technological capacity to receive information through one-way broadcast networks was 432 exabytes of (entropically compressed) information in 1986, to 1.9 zettabytes in 2007. The world's effective capacity to exchange information through two-way telecommunication networks was 281 petabytes of (entropically compressed) information in 1986, to 65 (entropically compressed) exabytes in 2007.
=== Entropy balance equation for open systems ===
In chemical engineering, the principles of thermodynamics are commonly applied to "open systems", i.e. those in which heat, work, and mass flow across the system boundary. In general, flow of heat
Q
˙
{\textstyle {\dot {Q}}}
, flow of shaft work
W
˙
S
{\textstyle {\dot {W}}_{\mathsf {S}}}
and pressure-volume work
P
V
˙
{\textstyle P{\dot {V}}}
across the system boundaries cause changes in the entropy of the system. Heat transfer entails entropy transfer
Q
˙
/
T
{\textstyle {\dot {Q}}/T}
, where
T
{\textstyle T}
is the absolute thermodynamic temperature of the system at the point of the heat flow. If there are mass flows across the system boundaries, they also influence the total entropy of the system. This account, in terms of heat and work, is valid only for cases in which the work and heat transfers are by paths physically distinct from the paths of entry and exit of matter from the system.
To derive a generalised entropy balanced equation, we start with the general balance equation for the change in any extensive quantity
θ
{\textstyle \theta }
in a thermodynamic system, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. The basic generic balance expression states that
d
θ
/
d
t
{\textstyle \mathrm {d} \theta /\mathrm {d} t}
, i.e. the rate of change of
θ
{\textstyle \theta }
in the system, equals the rate at which
θ
{\textstyle \theta }
enters the system at the boundaries, minus the rate at which
θ
{\textstyle \theta }
leaves the system across the system boundaries, plus the rate at which
θ
{\textstyle \theta }
is generated within the system. For an open thermodynamic system in which heat and work are transferred by paths separate from the paths for transfer of matter, using this generic balance equation, with respect to the rate of change with time
t
{\textstyle t}
of the extensive quantity entropy
S
{\textstyle S}
, the entropy balance equation is:
d
S
d
t
=
∑
k
=
1
K
M
˙
k
S
^
k
+
Q
˙
T
+
S
˙
g
e
n
{\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}=\sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}+{\frac {\dot {Q}}{T}}+{\dot {S}}_{\mathsf {gen}}}}
where
∑
k
=
1
K
M
˙
k
S
^
k
{\textstyle \sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}}}
is the net rate of entropy flow due to the flows of mass
M
˙
k
{\textstyle {\dot {M}}_{k}}
into and out of the system with entropy per unit mass
S
^
k
{\textstyle {\hat {S}}_{k}}
,
Q
˙
/
T
{\textstyle {\dot {Q}}/T}
is the rate of entropy flow due to the flow of heat across the system boundary and
S
˙
g
e
n
{\textstyle {\dot {S}}_{\mathsf {gen}}}
is the rate of entropy generation within the system, e.g. by chemical reactions, phase transitions, internal heat transfer or frictional effects such as viscosity.
In case of multiple heat flows the term
Q
˙
/
T
{\textstyle {\dot {Q}}/T}
is replaced by
∑
j
Q
˙
j
/
T
j
{\textstyle \sum _{j}{{\dot {Q}}_{j}/T_{j}}}
, where
Q
˙
j
{\textstyle {\dot {Q}}_{j}}
is the heat flow through
j
{\textstyle j}
-th port into the system and
T
j
{\textstyle T_{j}}
is the temperature at the
j
{\textstyle j}
-th port.
The nomenclature "entropy balance" is misleading and often deemed inappropriate because entropy is not a conserved quantity. In other words, the term
S
˙
g
e
n
{\textstyle {\dot {S}}_{\mathsf {gen}}}
is never a known quantity but always a derived one based on the expression above. Therefore, the open system version of the second law is more appropriately described as the "entropy generation equation" since it specifies that:
S
˙
g
e
n
≥
0
{\displaystyle {\dot {S}}_{\mathsf {gen}}\geq 0}
with zero for reversible process and positive values for irreversible one.
== Entropy change formulas for simple processes ==
For certain simple transformations in systems of constant composition, the entropy changes are given by simple formulas.
=== Isothermal expansion or compression of an ideal gas ===
For the expansion (or compression) of an ideal gas from an initial volume
V
0
{\textstyle V_{0}}
and pressure
P
0
{\textstyle P_{0}}
to a final volume
V
{\textstyle V}
and pressure
P
{\textstyle P}
at any constant temperature, the change in entropy is given by:
Δ
S
=
n
R
ln
V
V
0
=
−
n
R
ln
P
P
0
{\displaystyle \Delta S=nR\ln {\frac {V}{V_{0}}}=-nR\ln {\frac {P}{P_{0}}}}
Here
n
{\textstyle n}
is the amount of gas (in moles) and
R
{\textstyle R}
is the ideal gas constant. These equations also apply for expansion into a finite vacuum or a throttling process, where the temperature, internal energy and enthalpy for an ideal gas remain constant.
=== Cooling and heating ===
For pure heating or cooling of any system (gas, liquid or solid) at constant pressure from an initial temperature
T
0
{\textstyle T_{0}}
to a final temperature
T
{\textstyle T}
, the entropy change is:
Δ
S
=
n
C
P
ln
T
T
0
{\textstyle \Delta S=nC_{\mathrm {P} }\ln {\frac {T}{T_{0}}}}
provided that the constant-pressure molar heat capacity (or specific heat)
C
P
{\textstyle C_{\mathrm {P} }}
is constant and that no phase transition occurs in this temperature interval.
Similarly at constant volume, the entropy change is:
Δ
S
=
n
C
V
ln
T
T
0
{\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}}
where the constant-volume molar heat capacity
C
V
{\textstyle C_{\mathrm {V} }}
is constant and there is no phase change.
At low temperatures near absolute zero, heat capacities of solids quickly drop off to near zero, so the assumption of constant heat capacity does not apply.
Since entropy is a state function, the entropy change of any process in which temperature and volume both vary is the same as for a path divided into two steps – heating at constant volume and expansion at constant temperature. For an ideal gas, the total entropy change is:
Δ
S
=
n
C
V
ln
T
T
0
+
n
R
ln
V
V
0
{\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}+nR\ln {\frac {V}{V_{0}}}}
Similarly if the temperature and pressure of an ideal gas both vary:
Δ
S
=
n
C
P
ln
T
T
0
−
n
R
ln
P
P
0
{\displaystyle \Delta S=nC_{\mathrm {P} }\ln {\frac {T}{T_{0}}}-nR\ln {\frac {P}{P_{0}}}}
=== Phase transitions ===
Reversible phase transitions occur at constant temperature and pressure. The reversible heat is the enthalpy change for the transition, and the entropy change is the enthalpy change divided by the thermodynamic temperature. For fusion (i.e., melting) of a solid to a liquid at the melting point
T
m
{\textstyle T_{\mathsf {m}}}
, the entropy of fusion is:
Δ
S
f
u
s
=
Δ
H
f
u
s
T
m
.
{\displaystyle \Delta S_{\mathsf {fus}}={\frac {\Delta H_{\mathsf {fus}}}{T_{\mathsf {m}}}}.}
Similarly, for vaporisation of a liquid to a gas at the boiling point
T
b
{\displaystyle T_{\mathsf {b}}}
, the entropy of vaporisation is:
Δ
S
v
a
p
=
Δ
H
v
a
p
T
b
{\displaystyle \Delta S_{\mathsf {vap}}={\frac {\Delta H_{\mathsf {vap}}}{T_{\mathsf {b}}}}}
== Approaches to understanding entropy ==
As a fundamental aspect of thermodynamics and physics, several different approaches to entropy beyond that of Clausius and Boltzmann are valid.
=== Standard textbook definitions ===
The following is a list of additional definitions of entropy from a collection of textbooks:
a measure of energy dispersal at a specific temperature.
a measure of disorder in the universe or of the availability of the energy in a system to do work.
a measure of a system's thermal energy per unit temperature that is unavailable for doing useful work.
In Boltzmann's analysis in terms of constituent particles, entropy is a measure of the number of possible microscopic states (or microstates) of a system in thermodynamic equilibrium.
=== Order and disorder ===
Entropy is often loosely associated with the amount of order or disorder, or of chaos, in a thermodynamic system. The traditional qualitative description of entropy is that it refers to changes in the state of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state or form to another. In this direction, several recent authors have derived exact entropy formulas to account for and measure disorder and order in atomic and molecular assemblies. One of the simpler entropy order/disorder formulas is that derived in 1984 by thermodynamic physicist Peter Landsberg, based on a combination of thermodynamics and information theory arguments. He argues that when constraints operate on a system, such that it is prevented from entering one or more of its possible or permitted states, as contrasted with its forbidden states, the measure of the total amount of "disorder" and "order" in the system are each given by:: 69
D
i
s
o
r
d
e
r
=
C
D
C
I
{\displaystyle {\mathsf {Disorder}}={\frac {C_{\mathsf {D}}}{C_{\mathsf {I}}}}}
O
r
d
e
r
=
1
−
C
O
C
I
{\displaystyle {\mathsf {Order}}=1-{\frac {C_{\mathsf {O}}}{C_{\mathsf {I}}}}}
Here,
C
D
{\textstyle C_{\mathsf {D}}}
is the "disorder" capacity of the system, which is the entropy of the parts contained in the permitted ensemble,
C
I
{\textstyle C_{\mathsf {I}}}
is the "information" capacity of the system, an expression similar to Shannon's channel capacity, and
C
O
{\textstyle C_{\mathsf {O}}}
is the "order" capacity of the system.
=== Energy dispersal ===
The concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature. Similar terms have been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantised energy levels.
Ambiguities in the terms disorder and chaos, which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of entropy for most students. As the second law of thermodynamics shows, in an isolated system internal portions at different temperatures tend to adjust to a single uniform temperature and thus produce equilibrium. A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal, which leads to loss of the differentials required for work even though the total energy remains constant in accordance with the first law of thermodynamics (compare discussion in next section). Physical chemist Peter Atkins, in his textbook Physical Chemistry, introduces entropy with the statement that "spontaneous changes are always accompanied by a dispersal of energy or matter and often both".
=== Relating entropy to energy usefulness ===
It is possible (in a thermal context) to regard lower entropy as a measure of the effectiveness or usefulness of a particular quantity of energy. Energy supplied at a higher temperature (i.e. with low entropy) tends to be more useful than the same amount of energy available at a lower temperature. Mixing a hot parcel of a fluid with a cold one produces a parcel of intermediate temperature, in which the overall increase in entropy represents a "loss" that can never be replaced.
As the entropy of the universe is steadily increasing, its total energy is becoming less useful. Eventually, this is theorised to lead to the heat death of the universe.
=== Entropy and adiabatic accessibility ===
A definition of entropy based entirely on the relation of adiabatic accessibility between equilibrium states was given by E. H. Lieb and J. Yngvason in 1999. This approach has several predecessors, including the pioneering work of Constantin Carathéodory from 1909 and the monograph by R. Giles. In the setting of Lieb and Yngvason, one starts by picking, for a unit amount of the substance under consideration, two reference states
X
0
{\textstyle X_{0}}
and
X
1
{\textstyle X_{1}}
such that the latter is adiabatically accessible from the former but not conversely. Defining the entropies of the reference states to be 0 and 1 respectively, the entropy of a state
X
{\textstyle X}
is defined as the largest number
λ
{\textstyle \lambda }
such that
X
{\textstyle X}
is adiabatically accessible from a composite state consisting of an amount
λ
{\textstyle \lambda }
in the state
X
1
{\textstyle X_{1}}
and a complementary amount,
(
1
−
λ
)
{\textstyle (1-\lambda )}
, in the state
X
0
{\textstyle X_{0}}
. A simple but important result within this setting is that entropy is uniquely determined, apart from a choice of unit and an additive constant for each chemical element, by the following properties: it is monotonic with respect to the relation of adiabatic accessibility, additive on composite systems, and extensive under scaling.
=== Entropy in quantum mechanics ===
In quantum statistical mechanics, the concept of entropy was developed by John von Neumann and is generally referred to as "von Neumann entropy":
S
=
−
k
B
t
r
(
ρ
^
×
ln
ρ
^
)
{\displaystyle S=-k_{\mathsf {B}}\ \mathrm {tr} {\left({\hat {\rho }}\times \ln {\hat {\rho }}\right)}}
where
ρ
^
{\textstyle {\hat {\rho }}}
is the density matrix,
t
r
{\textstyle \mathrm {tr} }
is the trace operator and
k
B
{\textstyle k_{\mathsf {B}}}
is the Boltzmann constant.
This upholds the correspondence principle, because in the classical limit, when the phases between the basis states are purely random, this expression is equivalent to the familiar classical definition of entropy for states with classical probabilities
p
i
{\textstyle p_{i}}
:
S
=
−
k
B
∑
i
p
i
ln
p
i
{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
i.e. in such a basis the density matrix is diagonal.
Von Neumann established a rigorous mathematical framework for quantum mechanics with his work Mathematische Grundlagen der Quantenmechanik. He provided in this work a theory of measurement, where the usual notion of wave function collapse is described as an irreversible process (the so-called von Neumann or projective measurement). Using this concept, in conjunction with the density matrix he extended the classical concept of entropy into the quantum domain.
=== Information theory ===
When viewed in terms of information theory, the entropy state function is the amount of information in the system that is needed to fully specify the microstate of the system. Entropy is the measure of the amount of missing information before reception. Often called Shannon entropy, it was originally devised by Claude Shannon in 1948 to study the size of information of a transmitted message. The definition of information entropy is expressed in terms of a discrete set of probabilities
p
i
{\textstyle p_{i}}
so that:
H
(
X
)
=
−
∑
i
=
1
n
p
(
x
i
)
log
p
(
x
i
)
{\displaystyle H(X)=-\sum _{i=1}^{n}{p(x_{i})\log {p(x_{i})}}}
where the base of the logarithm determines the units (for example, the binary logarithm corresponds to bits).
In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually transmitted, and the entropy of the message system was a measure of the average size of information of a message. For the case of equal probabilities (i.e. each message is equally probable), the Shannon entropy (in bits) is just the number of binary questions needed to determine the content of the message.
Most researchers consider information entropy and thermodynamic entropy directly linked to the same concept, while others argue that they are distinct. Both expressions are mathematically similar. If
W
{\textstyle W}
is the number of microstates that can yield a given macrostate, and each microstate has the same a priori probability, then that probability is
p
=
1
/
W
{\textstyle p=1/W}
. The Shannon entropy (in nats) is:
H
=
−
∑
i
=
1
W
p
i
ln
p
i
=
ln
W
{\displaystyle H=-\sum _{i=1}^{W}{p_{i}\ln {p_{i}}}=\ln {W}}
and if entropy is measured in units of
k
{\textstyle k}
per nat, then the entropy is given by:
H
=
k
ln
W
{\displaystyle H=k\ln {W}}
which is the Boltzmann entropy formula, where
k
{\textstyle k}
is the Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat. Some authors argue for dropping the word entropy for the
H
{\textstyle H}
function of information theory and using Shannon's other term, "uncertainty", instead.
=== Measurement ===
The entropy of a substance can be measured, although in an indirect way. The measurement, known as entropymetry, is done on a closed system with constant number of particles
N
{\textstyle N}
and constant volume
V
{\textstyle V}
, and it uses the definition of temperature in terms of entropy, while limiting energy exchange to heat
d
U
→
d
Q
{\textstyle \mathrm {d} U\rightarrow \mathrm {d} Q}
:
T
:=
(
∂
U
∂
S
)
V
,
N
⇒
⋯
⇒
d
S
=
d
Q
T
{\displaystyle T:={\left({\frac {\partial U}{\partial S}}\right)}_{V,N}\ \Rightarrow \ \cdots \ \Rightarrow \ \mathrm {d} S={\frac {\mathrm {d} Q}{T}}}
The resulting relation describes how entropy changes
d
S
{\textstyle \mathrm {d} S}
when a small amount of energy
d
Q
{\textstyle \mathrm {d} Q}
is introduced into the system at a certain temperature
T
{\textstyle T}
.
The process of measurement goes as follows. First, a sample of the substance is cooled as close to absolute zero as possible. At such temperatures, the entropy approaches zero – due to the definition of temperature. Then, small amounts of heat are introduced into the sample and the change in temperature is recorded, until the temperature reaches a desired value (usually 25 °C). The obtained data allows the user to integrate the equation above, yielding the absolute value of entropy of the substance at the final temperature. This value of entropy is called calorimetric entropy.
== Interdisciplinary applications ==
Although the concept of entropy was originally a thermodynamic concept, it has been adapted in other fields of study, including information theory, psychodynamics, thermoeconomics/ecological economics, and evolution.
=== Philosophy and theoretical physics ===
Entropy is the only quantity in the physical sciences that seems to imply a particular direction of progress, sometimes called an arrow of time. As time progresses, the second law of thermodynamics states that the entropy of an isolated system never decreases in large systems over significant periods of time. Hence, from this perspective, entropy measurement is thought of as a clock in these conditions. Since the 19th century, a number the philosophers have drawn upon the concept of entropy to develop novel metaphysical and ethical systems. Examples of this work can be found in the thought of Friedrich Nietzsche and Philipp Mainländer, Claude Lévi-Strauss, Isabelle Stengers, Shannon Mussett, and Drew M. Dalton.
=== Biology ===
Chiavazzo et al. proposed that where cave spiders choose to lay their eggs can be explained through entropy minimisation.
Entropy has been proven useful in the analysis of base pair sequences in DNA. Many entropy-based measures have been shown to distinguish between different structural regions of the genome, differentiate between coding and non-coding regions of DNA, and can also be applied for the recreation of evolutionary trees by determining the evolutionary distance between different species.
=== Cosmology ===
Assuming that a finite universe is an isolated system, the second law of thermodynamics states that its total entropy is continually increasing. It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy so that no more work can be extracted from any source.
If the universe can be considered to have generally increasing entropy, then – as Roger Penrose has pointed out – gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole's event horizon. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. However, the escape of energy from black holes might be possible due to quantum activity (see Hawking radiation).
The role of entropy in cosmology remains a controversial subject since the time of Ludwig Boltzmann. Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer. This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.
Current theories suggest the entropy gap to have been originally opened up by the early rapid exponential expansion of the universe.
=== Economics ===
Romanian American economist Nicholas Georgescu-Roegen, a progenitor in economics and a paradigm founder of ecological economics, made extensive use of the entropy concept in his magnum opus on The Entropy Law and the Economic Process. Due to Georgescu-Roegen's work, the laws of thermodynamics form an integral part of the ecological economics school.: 204f : 29–35 Although his work was blemished somewhat by mistakes, a full chapter on the economics of Georgescu-Roegen has approvingly been included in one elementary physics textbook on the historical development of thermodynamics.: 95–112
In economics, Georgescu-Roegen's work has generated the term 'entropy pessimism'.: 116 Since the 1990s, leading ecological economist and steady-state theorist Herman Daly – a student of Georgescu-Roegen – has been the economics profession's most influential proponent of the entropy pessimism position.: 545f
== See also ==
== Notes ==
== References ==
David, Kover (14 August 2018). "Entropia – fyzikálna veličina vesmíru a nášho života". stejfree.sk. Archived from the original on 27 May 2022. Retrieved 13 April 2022.
== Further reading ==
== External links ==
"Entropy" at Scholarpedia
Entropy and the Clausius inequality MIT OCW lecture, part of 5.60 Thermodynamics & Kinetics, Spring 2008
Entropy and the Second Law of Thermodynamics – an A-level physics lecture with 'derivation' of entropy based on Carnot cycle
Khan Academy: entropy lectures, part of Chemistry playlist
Entropy Intuition
More on Entropy
Proof: S (or Entropy) is a valid state variable
Reconciling Thermodynamic and State Definitions of Entropy
Thermodynamic Entropy Definition Clarification
Moriarty, Philip; Merrifield, Michael (2009). "S Entropy". Sixty Symbols. Brady Haran for the University of Nottingham.
The Discovery of Entropy by Adam Shulman. Hour-long video, January 2013.
The Second Law of Thermodynamics and Entropy – Yale OYC lecture, part of Fundamentals of Physics I (PHYS 200) | Wikipedia/Specific_entropy |
In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined:
The Kirchhoff stress (
τ
{\displaystyle {\boldsymbol {\tau }}}
).
The nominal stress (
N
{\displaystyle {\boldsymbol {N}}}
).
The Piola–Kirchhoff stress tensors
The first Piola–Kirchhoff stress (
P
{\displaystyle {\boldsymbol {P}}}
). This stress tensor is the transpose of the nominal stress (
P
=
N
T
{\displaystyle {\boldsymbol {P}}={\boldsymbol {N}}^{T}}
).
The second Piola–Kirchhoff stress or PK2 stress (
S
{\displaystyle {\boldsymbol {S}}}
).
The Biot stress (
T
{\displaystyle {\boldsymbol {T}}}
)
== Definitions ==
Consider the situation shown in the following figure. The following definitions use the notations shown in the figure.
In the reference configuration
Ω
0
{\displaystyle \Omega _{0}}
, the outward normal to a surface element
d
Γ
0
{\displaystyle d\Gamma _{0}}
is
N
≡
n
0
{\displaystyle \mathbf {N} \equiv \mathbf {n} _{0}}
and the traction acting on that surface (assuming it deforms like a generic vector belonging to the deformation) is
t
0
{\displaystyle \mathbf {t} _{0}}
leading to a force vector
d
f
0
{\displaystyle d\mathbf {f} _{0}}
. In the deformed configuration
Ω
{\displaystyle \Omega }
, the surface element changes to
d
Γ
{\displaystyle d\Gamma }
with outward normal
n
{\displaystyle \mathbf {n} }
and traction vector
t
{\displaystyle \mathbf {t} }
leading to a force
d
f
{\displaystyle d\mathbf {f} }
. Note that this surface can either be a hypothetical cut inside the body or an actual surface. The quantity
F
{\displaystyle {\boldsymbol {F}}}
is the deformation gradient tensor,
J
{\displaystyle J}
is its determinant.
=== Cauchy stress ===
The Cauchy stress (or true stress) is a measure of the force acting on an element of area in the deformed configuration. This tensor is symmetric and is defined via
d
f
=
t
d
Γ
=
σ
T
⋅
n
d
Γ
{\displaystyle d\mathbf {f} =\mathbf {t} ~d\Gamma ={\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} ~d\Gamma }
or
t
=
σ
T
⋅
n
{\displaystyle \mathbf {t} ={\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} }
where
t
{\displaystyle \mathbf {t} }
is the traction and
n
{\displaystyle \mathbf {n} }
is the normal to the surface on which the traction acts.
=== Kirchhoff stress ===
The quantity,
τ
=
J
σ
{\displaystyle {\boldsymbol {\tau }}=J~{\boldsymbol {\sigma }}}
is called the Kirchhoff stress tensor, with
J
{\displaystyle J}
the determinant of
F
{\displaystyle {\boldsymbol {F}}}
. It is used widely in numerical algorithms in metal plasticity (where there
is no change in volume during plastic deformation). It can be called weighted Cauchy stress tensor as well.
=== Piola–Kirchhoff stress ===
==== Nominal stress/First Piola–Kirchhoff stress ====
The nominal stress
N
=
P
T
{\displaystyle {\boldsymbol {N}}={\boldsymbol {P}}^{T}}
is the transpose of the first Piola–Kirchhoff stress (PK1 stress, also called engineering stress)
P
{\displaystyle {\boldsymbol {P}}}
and is defined via
d
f
=
t
d
Γ
=
N
T
⋅
n
0
d
Γ
0
=
P
⋅
n
0
d
Γ
0
{\displaystyle d\mathbf {f} =\mathbf {t} ~d\Gamma ={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {P}}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
or
t
0
=
t
d
Γ
d
Γ
0
=
N
T
⋅
n
0
=
P
⋅
n
0
{\displaystyle \mathbf {t} _{0}=\mathbf {t} {\dfrac {d{\Gamma }}{d\Gamma _{0}}}={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {P}}\cdot \mathbf {n} _{0}}
This stress is unsymmetric and is a two-point tensor like the deformation gradient.
The asymmetry derives from the fact that, as a tensor, it has one index attached to the reference configuration and one to the deformed configuration.
==== Second Piola–Kirchhoff stress ====
If we pull back
d
f
{\displaystyle d\mathbf {f} }
to the reference configuration we obtain the traction acting on that surface before the deformation
d
f
0
{\displaystyle d\mathbf {f} _{0}}
assuming it behaves like a generic vector belonging to the deformation. In particular we have
d
f
0
=
F
−
1
⋅
d
f
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {F}}^{-1}\cdot d\mathbf {f} }
or,
d
f
0
=
F
−
1
⋅
N
T
⋅
n
0
d
Γ
0
=
F
−
1
⋅
t
0
d
Γ
0
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}~d\Gamma _{0}}
The PK2 stress (
S
{\displaystyle {\boldsymbol {S}}}
) is symmetric and is defined via the relation
d
f
0
=
S
T
⋅
n
0
d
Γ
0
=
F
−
1
⋅
t
0
d
Γ
0
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}~d\Gamma _{0}}
Therefore,
S
T
⋅
n
0
=
F
−
1
⋅
t
0
{\displaystyle {\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}}
=== Biot stress ===
The Biot stress is useful because it is energy conjugate to the right stretch tensor
U
{\displaystyle {\boldsymbol {U}}}
. The Biot stress is defined as the symmetric part of the tensor
P
T
⋅
R
{\displaystyle {\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}}}
where
R
{\displaystyle {\boldsymbol {R}}}
is the rotation tensor obtained from a polar decomposition of the deformation gradient. Therefore, the Biot stress tensor is defined as
T
=
1
2
(
R
T
⋅
P
+
P
T
⋅
R
)
.
{\displaystyle {\boldsymbol {T}}={\tfrac {1}{2}}({\boldsymbol {R}}^{T}\cdot {\boldsymbol {P}}+{\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}})~.}
The Biot stress is also called the Jaumann stress.
The quantity
T
{\displaystyle {\boldsymbol {T}}}
does not have any physical interpretation. However, the unsymmetrized Biot stress has the interpretation
R
T
d
f
=
(
P
T
⋅
R
)
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {R}}^{T}~d\mathbf {f} =({\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}})^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
== Relations ==
=== Relations between Cauchy stress and nominal stress ===
From Nanson's formula relating areas in the reference and deformed configurations:
n
d
Γ
=
J
F
−
T
⋅
n
0
d
Γ
0
{\displaystyle \mathbf {n} ~d\Gamma =J~{\boldsymbol {F}}^{-T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
Now,
σ
T
⋅
n
d
Γ
=
d
f
=
N
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} ~d\Gamma =d\mathbf {f} ={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
Hence,
σ
T
⋅
(
J
F
−
T
⋅
n
0
d
Γ
0
)
=
N
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {\sigma }}^{T}\cdot (J~{\boldsymbol {F}}^{-T}\cdot \mathbf {n} _{0}~d\Gamma _{0})={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
or,
N
T
=
J
(
F
−
1
⋅
σ
)
T
=
J
σ
T
⋅
F
−
T
{\displaystyle {\boldsymbol {N}}^{T}=J~({\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }})^{T}=J~{\boldsymbol {\sigma }}^{T}\cdot {\boldsymbol {F}}^{-T}}
or,
N
=
J
F
−
1
⋅
σ
and
N
T
=
P
=
J
σ
T
⋅
F
−
T
{\displaystyle {\boldsymbol {N}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}\qquad {\text{and}}\qquad {\boldsymbol {N}}^{T}={\boldsymbol {P}}=J~{\boldsymbol {\sigma }}^{T}\cdot {\boldsymbol {F}}^{-T}}
In index notation,
N
I
j
=
J
F
I
k
−
1
σ
k
j
and
P
i
J
=
J
σ
k
i
F
J
k
−
1
{\displaystyle N_{Ij}=J~F_{Ik}^{-1}~\sigma _{kj}\qquad {\text{and}}\qquad P_{iJ}=J~\sigma _{ki}~F_{Jk}^{-1}}
Therefore,
J
σ
=
F
⋅
N
=
F
⋅
P
T
.
{\displaystyle J~{\boldsymbol {\sigma }}={\boldsymbol {F}}\cdot {\boldsymbol {N}}={\boldsymbol {F}}\cdot {\boldsymbol {P}}^{T}~.}
Note that
N
{\displaystyle {\boldsymbol {N}}}
and
P
{\displaystyle {\boldsymbol {P}}}
are (generally) not symmetric because
F
{\displaystyle {\boldsymbol {F}}}
is (generally) not symmetric.
=== Relations between nominal stress and second P–K stress ===
Recall that
N
T
⋅
n
0
d
Γ
0
=
d
f
{\displaystyle {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}=d\mathbf {f} }
and
d
f
=
F
⋅
d
f
0
=
F
⋅
(
S
T
⋅
n
0
d
Γ
0
)
{\displaystyle d\mathbf {f} ={\boldsymbol {F}}\cdot d\mathbf {f} _{0}={\boldsymbol {F}}\cdot ({\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0})}
Therefore,
N
T
⋅
n
0
=
F
⋅
S
T
⋅
n
0
{\displaystyle {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {F}}\cdot {\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}}
or (using the symmetry of
S
{\displaystyle {\boldsymbol {S}}}
),
N
=
S
⋅
F
T
and
P
=
F
⋅
S
{\displaystyle {\boldsymbol {N}}={\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}\qquad {\text{and}}\qquad {\boldsymbol {P}}={\boldsymbol {F}}\cdot {\boldsymbol {S}}}
In index notation,
N
I
j
=
S
I
K
F
j
K
T
and
P
i
J
=
F
i
K
S
K
J
{\displaystyle N_{Ij}=S_{IK}~F_{jK}^{T}\qquad {\text{and}}\qquad P_{iJ}=F_{iK}~S_{KJ}}
Alternatively, we can write
S
=
N
⋅
F
−
T
and
S
=
F
−
1
⋅
P
{\displaystyle {\boldsymbol {S}}={\boldsymbol {N}}\cdot {\boldsymbol {F}}^{-T}\qquad {\text{and}}\qquad {\boldsymbol {S}}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {P}}}
=== Relations between Cauchy stress and second P–K stress ===
Recall that
N
=
J
F
−
1
⋅
σ
{\displaystyle {\boldsymbol {N}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}}
In terms of the 2nd PK stress, we have
S
⋅
F
T
=
J
F
−
1
⋅
σ
{\displaystyle {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}}
Therefore,
S
=
J
F
−
1
⋅
σ
⋅
F
−
T
=
F
−
1
⋅
τ
⋅
F
−
T
{\displaystyle {\boldsymbol {S}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}\cdot {\boldsymbol {F}}^{-T}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\tau }}\cdot {\boldsymbol {F}}^{-T}}
In index notation,
S
I
J
=
F
I
k
−
1
τ
k
l
F
J
l
−
1
{\displaystyle S_{IJ}=F_{Ik}^{-1}~\tau _{kl}~F_{Jl}^{-1}}
Since the Cauchy stress (and hence the Kirchhoff stress) is symmetric, the 2nd PK stress is also symmetric.
Alternatively, we can write
σ
=
J
−
1
F
⋅
S
⋅
F
T
{\displaystyle {\boldsymbol {\sigma }}=J^{-1}~{\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}}
or,
τ
=
F
⋅
S
⋅
F
T
.
{\displaystyle {\boldsymbol {\tau }}={\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}~.}
Clearly, from definition of the push-forward and pull-back operations, we have
S
=
φ
∗
[
τ
]
=
F
−
1
⋅
τ
⋅
F
−
T
{\displaystyle {\boldsymbol {S}}=\varphi ^{*}[{\boldsymbol {\tau }}]={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\tau }}\cdot {\boldsymbol {F}}^{-T}}
and
τ
=
φ
∗
[
S
]
=
F
⋅
S
⋅
F
T
.
{\displaystyle {\boldsymbol {\tau }}=\varphi _{*}[{\boldsymbol {S}}]={\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}~.}
Therefore,
S
{\displaystyle {\boldsymbol {S}}}
is the pull back of
τ
{\displaystyle {\boldsymbol {\tau }}}
by
F
{\displaystyle {\boldsymbol {F}}}
and
τ
{\displaystyle {\boldsymbol {\tau }}}
is the push forward of
S
{\displaystyle {\boldsymbol {S}}}
.
=== Summary of conversion formula ===
Key:
J
=
det
(
F
)
,
C
=
F
T
F
=
U
2
,
F
=
R
U
,
R
T
=
R
−
1
,
{\displaystyle J=\det \left({\boldsymbol {F}}\right),\quad {\boldsymbol {C}}={\boldsymbol {F}}^{T}{\boldsymbol {F}}={\boldsymbol {U}}^{2},\quad {\boldsymbol {F}}={\boldsymbol {R}}{\boldsymbol {U}},\quad {\boldsymbol {R}}^{T}={\boldsymbol {R}}^{-1},}
P
=
J
σ
F
−
T
,
τ
=
J
σ
,
S
=
J
F
−
1
σ
F
−
T
,
T
=
R
T
P
,
M
=
C
S
{\displaystyle {\boldsymbol {P}}=J{\boldsymbol {\sigma }}{\boldsymbol {F}}^{-T},\quad {\boldsymbol {\tau }}=J{\boldsymbol {\sigma }},\quad {\boldsymbol {S}}=J{\boldsymbol {F}}^{-1}{\boldsymbol {\sigma }}{\boldsymbol {F}}^{-T},\quad {\boldsymbol {T}}={\boldsymbol {R}}^{T}{\boldsymbol {P}},\quad {\boldsymbol {M}}={\boldsymbol {C}}{\boldsymbol {S}}}
== See also ==
Stress (physics)
Finite strain theory
Continuum mechanics
Hyperelastic material
Cauchy elastic material
Critical plane analysis
== References == | Wikipedia/Kirchhoff_stress_tensor |
As described by the third of Newton's laws of motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first. The third law is also more generally stated as: "To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." The attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can be considered the action, while the other is its associated reaction.
== Examples ==
=== Interaction with ground ===
When something is exerting force on the ground, the ground will push back with equal force in the opposite direction. In certain fields of applied physics, such as biomechanics, this force by the ground is called 'ground reaction force'; the force by the object on the ground is viewed as the 'action'.
When someone wants to jump, he or she exerts additional downward force on the ground ('action'). Simultaneously, the ground exerts upward force on the person ('reaction'). If this upward force is greater than the person's weight, this will result in upward acceleration. When these forces are perpendicular to the ground, they are also called a normal force.
Likewise, the spinning wheels of a vehicle attempt to slide backward across the ground. If the ground is not too slippery, this results in a pair of friction forces: the 'action' by the wheel on the ground in backward direction, and the 'reaction' by the ground on the wheel in forward direction. This forward force propels the vehicle.
=== Gravitational forces ===
The Earth, among other planets, orbits the Sun because the Sun exerts a gravitational pull that acts as a centripetal force, holding the Earth to it, which would otherwise go shooting off into space. If the Sun's pull is considered an action, then Earth simultaneously exerts a reaction as a gravitational pull on the Sun. Earth's pull has the same amplitude as the Sun but in the opposite direction. Since the Sun's mass is so much larger than Earth's, the Sun does not generally appear to react to the pull of Earth, but in fact it does, as demonstrated in the animation (not to precise scale). A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass, referred to in astronomy as the barycenter, of the combined system.
=== Supported mass ===
Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight. The corresponding 'reaction' is the gravitational force that mass exerts on the planet.
If the object is supported so that it remains at rest, for instance by a cable from which it is hanging, or by a surface underneath, or by a liquid on which it is floating, there is also a support force in upward direction (tension force, normal force, buoyant force, respectively). This support force is an 'equal and opposite' force; we know this not because of Newton's third law, but because the object remains at rest, so that the forces must be balanced.
To this support force there is also a 'reaction': the object pulls down on the supporting cable, or pushes down on the supporting surface or liquid. In this case, there are therefore four forces of equal magnitude:
F1. gravitational force by earth on object (downward)
F2. gravitational force by object on earth (upward)
F3. force by support on object (upward)
F4. force by object on support (downward)
Forces F1 and F2 are equal, due to Newton's third law; the same is true for forces F3 and F4.
Forces F1 and F3 are equal if and only if the object is in equilibrium, and no other forces are applied. (This has nothing to do with Newton's third law.)
=== Mass on a spring ===
If a mass is hanging from a spring, the same considerations apply as before. However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's second law that a net force is responsible for the observed change in velocity. The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F1 and F3 are no longer equal.
However, it is still true that F1 = F2 and F3 = F4, as this is required by Newton's third law.
== Causal misinterpretation ==
The terms 'action' and 'reaction' have the misleading suggestion of causality, as if the 'action' is the cause and 'reaction' is the effect. It is therefore easy to think of the second force as being there because of the first, and even happening some time after the first. This is incorrect; the forces are perfectly simultaneous, and are there for the same reason.
When the forces are caused by a person's volition (e.g. a soccer player kicks a ball), this volitional cause often leads to an asymmetric interpretation, where the force by the player on the ball is considered the 'action' and the force by the ball on the player, the 'reaction'. But physically, the situation is symmetric. The forces on ball and player are both explained by their nearness, which results in a pair of contact forces (ultimately due to electric repulsion). That this nearness is caused by a decision of the player has no bearing on the physical analysis. As far as the physics is concerned, the labels 'action' and 'reaction' can be flipped.
=== 'Equal and opposite' ===
One problem frequently observed by physics educators is that students tend to apply Newton's third law to pairs of 'equal and opposite' forces acting on the same object.
This is incorrect; the third law refers to forces on two different objects. In contrast, a book lying on a table is subject to a downward gravitational force (exerted by the earth) and to an upward normal force by the table, both forces acting on the same book. Since the book is not accelerating, these forces must be exactly balanced, according to Newton's second law. They are therefore 'equal and opposite', yet they are acting on the same object, hence they are not action-reaction forces in the sense of Newton's third law. The actual action-reaction forces in the sense of Newton's third law are the weight of the book (the attraction of the Earth on the book) and the book's upward gravitational force on the earth. The book also pushes down on the table and the table pushes upwards on the book.
Moreover, the forces acting on the book are not always equally strong; they will be different if the book is pushed down by a third force, or if the table is slanted, or if the table-and-book system is in an accelerating elevator. The case of any number of forces acting on the same object is covered by considering the sum of all forces.
A possible cause of this problem is that the third law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, without the details, namely that these forces act on two different objects. Moreover, there is a causal connection between the weight of something and the normal force: if an object had no weight, it would not experience support force from the table, and the weight dictates how strong the support force will be. This causal relationship is not due to the third law but to other physical relations in the system.
=== Centripetal and centrifugal force ===
Another common mistake is to state that "the centrifugal force that an object experiences is the reaction to the centripetal force on that object."
If an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force, the resultant force would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames.
== See also ==
Ground reaction force
Reactive centrifugal force
Isaac Newton
Ibn Bajjah
Reaction engine/jet engine
Shear force
== References ==
== Bibliography ==
Feynman, R. P., Leighton and Sands (1970) The Feynman Lectures on Physics, Volume 1, Addison Wesley Longman, ISBN 0-201-02115-3.
Resnick, R. and D. Halliday (1966) Physics, Part 1, John Wiley & Sons, New York, 646 pp + Appendices.
Warren, J. W. (1965) The Teaching of Physics, Butterworths, London,130 pp. | Wikipedia/Reaction_force |
In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined:
The Kirchhoff stress (
τ
{\displaystyle {\boldsymbol {\tau }}}
).
The nominal stress (
N
{\displaystyle {\boldsymbol {N}}}
).
The Piola–Kirchhoff stress tensors
The first Piola–Kirchhoff stress (
P
{\displaystyle {\boldsymbol {P}}}
). This stress tensor is the transpose of the nominal stress (
P
=
N
T
{\displaystyle {\boldsymbol {P}}={\boldsymbol {N}}^{T}}
).
The second Piola–Kirchhoff stress or PK2 stress (
S
{\displaystyle {\boldsymbol {S}}}
).
The Biot stress (
T
{\displaystyle {\boldsymbol {T}}}
)
== Definitions ==
Consider the situation shown in the following figure. The following definitions use the notations shown in the figure.
In the reference configuration
Ω
0
{\displaystyle \Omega _{0}}
, the outward normal to a surface element
d
Γ
0
{\displaystyle d\Gamma _{0}}
is
N
≡
n
0
{\displaystyle \mathbf {N} \equiv \mathbf {n} _{0}}
and the traction acting on that surface (assuming it deforms like a generic vector belonging to the deformation) is
t
0
{\displaystyle \mathbf {t} _{0}}
leading to a force vector
d
f
0
{\displaystyle d\mathbf {f} _{0}}
. In the deformed configuration
Ω
{\displaystyle \Omega }
, the surface element changes to
d
Γ
{\displaystyle d\Gamma }
with outward normal
n
{\displaystyle \mathbf {n} }
and traction vector
t
{\displaystyle \mathbf {t} }
leading to a force
d
f
{\displaystyle d\mathbf {f} }
. Note that this surface can either be a hypothetical cut inside the body or an actual surface. The quantity
F
{\displaystyle {\boldsymbol {F}}}
is the deformation gradient tensor,
J
{\displaystyle J}
is its determinant.
=== Cauchy stress ===
The Cauchy stress (or true stress) is a measure of the force acting on an element of area in the deformed configuration. This tensor is symmetric and is defined via
d
f
=
t
d
Γ
=
σ
T
⋅
n
d
Γ
{\displaystyle d\mathbf {f} =\mathbf {t} ~d\Gamma ={\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} ~d\Gamma }
or
t
=
σ
T
⋅
n
{\displaystyle \mathbf {t} ={\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} }
where
t
{\displaystyle \mathbf {t} }
is the traction and
n
{\displaystyle \mathbf {n} }
is the normal to the surface on which the traction acts.
=== Kirchhoff stress ===
The quantity,
τ
=
J
σ
{\displaystyle {\boldsymbol {\tau }}=J~{\boldsymbol {\sigma }}}
is called the Kirchhoff stress tensor, with
J
{\displaystyle J}
the determinant of
F
{\displaystyle {\boldsymbol {F}}}
. It is used widely in numerical algorithms in metal plasticity (where there
is no change in volume during plastic deformation). It can be called weighted Cauchy stress tensor as well.
=== Piola–Kirchhoff stress ===
==== Nominal stress/First Piola–Kirchhoff stress ====
The nominal stress
N
=
P
T
{\displaystyle {\boldsymbol {N}}={\boldsymbol {P}}^{T}}
is the transpose of the first Piola–Kirchhoff stress (PK1 stress, also called engineering stress)
P
{\displaystyle {\boldsymbol {P}}}
and is defined via
d
f
=
t
d
Γ
=
N
T
⋅
n
0
d
Γ
0
=
P
⋅
n
0
d
Γ
0
{\displaystyle d\mathbf {f} =\mathbf {t} ~d\Gamma ={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {P}}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
or
t
0
=
t
d
Γ
d
Γ
0
=
N
T
⋅
n
0
=
P
⋅
n
0
{\displaystyle \mathbf {t} _{0}=\mathbf {t} {\dfrac {d{\Gamma }}{d\Gamma _{0}}}={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {P}}\cdot \mathbf {n} _{0}}
This stress is unsymmetric and is a two-point tensor like the deformation gradient.
The asymmetry derives from the fact that, as a tensor, it has one index attached to the reference configuration and one to the deformed configuration.
==== Second Piola–Kirchhoff stress ====
If we pull back
d
f
{\displaystyle d\mathbf {f} }
to the reference configuration we obtain the traction acting on that surface before the deformation
d
f
0
{\displaystyle d\mathbf {f} _{0}}
assuming it behaves like a generic vector belonging to the deformation. In particular we have
d
f
0
=
F
−
1
⋅
d
f
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {F}}^{-1}\cdot d\mathbf {f} }
or,
d
f
0
=
F
−
1
⋅
N
T
⋅
n
0
d
Γ
0
=
F
−
1
⋅
t
0
d
Γ
0
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}~d\Gamma _{0}}
The PK2 stress (
S
{\displaystyle {\boldsymbol {S}}}
) is symmetric and is defined via the relation
d
f
0
=
S
T
⋅
n
0
d
Γ
0
=
F
−
1
⋅
t
0
d
Γ
0
{\displaystyle d\mathbf {f} _{0}={\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}~d\Gamma _{0}}
Therefore,
S
T
⋅
n
0
=
F
−
1
⋅
t
0
{\displaystyle {\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {F}}^{-1}\cdot \mathbf {t} _{0}}
=== Biot stress ===
The Biot stress is useful because it is energy conjugate to the right stretch tensor
U
{\displaystyle {\boldsymbol {U}}}
. The Biot stress is defined as the symmetric part of the tensor
P
T
⋅
R
{\displaystyle {\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}}}
where
R
{\displaystyle {\boldsymbol {R}}}
is the rotation tensor obtained from a polar decomposition of the deformation gradient. Therefore, the Biot stress tensor is defined as
T
=
1
2
(
R
T
⋅
P
+
P
T
⋅
R
)
.
{\displaystyle {\boldsymbol {T}}={\tfrac {1}{2}}({\boldsymbol {R}}^{T}\cdot {\boldsymbol {P}}+{\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}})~.}
The Biot stress is also called the Jaumann stress.
The quantity
T
{\displaystyle {\boldsymbol {T}}}
does not have any physical interpretation. However, the unsymmetrized Biot stress has the interpretation
R
T
d
f
=
(
P
T
⋅
R
)
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {R}}^{T}~d\mathbf {f} =({\boldsymbol {P}}^{T}\cdot {\boldsymbol {R}})^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
== Relations ==
=== Relations between Cauchy stress and nominal stress ===
From Nanson's formula relating areas in the reference and deformed configurations:
n
d
Γ
=
J
F
−
T
⋅
n
0
d
Γ
0
{\displaystyle \mathbf {n} ~d\Gamma =J~{\boldsymbol {F}}^{-T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
Now,
σ
T
⋅
n
d
Γ
=
d
f
=
N
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {\sigma }}^{T}\cdot \mathbf {n} ~d\Gamma =d\mathbf {f} ={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
Hence,
σ
T
⋅
(
J
F
−
T
⋅
n
0
d
Γ
0
)
=
N
T
⋅
n
0
d
Γ
0
{\displaystyle {\boldsymbol {\sigma }}^{T}\cdot (J~{\boldsymbol {F}}^{-T}\cdot \mathbf {n} _{0}~d\Gamma _{0})={\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}}
or,
N
T
=
J
(
F
−
1
⋅
σ
)
T
=
J
σ
T
⋅
F
−
T
{\displaystyle {\boldsymbol {N}}^{T}=J~({\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }})^{T}=J~{\boldsymbol {\sigma }}^{T}\cdot {\boldsymbol {F}}^{-T}}
or,
N
=
J
F
−
1
⋅
σ
and
N
T
=
P
=
J
σ
T
⋅
F
−
T
{\displaystyle {\boldsymbol {N}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}\qquad {\text{and}}\qquad {\boldsymbol {N}}^{T}={\boldsymbol {P}}=J~{\boldsymbol {\sigma }}^{T}\cdot {\boldsymbol {F}}^{-T}}
In index notation,
N
I
j
=
J
F
I
k
−
1
σ
k
j
and
P
i
J
=
J
σ
k
i
F
J
k
−
1
{\displaystyle N_{Ij}=J~F_{Ik}^{-1}~\sigma _{kj}\qquad {\text{and}}\qquad P_{iJ}=J~\sigma _{ki}~F_{Jk}^{-1}}
Therefore,
J
σ
=
F
⋅
N
=
F
⋅
P
T
.
{\displaystyle J~{\boldsymbol {\sigma }}={\boldsymbol {F}}\cdot {\boldsymbol {N}}={\boldsymbol {F}}\cdot {\boldsymbol {P}}^{T}~.}
Note that
N
{\displaystyle {\boldsymbol {N}}}
and
P
{\displaystyle {\boldsymbol {P}}}
are (generally) not symmetric because
F
{\displaystyle {\boldsymbol {F}}}
is (generally) not symmetric.
=== Relations between nominal stress and second P–K stress ===
Recall that
N
T
⋅
n
0
d
Γ
0
=
d
f
{\displaystyle {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0}=d\mathbf {f} }
and
d
f
=
F
⋅
d
f
0
=
F
⋅
(
S
T
⋅
n
0
d
Γ
0
)
{\displaystyle d\mathbf {f} ={\boldsymbol {F}}\cdot d\mathbf {f} _{0}={\boldsymbol {F}}\cdot ({\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}~d\Gamma _{0})}
Therefore,
N
T
⋅
n
0
=
F
⋅
S
T
⋅
n
0
{\displaystyle {\boldsymbol {N}}^{T}\cdot \mathbf {n} _{0}={\boldsymbol {F}}\cdot {\boldsymbol {S}}^{T}\cdot \mathbf {n} _{0}}
or (using the symmetry of
S
{\displaystyle {\boldsymbol {S}}}
),
N
=
S
⋅
F
T
and
P
=
F
⋅
S
{\displaystyle {\boldsymbol {N}}={\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}\qquad {\text{and}}\qquad {\boldsymbol {P}}={\boldsymbol {F}}\cdot {\boldsymbol {S}}}
In index notation,
N
I
j
=
S
I
K
F
j
K
T
and
P
i
J
=
F
i
K
S
K
J
{\displaystyle N_{Ij}=S_{IK}~F_{jK}^{T}\qquad {\text{and}}\qquad P_{iJ}=F_{iK}~S_{KJ}}
Alternatively, we can write
S
=
N
⋅
F
−
T
and
S
=
F
−
1
⋅
P
{\displaystyle {\boldsymbol {S}}={\boldsymbol {N}}\cdot {\boldsymbol {F}}^{-T}\qquad {\text{and}}\qquad {\boldsymbol {S}}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {P}}}
=== Relations between Cauchy stress and second P–K stress ===
Recall that
N
=
J
F
−
1
⋅
σ
{\displaystyle {\boldsymbol {N}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}}
In terms of the 2nd PK stress, we have
S
⋅
F
T
=
J
F
−
1
⋅
σ
{\displaystyle {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}}
Therefore,
S
=
J
F
−
1
⋅
σ
⋅
F
−
T
=
F
−
1
⋅
τ
⋅
F
−
T
{\displaystyle {\boldsymbol {S}}=J~{\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\sigma }}\cdot {\boldsymbol {F}}^{-T}={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\tau }}\cdot {\boldsymbol {F}}^{-T}}
In index notation,
S
I
J
=
F
I
k
−
1
τ
k
l
F
J
l
−
1
{\displaystyle S_{IJ}=F_{Ik}^{-1}~\tau _{kl}~F_{Jl}^{-1}}
Since the Cauchy stress (and hence the Kirchhoff stress) is symmetric, the 2nd PK stress is also symmetric.
Alternatively, we can write
σ
=
J
−
1
F
⋅
S
⋅
F
T
{\displaystyle {\boldsymbol {\sigma }}=J^{-1}~{\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}}
or,
τ
=
F
⋅
S
⋅
F
T
.
{\displaystyle {\boldsymbol {\tau }}={\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}~.}
Clearly, from definition of the push-forward and pull-back operations, we have
S
=
φ
∗
[
τ
]
=
F
−
1
⋅
τ
⋅
F
−
T
{\displaystyle {\boldsymbol {S}}=\varphi ^{*}[{\boldsymbol {\tau }}]={\boldsymbol {F}}^{-1}\cdot {\boldsymbol {\tau }}\cdot {\boldsymbol {F}}^{-T}}
and
τ
=
φ
∗
[
S
]
=
F
⋅
S
⋅
F
T
.
{\displaystyle {\boldsymbol {\tau }}=\varphi _{*}[{\boldsymbol {S}}]={\boldsymbol {F}}\cdot {\boldsymbol {S}}\cdot {\boldsymbol {F}}^{T}~.}
Therefore,
S
{\displaystyle {\boldsymbol {S}}}
is the pull back of
τ
{\displaystyle {\boldsymbol {\tau }}}
by
F
{\displaystyle {\boldsymbol {F}}}
and
τ
{\displaystyle {\boldsymbol {\tau }}}
is the push forward of
S
{\displaystyle {\boldsymbol {S}}}
.
=== Summary of conversion formula ===
Key:
J
=
det
(
F
)
,
C
=
F
T
F
=
U
2
,
F
=
R
U
,
R
T
=
R
−
1
,
{\displaystyle J=\det \left({\boldsymbol {F}}\right),\quad {\boldsymbol {C}}={\boldsymbol {F}}^{T}{\boldsymbol {F}}={\boldsymbol {U}}^{2},\quad {\boldsymbol {F}}={\boldsymbol {R}}{\boldsymbol {U}},\quad {\boldsymbol {R}}^{T}={\boldsymbol {R}}^{-1},}
P
=
J
σ
F
−
T
,
τ
=
J
σ
,
S
=
J
F
−
1
σ
F
−
T
,
T
=
R
T
P
,
M
=
C
S
{\displaystyle {\boldsymbol {P}}=J{\boldsymbol {\sigma }}{\boldsymbol {F}}^{-T},\quad {\boldsymbol {\tau }}=J{\boldsymbol {\sigma }},\quad {\boldsymbol {S}}=J{\boldsymbol {F}}^{-1}{\boldsymbol {\sigma }}{\boldsymbol {F}}^{-T},\quad {\boldsymbol {T}}={\boldsymbol {R}}^{T}{\boldsymbol {P}},\quad {\boldsymbol {M}}={\boldsymbol {C}}{\boldsymbol {S}}}
== See also ==
Stress (physics)
Finite strain theory
Continuum mechanics
Hyperelastic material
Cauchy elastic material
Critical plane analysis
== References == | Wikipedia/Biot_stress_tensor |
The newton (symbol: N) is the unit of force in the International System of Units (SI). Expressed in terms of SI base units, it is 1 kg⋅m/s2, the force that accelerates a mass of one kilogram at one metre per second squared.
The unit is named after Isaac Newton in recognition of his work on classical mechanics, specifically his second law of motion.
== Definition ==
A newton is defined as 1 kg⋅m/s2 (it is a named derived unit defined in terms of the SI base units).: 137 One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.
The units "metre per second squared" can be understood as measuring a rate of change in velocity per unit of time, i.e. an increase in velocity by one metre per second every second.
In 1946, the General Conference on Weights and Measures (CGPM) Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate one kilogram of mass at the rate of one metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name newton for this force. The MKS system then became the blueprint for today's SI system of units. The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units.
The newton is named after Isaac Newton. As with every SI unit named after a person, its symbol starts with an upper case letter (N), but when written in full, it follows the rules for capitalisation of a common noun; i.e., newton becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.
The connection to Newton comes from Newton's second law of motion, which states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus:
F
=
m
a
,
{\displaystyle F=ma,}
where
m
{\displaystyle m}
represents the mass of the object undergoing an acceleration
a
{\displaystyle a}
. When using the SI unit of mass, the kilogram (kg), and SI units for distance metre (m), and time, second (s) we arrive at the SI definition of the newton: 1 kg⋅m/s2.
== Examples ==
At average gravity on Earth (conventionally,
g
n
{\displaystyle g_{\text{n}}}
= 9.80665 m/s2), a kilogram mass exerts a force of about 9.81 N.
An average-sized apple with mass 200 g exerts about two newtons of force at Earth's surface, which we measure as the apple's weight on Earth.
0.200
kg
×
9.80665
m/s
2
=
1.961
N
.
{\displaystyle 0.200{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=1.961{\text{ N}}.}
An average adult exerts a force of about 608 N on Earth.
62
kg
×
9.80665
m/s
2
=
608
N
{\displaystyle 62{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=608{\text{ N}}}
(where 62 kg is the world average adult mass).
== Kilonewtons ==
Large forces may be expressed in kilonewtons (kN), where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train locomotive and the thrust of an F100 jet engine are both around 130 kN.
Climbing ropes are tested by assuming a human can withstand a fall that creates 12 kN of force. The ropes must not break when tested against 5 such falls.: 11
== Conversion factors ==
== See also ==
== References == | Wikipedia/Newton_(force) |
In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the relative deformation) of a material in the neighborhood of a certain point, at a certain moment of time. It can be defined as the derivative of the strain tensor with respect to time, or as the symmetric component of the Jacobian matrix (derivative with respect to position) of the flow velocity. In fluid mechanics it also can be described as the velocity gradient, a measure of how the velocity of a fluid changes between different points within the fluid. Though the term can refer to a velocity profile (variation in velocity across layers of flow in a pipe), it is often used to mean the gradient of a flow's velocity with respect to its coordinates. The concept has implications in a variety of areas of physics and engineering, including magnetohydrodynamics, mining and water treatment.
The strain rate tensor is a purely kinematic concept that describes the macroscopic motion of the material. Therefore, it does not depend on the nature of the material, or on the forces and stresses that may be acting on it; and it applies to any continuous medium, whether solid, liquid or gas.
On the other hand, for any fluid except superfluids, any gradual change in its deformation (i.e. a non-zero strain rate tensor) gives rise to viscous forces in its interior, due to friction between adjacent fluid elements, that tend to oppose that change. At any point in the fluid, these stresses can be described by a viscous stress tensor that is, almost always, completely determined by the strain rate tensor and by certain intrinsic properties of the fluid at that point. Viscous stress also occur in solids, in addition to the elastic stress observed in static deformation; when it is too large to be ignored, the material is said to be viscoelastic.
== Dimensional analysis ==
By performing dimensional analysis, the dimensions of velocity gradient can be determined. The dimensions of velocity are
L
1
T
−
1
{\displaystyle {\mathsf {L^{1}T^{-1}}}}
, and the dimensions of distance are
L
1
{\displaystyle {\mathsf {L^{1}}}}
. Since the velocity gradient can be expressed as
Δ
velocity
Δ
distance
{\displaystyle {\frac {\Delta {\text{velocity}}}{\Delta {\text{distance}}}}}
. Therefore, the velocity gradient has the same dimensions as this ratio, i.e.,
T
−
1
{\displaystyle {\mathsf {T^{-1}}}}
.
== In continuum mechanics ==
In 3 dimensions, the gradient
∇
v
{\displaystyle \nabla \mathbf {v} }
of the velocity
v
{\displaystyle \mathbf {v} }
is a second-order tensor which can be expressed as the matrix
L
{\displaystyle \mathbf {L} }
:
L
=
∇
v
=
[
∂
v
x
∂
x
∂
v
y
∂
x
∂
v
z
∂
x
∂
v
x
∂
y
∂
v
y
∂
y
∂
v
z
∂
y
∂
v
x
∂
z
∂
v
y
∂
z
∂
v
z
∂
z
]
{\displaystyle \mathbf {L} =\nabla \mathbf {v} ={\begin{bmatrix}{\frac {\partial v_{x}}{\partial x}}&{\frac {\partial v_{y}}{\partial x}}&{\frac {\partial v_{z}}{\partial x}}\\{\frac {\partial v_{x}}{\partial y}}&{\frac {\partial v_{y}}{\partial y}}&{{\frac {\partial v_{z}}{\partial y}}\ }\\{\frac {\partial v_{x}}{\partial z}}&{\frac {\partial v_{y}}{\partial z}}&{\frac {\partial v_{z}}{\partial z}}\end{bmatrix}}}
L
{\displaystyle \mathbf {L} }
can be decomposed into the sum of a symmetric matrix
E
{\displaystyle {\textbf {E}}}
and a skew-symmetric matrix
W
{\displaystyle {\textbf {W}}}
as follows
E
=
1
2
(
L
+
L
T
)
W
=
1
2
(
L
−
L
T
)
{\displaystyle {\begin{aligned}\mathbf {E} &={\frac {1}{2}}\left(\mathbf {L} +\mathbf {L} ^{\textsf {T}}\right)\\\mathbf {W} &={\frac {1}{2}}\left(\mathbf {L} -\mathbf {L} ^{\textsf {T}}\right)\end{aligned}}}
E
{\displaystyle {\textbf {E}}}
is called the strain rate tensor and describes the rate of stretching and shearing.
W
{\displaystyle {\textbf {W}}}
is called the spin tensor and describes the rate of rotation.
== Relationship between shear stress and the velocity field ==
Sir Isaac Newton proposed that shear stress is directly proportional to the velocity gradient:
τ
=
μ
∂
u
∂
y
.
{\displaystyle \tau =\mu {\frac {\partial u}{\partial y}}.}
The constant of proportionality,
μ
{\displaystyle \mu }
, is called the dynamic viscosity.
== Formal definition ==
Consider a material body, solid or fluid, that is flowing and/or moving in space. Let v be the velocity field within the body; that is, a smooth function from R3 × R such that v(p, t) is the macroscopic velocity of the material that is passing through the point p at time t.
The velocity v(p + r, t) at a point displaced from p by a small vector r can be written as a Taylor series:
v
(
p
+
r
,
t
)
=
v
(
p
,
t
)
+
(
∇
v
)
(
p
,
t
)
(
r
)
+
higher order terms
,
{\displaystyle \mathbf {v} (\mathbf {p} +\mathbf {r} ,t)=\mathbf {v} (\mathbf {p} ,t)+(\nabla \mathbf {v} )(\mathbf {p} ,t)(\mathbf {r} )+{\text{higher order terms}},}
where ∇v the gradient of the velocity field, understood as a linear map that takes a displacement vector r to the corresponding change in the velocity.
In an arbitrary reference frame, ∇v is related to the Jacobian matrix of the field, namely in 3 dimensions it is the 3 × 3 matrix
(
∇
v
)
T
=
[
∂
1
v
1
∂
2
v
1
∂
3
v
1
∂
1
v
2
∂
2
v
2
∂
3
v
2
∂
1
v
3
∂
2
v
3
∂
3
v
3
]
=
J
.
{\displaystyle \left(\nabla \mathbf {v} \right)^{\mathrm {T} }={\begin{bmatrix}\partial _{1}v_{1}&\partial _{2}v_{1}&\partial _{3}v_{1}\\\partial _{1}v_{2}&\partial _{2}v_{2}&\partial _{3}v_{2}\\\partial _{1}v_{3}&\partial _{2}v_{3}&\partial _{3}v_{3}\end{bmatrix}}=\mathbf {J} .}
where vi is the component of v parallel to axis i and ∂jf denotes the partial derivative of a function f with respect to the space coordinate xj. Note that J is a function of p and t.
In this coordinate system, the Taylor approximation for the velocity near p is
v
i
(
p
+
r
,
t
)
=
v
i
(
p
,
t
)
+
∑
j
J
i
j
(
p
,
t
)
r
j
=
v
i
(
p
,
t
)
+
∑
j
∂
j
v
i
(
p
,
t
)
r
j
;
{\displaystyle v_{i}(\mathbf {p} +\mathbf {r} ,t)=v_{i}(\mathbf {p} ,t)+\sum _{j}J_{ij}(\mathbf {p} ,t)r_{j}=v_{i}(\mathbf {p} ,t)+\sum _{j}\partial _{j}v_{i}(\mathbf {p} ,t)r_{j};}
or simply
v
(
p
+
r
,
t
)
=
v
(
p
,
t
)
+
J
(
p
,
t
)
r
{\displaystyle \mathbf {v} (\mathbf {p} +\mathbf {r} ,t)=\mathbf {v} (\mathbf {p} ,t)+\mathbf {J} (\mathbf {p} ,t)\mathbf {r} }
if v and r are viewed as 3 × 1 matrices.
=== Symmetric and antisymmetric parts ===
Any matrix can be decomposed into the sum of a symmetric matrix and an antisymmetric matrix. Applying this to the Jacobian matrix with symmetric and antisymmetric components E and R respectively:
E
=
1
2
(
J
+
J
T
)
R
=
1
2
(
J
−
J
T
)
E
i
j
=
1
2
(
∂
j
v
i
+
∂
i
v
j
)
R
i
j
=
1
2
(
∂
j
v
i
−
∂
i
v
j
)
{\displaystyle {\begin{aligned}\mathbf {E} &={\frac {1}{2}}\left(\mathbf {J} +\mathbf {J} ^{\textsf {T}}\right)&\mathbf {R} &={\frac {1}{2}}\left(\mathbf {J} -\mathbf {J} ^{\textsf {T}}\right)\\E_{ij}&={\frac {1}{2}}\left(\partial _{j}v_{i}+\partial _{i}v_{j}\right)&R_{ij}&={\frac {1}{2}}\left(\partial _{j}v_{i}-\partial _{i}v_{j}\right)\end{aligned}}}
This decomposition is independent of coordinate system, and so has physical significance. Then the velocity field may be approximated as
v
(
p
+
r
,
t
)
≈
v
(
p
,
t
)
+
E
(
p
,
t
)
(
r
)
+
R
(
p
,
t
)
(
r
)
,
{\displaystyle \mathbf {v} (\mathbf {p} +\mathbf {r} ,t)\approx \mathbf {v} (\mathbf {p} ,t)+\mathbf {E} (\mathbf {p} ,t)(\mathbf {r} )+\mathbf {R} (\mathbf {p} ,t)(\mathbf {r} ),}
that is,
v
i
(
p
+
r
,
t
)
=
v
i
(
p
,
t
)
+
∑
j
E
i
j
(
p
,
t
)
r
j
+
∑
j
R
i
j
(
p
,
t
)
r
j
=
v
i
(
p
,
t
)
+
1
2
∑
j
(
∂
j
v
i
(
p
,
t
)
+
∂
i
v
j
(
p
,
t
)
)
r
j
+
1
2
∑
j
(
∂
j
v
i
(
p
,
t
)
−
∂
i
v
j
(
p
,
t
)
)
r
j
{\displaystyle {\begin{aligned}v_{i}(\mathbf {p} +\mathbf {r} ,t)&=v_{i}(\mathbf {p} ,t)+\sum _{j}E_{ij}(\mathbf {p} ,t)r_{j}+\sum _{j}R_{ij}(\mathbf {p} ,t)r_{j}\\&=v_{i}(\mathbf {p} ,t)+{\frac {1}{2}}\sum _{j}\left(\partial _{j}v_{i}(\mathbf {p} ,t)+\partial _{i}v_{j}(\mathbf {p} ,t)\right)r_{j}+{\frac {1}{2}}\sum _{j}\left(\partial _{j}v_{i}(\mathbf {p} ,t)-\partial _{i}v_{j}(\mathbf {p} ,t)\right)r_{j}\end{aligned}}}
The antisymmetric term R represents a rigid-like rotation of the fluid about the point p. Its angular velocity
ω
→
{\displaystyle {\vec {\omega }}}
is
ω
→
=
1
2
∇
×
v
=
1
2
[
∂
2
v
3
−
∂
3
v
2
∂
3
v
1
−
∂
1
v
3
∂
1
v
2
−
∂
2
v
1
]
.
{\displaystyle {\vec {\omega }}={\frac {1}{2}}\nabla \times \mathbf {v} ={\frac {1}{2}}{\begin{bmatrix}\partial _{2}v_{3}-\partial _{3}v_{2}\\\partial _{3}v_{1}-\partial _{1}v_{3}\\\partial _{1}v_{2}-\partial _{2}v_{1}\end{bmatrix}}.}
The product ∇ × v is called the vorticity of the vector field. A rigid rotation does not change the relative positions of the fluid elements, so the antisymmetric term R of the velocity gradient does not contribute to the rate of change of the deformation. The actual strain rate is therefore described by the symmetric E term, which is the strain rate tensor.
=== Shear rate and compression rate ===
The symmetric term E (the rate-of-strain tensor) can be broken down further as the sum of a scalar times the unit tensor, that represents a gradual isotropic expansion or contraction; and a traceless symmetric tensor which represents a gradual shearing deformation, with no change in volume:
E
(
p
,
t
)
(
r
)
=
S
(
p
,
t
)
(
r
)
+
D
(
p
,
t
)
(
r
)
.
{\displaystyle \mathbf {E} (\mathbf {p} ,t)(\mathbf {r} )=\mathbf {S} (\mathbf {p} ,t)(\mathbf {r} )+\mathbf {D} (\mathbf {p} ,t)(\mathbf {r} ).}
That is,
E
i
j
=
1
3
(
∑
k
∂
k
v
k
)
δ
i
j
⏟
rate-of-expansion tensor
S
i
j
+
1
2
(
∂
i
v
j
+
∂
j
v
i
)
⏞
E
i
j
−
S
i
j
⏟
rate-of-shear tensor
D
i
j
,
{\displaystyle E_{ij}=\underbrace {{\frac {1}{3}}\left(\sum _{k}\partial _{k}v_{k}\right)\delta _{ij}} _{{\text{rate-of-expansion tensor }}S_{ij}}+\underbrace {\overbrace {{\frac {1}{2}}\left(\partial _{i}v_{j}+\partial _{j}v_{i}\right)} ^{E_{ij}}-S_{ij}} _{{\text{rate-of-shear tensor }}D_{ij}},}
Here δ is the unit tensor, such that δij is 1 if i = j and 0 if i ≠ j. This decomposition is independent of the choice of coordinate system, and is therefore physically significant.
The trace of the expansion rate tensor is the divergence of the velocity field:
∇
⋅
v
=
∂
1
v
1
+
∂
2
v
2
+
∂
3
v
3
;
{\displaystyle \nabla \cdot \mathbf {v} =\partial _{1}v_{1}+\partial _{2}v_{2}+\partial _{3}v_{3};}
which is the rate at which the volume of a fixed amount of fluid increases at that point.
The shear rate tensor is represented by a symmetric 3 × 3 matrix, and describes a flow that combines compression and expansion flows along three orthogonal axes, such that there is no change in volume. This type of flow occurs, for example, when a rubber strip is stretched by pulling at the ends, or when honey falls from a spoon as a smooth unbroken stream.
For a two-dimensional flow, the divergence of v has only two terms and quantifies the change in area rather than volume. The factor 1/3 in the expansion rate term should be replaced by 1/2 in that case.
== Examples ==
The study of velocity gradients is useful in analysing path dependent materials and in the subsequent study of stresses and strains; e.g., Plastic deformation of metals. The near-wall velocity gradient of the unburned reactants flowing from a tube is a key parameter for characterising flame stability.: 1–3 The velocity gradient of a plasma can define conditions for the solutions to fundamental equations in magnetohydrodynamics.
=== Fluid in a pipe ===
Consider the velocity field of a fluid flowing through a pipe. The layer of fluid in contact with the pipe tends to be at rest with respect to the pipe. This is called the no slip condition. If the velocity difference between fluid layers at the centre of the pipe and at the sides of the pipe is sufficiently small, then the fluid flow is observed in the form of continuous layers. This type of flow is called laminar flow.
The flow velocity difference between adjacent layers can be measured in terms of a velocity gradient, given by
Δ
u
/
Δ
y
{\displaystyle \Delta u/\Delta y}
. Where
Δ
u
{\displaystyle \Delta u}
is the difference in flow velocity between the two layers and
Δ
y
{\displaystyle \Delta y}
is the distance between the layers.
== See also ==
Stress tensor (disambiguation)
Finite strain theory § Time-derivative of the deformation gradient, the spatial and material velocity gradient from continuum mechanics
== References == | Wikipedia/Strain_rate_tensor |
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies.
A child may carry out basic experiments to understand how things fall to the ground, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and informal natural comparisons (e.g. tasting a range of chocolates to find a favorite), to highly controlled (e.g. tests requiring complex apparatus overseen by many scientists that hope to discover information about subatomic particles). Uses of experiments vary considerably between the natural and human sciences.
Experiments typically include controls, which are designed to minimize the effects of variables other than the single independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements. Scientific controls are a part of the scientific method. Ideally, all variables in an experiment are controlled (accounted for by the control measurements) and none are uncontrolled. In such an experiment, if all controls work as expected, it is possible to conclude that the experiment works as intended, and that results are due to the effect of the tested variables.
== Overview ==
In the scientific method, an experiment is an empirical procedure that arbitrates competing models or hypotheses. Researchers also use experimentation to test existing theories or new hypotheses to support or disprove them.
An experiment usually tests a hypothesis, which is an expectation about how a particular process or phenomenon works. However, an experiment may also aim to answer a "what-if" question, without a specific expectation about what the experiment reveals, or to confirm prior results. If an experiment is carefully conducted, the results usually either support or disprove the hypothesis. According to some philosophies of science, an experiment can never "prove" a hypothesis, it can only add support. On the other hand, an experiment that provides a counterexample can disprove a theory or hypothesis, but a theory can always be salvaged by appropriate ad hoc modifications at the expense of simplicity.
An experiment must also control the possible confounding factors—any factors that would mar the accuracy or repeatability of the experiment or the ability to interpret the results. Confounding is commonly eliminated through scientific controls and/or, in randomized experiments, through random assignment.
In engineering and the physical sciences, experiments are a primary component of the scientific method. They are used to test theories and hypotheses about how physical processes work under particular conditions (e.g., whether a particular engineering process can produce a desired chemical compound). Typically, experiments in these fields focus on replication of identical procedures in hopes of producing identical results in each replication. Random assignment is uncommon.
In medicine and the social sciences, the prevalence of experimental research varies widely across disciplines. When used, however, experiments typically follow the form of the clinical trial, where experimental units (usually individual human beings) are randomly assigned to a treatment or control condition where one or more outcomes are assessed. In contrast to norms in the physical sciences, the focus is typically on the average treatment effect (the difference in outcomes between the treatment and control groups) or another test statistic produced by the experiment. A single study typically does not involve replications of the experiment, but separate studies may be aggregated through systematic review and meta-analysis.
There are various differences in experimental practice in each of the branches of science. For example, agricultural research frequently uses randomized experiments (e.g., to test the comparative effectiveness of different fertilizers), while experimental economics often involves experimental tests of theorized human behaviors without relying on random assignment of individuals to treatment and control conditions.
== History ==
One of the first methodical approaches to experiments in the modern sense is visible in the works of the Arab mathematician and scholar Ibn al-Haytham. He conducted his experiments in the field of optics—going back to optical and mathematical problems in the works of Ptolemy—by controlling his experiments due to factors such as self-criticality, reliance on visible results of the experiments as well as a criticality in terms of earlier results. He was one of the first scholars to use an inductive-experimental method for achieving results. In his Book of Optics he describes the fundamentally new approach to knowledge and research in an experimental sense:
We should, that is, recommence the inquiry into its principles and premisses, beginning our investigation with an inspection of the things that exist and a survey of the conditions of visible objects. We should distinguish the properties of particulars, and gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging, manifest and not subject to doubt. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premisses and exercising caution in regard to conclusions—our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not to be swayed by opinion. We may in this way eventually come to the truth that gratifies the heart and gradually and carefully reach the end at which certainty appears; while through criticism and caution we may seize the truth that dispels disagreement and resolves doubtful matters. For all that, we are not free from that human turbidity which is in the nature of man; but we must do our best with what we possess of human power. From God we derive support in all things.
According to his explanation, a strictly controlled test execution with a sensibility for the subjectivity and susceptibility of outcomes due to the nature of man is necessary. Furthermore, a critical view on the results and outcomes of earlier scholars is necessary:
It is thus the duty of the man who studies the writings of scientists, if learning the truth is his goal, to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.
Thus, a comparison of earlier results with the experimental results is necessary for an objective experiment—the visible results being more important. In the end, this may mean that an experimental researcher must find enough courage to discard traditional opinions or results, especially if these results are not experimental but results from a logical/ mental derivation. In this process of critical consideration, the man himself should not forget that he tends to subjective opinions—through "prejudices" and "leniency"—and thus has to be critical about his own way of building hypotheses.
Francis Bacon (1561–1626), an English philosopher and scientist active in the 17th century, became an influential supporter of experimental science in the English renaissance. He disagreed with the method of answering scientific questions by deduction—similar to Ibn al-Haytham—and described it as follows: "Having first determined the question according to his will, man then resorts to experience, and bending her to conformity with his placets, leads her about like a captive in a procession." Bacon wanted a method that relied on repeatable observations, or experiments. Notably, he first ordered the scientific method as we understand it today. There remains simple experience; which, if taken as it comes, is called accident, if sought for, experiment. The true method of experience first lights the candle [hypothesis], and then by means of the candle shows the way [arranges and delimits the experiment]; commencing as it does with experience duly ordered and digested, not bungling or erratic, and from it deducing axioms [theories], and from established axioms again new experiments.: 101
In the centuries that followed, people who applied the scientific method in different areas made important advances and discoveries. For example, Galileo Galilei (1564–1642) accurately measured time and experimented to make accurate measurements and conclusions about the speed of a falling body. Antoine Lavoisier (1743–1794), a French chemist, used experiment to describe new areas, such as combustion and biochemistry and to develop the theory of conservation of mass (matter). Louis Pasteur (1822–1895) used the scientific method to disprove the prevailing theory of spontaneous generation and to develop the germ theory of disease. Because of the importance of controlling potentially confounding variables, the use of well-designed laboratory experiments is preferred when possible.
A considerable amount of progress on the design and analysis of experiments occurred in the early 20th century, with contributions from statisticians such as Ronald Fisher (1890–1962), Jerzy Neyman (1894–1981), Oscar Kempthorne (1919–2000), Gertrude Mary Cox (1900–1978), and William Gemmell Cochran (1909–1980), among others.
== Types ==
Experiments might be categorized according to a number of dimensions, depending upon professional norms and standards in different fields of study.
In some disciplines (e.g., psychology or political science), a 'true experiment' is a method of social research in which there are two kinds of variables. The independent variable is manipulated by the experimenter, and the dependent variable is measured. The signifying characteristic of a true experiment is that it randomly allocates the subjects to neutralize experimenter bias, and ensures, over a large number of iterations of the experiment, that it controls for all confounding factors.
Depending on the discipline, experiments can be conducted to accomplish different but not mutually exclusive goals: test theories, search for and document phenomena, develop theories, or advise policymakers. These goals also relate differently to validity concerns.
=== Controlled experiments ===
A controlled experiment often compares the results obtained from experimental samples against control samples, which are practically identical to the experimental sample except for the one aspect whose effect is being tested (the independent variable). A good example would be a drug trial. The sample or group receiving the drug would be the experimental group (treatment group); and the one receiving the placebo or regular treatment would be the control one. In many laboratory experiments it is good practice to have several replicate samples for the test being performed and have both a positive control and a negative control. The results from replicate samples can often be averaged, or if one of the replicates is obviously inconsistent with the results from the other samples, it can be discarded as being the result of an experimental error (some step of the test procedure may have been mistakenly omitted for that sample). Most often, tests are done in duplicate or triplicate. A positive control is a procedure similar to the actual experimental test but is known from previous experience to give a positive result. A negative control is known to give a negative result. The positive control confirms that the basic conditions of the experiment were able to produce a positive result, even if none of the actual experimental samples produce a positive result. The negative control demonstrates the base-line result obtained when a test does not produce a measurable positive result. Most often the value of the negative control is treated as a "background" value to subtract from the test sample results. Sometimes the positive control takes the quadrant of a standard curve.
An example that is often used in teaching laboratories is a controlled protein assay. Students might be given a fluid sample containing an unknown (to the student) amount of protein. It is their job to correctly perform a controlled experiment in which they determine the concentration of protein in the fluid sample (usually called the "unknown sample"). The teaching lab would be equipped with a protein standard solution with a known protein concentration. Students could make several positive control samples containing various dilutions of the protein standard. Negative control samples would contain all of the reagents for the protein assay but no protein. In this example, all samples are performed in duplicate. The assay is a colorimetric assay in which a spectrophotometer can measure the amount of protein in samples by detecting a colored complex formed by the interaction of protein molecules and molecules of an added dye. In the illustration, the results for the diluted test samples can be compared to the results of the standard curve (the blue line in the illustration) to estimate the amount of protein in the unknown sample.
Controlled experiments can be performed when it is difficult to exactly control all the conditions in an experiment. In this case, the experiment begins by creating two or more sample groups that are probabilistically equivalent, which means that measurements of traits should be similar among the groups and that the groups should respond in the same manner if given the same treatment. This equivalency is determined by statistical methods that take into account the amount of variation between individuals and the number of individuals in each group. In fields such as microbiology and chemistry, where there is very little variation between individuals and the group size is easily in the millions, these statistical methods are often bypassed and simply splitting a solution into equal parts is assumed to produce identical sample groups.
Once equivalent groups have been formed, the experimenter tries to treat them identically except for the one variable that he or she wishes to isolate. Human experimentation requires special safeguards against outside variables such as the placebo effect. Such experiments are generally double blind, meaning that neither the volunteer nor the researcher knows which individuals are in the control group or the experimental group until after all of the data have been collected. This ensures that any effects on the volunteer are due to the treatment itself and are not a response to the knowledge that he is being treated.
In human experiments, researchers may give a subject (person) a stimulus that the subject responds to. The goal of the experiment is to measure the response to the stimulus by a test method.
In the design of experiments, two or more "treatments" are applied to estimate the difference between the mean responses for the treatments. For example, an experiment on baking bread could estimate the difference in the responses associated with quantitative variables, such as the ratio of water to flour, and with qualitative variables, such as strains of yeast. Experimentation is the step in the scientific method that helps people decide between two or more competing explanations—or hypotheses. These hypotheses suggest reasons to explain a phenomenon or predict the results of an action. An example might be the hypothesis that "if I release this ball, it will fall to the floor": this suggestion can then be tested by carrying out the experiment of letting go of the ball, and observing the results. Formally, a hypothesis is compared against its opposite or null hypothesis ("if I release this ball, it will not fall to the floor"). The null hypothesis is that there is no explanation or predictive power of the phenomenon through the reasoning that is being investigated. Once hypotheses are defined, an experiment can be carried out and the results analysed to confirm, refute, or define the accuracy of the hypotheses.
Experiments can be also designed to estimate spillover effects onto nearby untreated units.
=== Natural experiments ===
The term "experiment" usually implies a controlled experiment, but sometimes controlled experiments are prohibitively difficult, impossible, unethical or illegal. In this case researchers resort to natural experiments or quasi-experiments. Natural experiments rely solely on observations of the variables of the system under study, rather than manipulation of just one or a few variables as occurs in controlled experiments. To the degree possible, they attempt to collect data for the system in such a way that contribution from all variables can be determined, and where the effects of variation in certain variables remain approximately constant so that the effects of other variables can be discerned. The degree to which this is possible depends on the observed correlation between explanatory variables in the observed data. When these variables are not well correlated, natural experiments can approach the power of controlled experiments. Usually, however, there is some correlation between these variables, which reduces the reliability of natural experiments relative to what could be concluded if a controlled experiment were performed. Also, because natural experiments usually take place in uncontrolled environments, variables from undetected sources are neither measured nor held constant, and these may produce illusory correlations in variables under study.
Much research in several science disciplines, including economics, human geography, archaeology, sociology, cultural anthropology, geology, paleontology, ecology, meteorology, and astronomy, relies on quasi-experiments. For example, in astronomy it is clearly impossible, when testing the hypothesis "Stars are collapsed clouds of hydrogen", to start out with a giant cloud of hydrogen, and then perform the experiment of waiting a few billion years for it to form a star. However, by observing various clouds of hydrogen in various states of collapse, and other implications of the hypothesis (for example, the presence of various spectral emissions from the light of stars), we can collect data we require to support the hypothesis. An early example of this type of experiment was the first verification in the 17th century that light does not travel from place to place instantaneously, but instead has a measurable speed. Observation of the appearance of the moons of Jupiter were slightly delayed when Jupiter was farther from Earth, as opposed to when Jupiter was closer to Earth; and this phenomenon was used to demonstrate that the difference in the time of appearance of the moons was consistent with a measurable speed.
=== Field experiments ===
Field experiments are so named to distinguish them from laboratory experiments, which enforce scientific control by testing a hypothesis in the artificial and highly controlled setting of a laboratory. Often used in the social sciences, and especially in economic analyses of education and health interventions, field experiments have the advantage that outcomes are observed in a natural setting rather than in a contrived laboratory environment. For this reason, field experiments are sometimes seen as having higher external validity than laboratory experiments. However, like natural experiments, field experiments suffer from the possibility of contamination: experimental conditions can be controlled with more precision and certainty in the lab. Yet some phenomena (e.g., voter turnout in an election) cannot be easily studied in a laboratory.
== Observational studies ==
An observational study is used when it is impractical, unethical, cost-prohibitive (or otherwise inefficient) to fit a physical or social system into a laboratory setting, to completely control confounding factors, or to apply random assignment. It can also be used when confounding factors are either limited or known well enough to analyze the data in light of them (though this may be rare when social phenomena are under examination). For an observational science to be valid, the experimenter must know and account for confounding factors. In these situations, observational studies have value because they often suggest hypotheses that can be tested with randomized experiments or by collecting fresh data.
Fundamentally, however, observational studies are not experiments. By definition, observational studies lack the manipulation required for Baconian experiments. In addition, observational studies (e.g., in biological or social systems) often involve variables that are difficult to quantify or control. Observational studies are limited because they lack the statistical properties of randomized experiments. In a randomized experiment, the method of randomization specified in the experimental protocol guides the statistical analysis, which is usually specified also by the experimental protocol. Without a statistical model that reflects an objective randomization, the statistical analysis relies on a subjective model. Inferences from subjective models are unreliable in theory and practice. In fact, there are several cases where carefully conducted observational studies consistently give wrong results, that is, where the results of the observational studies are inconsistent and also differ from the results of experiments. For example, epidemiological studies of colon cancer consistently show beneficial correlations with broccoli consumption, while experiments find no benefit.
A particular problem with observational studies involving human subjects is the great difficulty attaining fair comparisons between treatments (or exposures), because such studies are prone to selection bias, and groups receiving different treatments (exposures) may differ greatly according to their covariates (age, height, weight, medications, exercise, nutritional status, ethnicity, family medical history, etc.). In contrast, randomization implies that for each covariate, the mean for each group is expected to be the same. For any randomized trial, some variation from the mean is expected, of course, but the randomization ensures that the experimental groups have mean values that are close, due to the central limit theorem and Markov's inequality. With inadequate randomization or low sample size, the systematic variation in covariates between the treatment groups (or exposure groups) makes it difficult to separate the effect of the treatment (exposure) from the effects of the other covariates, most of which have not been measured. The mathematical models used to analyze such data must consider each differing covariate (if measured), and results are not meaningful if a covariate is neither randomized nor included in the model.
To avoid conditions that render an experiment far less useful, physicians conducting medical trials—say for U.S. Food and Drug Administration approval—quantify and randomize the covariates that can be identified. Researchers attempt to reduce the biases of observational studies with matching methods such as propensity score matching, which require large populations of subjects and extensive information on covariates. However, propensity score matching is no longer recommended as a technique because it can increase, rather than decrease, bias. Outcomes are also quantified when possible (bone density, the amount of some cell or substance in the blood, physical strength or endurance, etc.) and not based on a subject's or a professional observer's opinion. In this way, the design of an observational study can render the results more objective and therefore, more convincing.
== Ethics ==
By placing the distribution of the independent variable(s) under the control of the researcher, an experiment—particularly when it involves human subjects—introduces potential ethical considerations, such as balancing benefit and harm, fairly distributing interventions (e.g., treatments for a disease), and informed consent. For example, in psychology or health care, it is unethical to provide a substandard treatment to patients. Therefore, ethical review boards are supposed to stop clinical trials and other experiments unless a new treatment is believed to offer benefits as good as current best practice. It is also generally unethical (and often illegal) to conduct randomized experiments on the effects of substandard or harmful treatments, such as the effects of ingesting arsenic on human health. To understand the effects of such exposures, scientists sometimes use observational studies to understand the effects of those factors.
Even when experimental research does not directly involve human subjects, it may still present ethical concerns. For example, the nuclear bomb experiments conducted by the Manhattan Project implied the use of nuclear reactions to harm human beings even though the experiments did not directly involve any human subjects.
== See also ==
== Notes ==
== Further reading ==
Dunning, Thad (2012). Natural experiments in the social sciences : a design-based approach. Cambridge: Cambridge University Press. ISBN 978-1107698000.
Shadish, William R.; Cook, Thomas D.; Campbell, Donald T. (2002). Experimental and quasi-experimental designs for generalized causal inference (Nachdr. ed.). Boston: Houghton Mifflin. ISBN 0-395-61556-9. (Excerpts)
Jeremy, Teigen (2014). "Experimental Methods in Military and Veteran Studies". In Soeters, Joseph; Shields, Patricia; Rietjens, Sebastiaan (eds.). Routledge Handbook of Research Methods in Military Studies. New York: Routledge. pp. 228–238.
== External links ==
Media related to Experiments at Wikimedia Commons
Lessons In Electric Circuits – Volume VI – Experiments
Experiment in Physics from Stanford Encyclopedia of Philosophy | Wikipedia/Experimental_method |
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non-rigid body, from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation). A configuration is a set containing the positions of all particles of the body.
A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc.
In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the conditions of the body. The relation between stress and strain (relative deformation) is expressed by constitutive equations, e.g., Hooke's law for linear elastic materials.
Deformations which cease to exist after the stress field is removed are termed as elastic deformation. In this case, the continuum completely recovers its original configuration. On the other hand, irreversible deformations may remain, and these exist even after stresses have been removed. One type of irreversible deformation is plastic deformation, which occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level. Another type of irreversible deformation is viscous deformation, which is the irreversible part of viscoelastic deformation.
In the case of elastic deformations, the response function linking strain to the deforming stress is the compliance tensor of the material.
== Definition and formulation ==
Deformation is the change in the metric properties of a continuous body, meaning that a curve drawn in the initial body placement changes its length when displaced to a curve in the final placement. If none of the curves changes length, it is said that a rigid body displacement occurred.
It is convenient to identify a reference configuration or initial geometric state of the continuum body which all subsequent configurations are referenced from. The reference configuration need not be one the body actually will ever occupy. Often, the configuration at t = 0 is considered the reference configuration, κ0(B). The configuration at the current time t is the current configuration.
For deformation analysis, the reference configuration is identified as undeformed configuration, and the current configuration as deformed configuration. Additionally, time is not considered when analyzing deformation, thus the sequence of configurations between the undeformed and deformed configurations are of no interest.
The components Xi of the position vector X of a particle in the reference configuration, taken with respect to the reference coordinate system, are called the material or reference coordinates. On the other hand, the components xi of the position vector x of a particle in the deformed configuration, taken with respect to the spatial coordinate system of reference, are called the spatial coordinates
There are two methods for analysing the deformation of a continuum. One description is made in terms of the material or referential coordinates, called material description or Lagrangian description. A second description of deformation is made in terms of the spatial coordinates it is called the spatial description or Eulerian description.
There is continuity during deformation of a continuum body in the sense that:
The material points forming a closed curve at any instant will always form a closed curve at any subsequent time.
The material points forming a closed surface at any instant will always form a closed surface at any subsequent time and the matter within the closed surface will always remain within.
=== Affine deformation ===
An affine deformation is a deformation that can be completely described by an affine transformation. Such a transformation is composed of a linear transformation (such as rotation, shear, extension and compression) and a rigid body translation. Affine deformations are also called homogeneous deformations.
Therefore, an affine deformation has the form
x
(
X
,
t
)
=
F
(
t
)
⋅
X
+
c
(
t
)
{\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {F}}(t)\cdot \mathbf {X} +\mathbf {c} (t)}
where x is the position of a point in the deformed configuration, X is the position in a reference configuration, t is a time-like parameter, F is the linear transformer and c is the translation. In matrix form, where the components are with respect to an orthonormal basis,
[
x
1
(
X
1
,
X
2
,
X
3
,
t
)
x
2
(
X
1
,
X
2
,
X
3
,
t
)
x
3
(
X
1
,
X
2
,
X
3
,
t
)
]
=
[
F
11
(
t
)
F
12
(
t
)
F
13
(
t
)
F
21
(
t
)
F
22
(
t
)
F
23
(
t
)
F
31
(
t
)
F
32
(
t
)
F
33
(
t
)
]
[
X
1
X
2
X
3
]
+
[
c
1
(
t
)
c
2
(
t
)
c
3
(
t
)
]
{\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}F_{11}(t)&F_{12}(t)&F_{13}(t)\\F_{21}(t)&F_{22}(t)&F_{23}(t)\\F_{31}(t)&F_{32}(t)&F_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}}
The above deformation becomes non-affine or inhomogeneous if F = F(X,t) or c = c(X,t).
=== Rigid body motion ===
A rigid body motion is a special affine deformation that does not involve any shear, extension or compression. The transformation matrix F is proper orthogonal in order to allow rotations but no reflections.
A rigid body motion can be described by
x
(
X
,
t
)
=
Q
(
t
)
⋅
X
+
c
(
t
)
{\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {Q}}(t)\cdot \mathbf {X} +\mathbf {c} (t)}
where
Q
⋅
Q
T
=
Q
T
⋅
Q
=
1
{\displaystyle {\boldsymbol {Q}}\cdot {\boldsymbol {Q}}^{T}={\boldsymbol {Q}}^{T}\cdot {\boldsymbol {Q}}={\boldsymbol {\mathit {1}}}}
In matrix form,
[
x
1
(
X
1
,
X
2
,
X
3
,
t
)
x
2
(
X
1
,
X
2
,
X
3
,
t
)
x
3
(
X
1
,
X
2
,
X
3
,
t
)
]
=
[
Q
11
(
t
)
Q
12
(
t
)
Q
13
(
t
)
Q
21
(
t
)
Q
22
(
t
)
Q
23
(
t
)
Q
31
(
t
)
Q
32
(
t
)
Q
33
(
t
)
]
[
X
1
X
2
X
3
]
+
[
c
1
(
t
)
c
2
(
t
)
c
3
(
t
)
]
{\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}Q_{11}(t)&Q_{12}(t)&Q_{13}(t)\\Q_{21}(t)&Q_{22}(t)&Q_{23}(t)\\Q_{31}(t)&Q_{32}(t)&Q_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}}
== Background: displacement ==
A change in the configuration of a continuum body results in a displacement. The displacement of a body has two components: a rigid-body displacement and a deformation. A rigid-body displacement consists of a simultaneous translation and rotation of the body without changing its shape or size. Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration κ0(B) to a current or deformed configuration κt(B) (Figure 1).
If after a displacement of the continuum there is a relative displacement between particles, a deformation has occurred. On the other hand, if after displacement of the continuum the relative displacement between particles in the current configuration is zero, then there is no deformation and a rigid-body displacement is said to have occurred.
The vector joining the positions of a particle P in the undeformed configuration and deformed configuration is called the displacement vector u(X,t) = uiei in the Lagrangian description, or U(x,t) = UJEJ in the Eulerian description.
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. It is convenient to do the analysis of deformation or motion of a continuum body in terms of the displacement field. In general, the displacement field is expressed in terms of the material coordinates as
u
(
X
,
t
)
=
b
(
X
,
t
)
+
x
(
X
,
t
)
−
X
or
u
i
=
α
i
J
b
J
+
x
i
−
α
i
J
X
J
{\displaystyle \mathbf {u} (\mathbf {X} ,t)=\mathbf {b} (\mathbf {X} ,t)+\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=\alpha _{iJ}b_{J}+x_{i}-\alpha _{iJ}X_{J}}
or in terms of the spatial coordinates as
U
(
x
,
t
)
=
b
(
x
,
t
)
+
x
−
X
(
x
,
t
)
or
U
J
=
b
J
+
α
J
i
x
i
−
X
J
{\displaystyle \mathbf {U} (\mathbf {x} ,t)=\mathbf {b} (\mathbf {x} ,t)+\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=b_{J}+\alpha _{Ji}x_{i}-X_{J}}
where αJi are the direction cosines between the material and spatial coordinate systems with unit vectors EJ and ei, respectively. Thus
E
J
⋅
e
i
=
α
J
i
=
α
i
J
{\displaystyle \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\alpha _{Ji}=\alpha _{iJ}}
and the relationship between ui and UJ is then given by
u
i
=
α
i
J
U
J
or
U
J
=
α
J
i
u
i
{\displaystyle u_{i}=\alpha _{iJ}U_{J}\qquad {\text{or}}\qquad U_{J}=\alpha _{Ji}u_{i}}
Knowing that
e
i
=
α
i
J
E
J
{\displaystyle \mathbf {e} _{i}=\alpha _{iJ}\mathbf {E} _{J}}
then
u
(
X
,
t
)
=
u
i
e
i
=
u
i
(
α
i
J
E
J
)
=
U
J
E
J
=
U
(
x
,
t
)
{\displaystyle \mathbf {u} (\mathbf {X} ,t)=u_{i}\mathbf {e} _{i}=u_{i}(\alpha _{iJ}\mathbf {E} _{J})=U_{J}\mathbf {E} _{J}=\mathbf {U} (\mathbf {x} ,t)}
It is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in b = 0, and the direction cosines become Kronecker deltas:
E
J
⋅
e
i
=
δ
J
i
=
δ
i
J
{\displaystyle \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\delta _{Ji}=\delta _{iJ}}
Thus, we have
u
(
X
,
t
)
=
x
(
X
,
t
)
−
X
or
u
i
=
x
i
−
δ
i
J
X
J
=
x
i
−
X
i
{\displaystyle \mathbf {u} (\mathbf {X} ,t)=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}}
or in terms of the spatial coordinates as
U
(
x
,
t
)
=
x
−
X
(
x
,
t
)
or
U
J
=
δ
J
i
x
i
−
X
J
=
x
J
−
X
J
{\displaystyle \mathbf {U} (\mathbf {x} ,t)=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}}
=== Displacement gradient tensor ===
The partial differentiation of the displacement vector with respect to the material coordinates yields the material displacement gradient tensor ∇Xu. Thus we have:
u
(
X
,
t
)
=
x
(
X
,
t
)
−
X
∇
X
u
=
∇
X
x
−
I
∇
X
u
=
F
−
I
{\displaystyle {\begin{aligned}\mathbf {u} (\mathbf {X} ,t)&=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \\\nabla _{\mathbf {X} }\mathbf {u} &=\nabla _{\mathbf {X} }\mathbf {x} -\mathbf {I} \\\nabla _{\mathbf {X} }\mathbf {u} &=\mathbf {F} -\mathbf {I} \end{aligned}}}
or
u
i
=
x
i
−
δ
i
J
X
J
=
x
i
−
X
i
∂
u
i
∂
X
K
=
∂
x
i
∂
X
K
−
δ
i
K
{\displaystyle {\begin{aligned}u_{i}&=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}\\{\frac {\partial u_{i}}{\partial X_{K}}}&={\frac {\partial x_{i}}{\partial X_{K}}}-\delta _{iK}\end{aligned}}}
where F is the deformation gradient tensor.
Similarly, the partial differentiation of the displacement vector with respect to the spatial coordinates yields the spatial displacement gradient tensor ∇xU. Thus we have,
U
(
x
,
t
)
=
x
−
X
(
x
,
t
)
∇
x
U
=
I
−
∇
x
X
∇
x
U
=
I
−
F
−
1
{\displaystyle {\begin{aligned}\mathbf {U} (\mathbf {x} ,t)&=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\nabla _{\mathbf {x} }\mathbf {X} \\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\mathbf {F} ^{-1}\end{aligned}}}
or
U
J
=
δ
J
i
x
i
−
X
J
=
x
J
−
X
J
∂
U
J
∂
x
k
=
δ
J
k
−
∂
X
J
∂
x
k
{\displaystyle {\begin{aligned}U_{J}&=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}\\{\frac {\partial U_{J}}{\partial x_{k}}}&=\delta _{Jk}-{\frac {\partial X_{J}}{\partial x_{k}}}\end{aligned}}}
== Examples ==
Homogeneous (or affine) deformations are useful in elucidating the behavior of materials. Some homogeneous deformations of interest are
uniform extension
pure dilation
equibiaxial tension
simple shear
pure shear
Linear or longitudinal deformations of long objects, such as beams and fibers, are called elongation or shortening; derived quantities are the relative elongation and the stretch ratio.
Plane deformations are also of interest, particularly in the experimental context.
Volume deformation is a uniform scaling due to isotropic compression; the relative volume deformation is called volumetric strain.
=== Plane deformation ===
A plane deformation, also called plane strain, is one where the deformation is restricted to one of the planes in the reference configuration. If the deformation is restricted to the plane described by the basis vectors e1, e2, the deformation gradient has the form
F
=
F
11
e
1
⊗
e
1
+
F
12
e
1
⊗
e
2
+
F
21
e
2
⊗
e
1
+
F
22
e
2
⊗
e
2
+
e
3
⊗
e
3
{\displaystyle {\boldsymbol {F}}=F_{11}\mathbf {e} _{1}\otimes \mathbf {e} _{1}+F_{12}\mathbf {e} _{1}\otimes \mathbf {e} _{2}+F_{21}\mathbf {e} _{2}\otimes \mathbf {e} _{1}+F_{22}\mathbf {e} _{2}\otimes \mathbf {e} _{2}+\mathbf {e} _{3}\otimes \mathbf {e} _{3}}
In matrix form,
F
=
[
F
11
F
12
0
F
21
F
22
0
0
0
1
]
{\displaystyle {\boldsymbol {F}}={\begin{bmatrix}F_{11}&F_{12}&0\\F_{21}&F_{22}&0\\0&0&1\end{bmatrix}}}
From the polar decomposition theorem, the deformation gradient, up to a change of coordinates, can be decomposed into a stretch and a rotation. Since all the deformation is in a plane, we can write
F
=
R
⋅
U
=
[
cos
θ
sin
θ
0
−
sin
θ
cos
θ
0
0
0
1
]
[
λ
1
0
0
0
λ
2
0
0
0
1
]
{\displaystyle {\boldsymbol {F}}={\boldsymbol {R}}\cdot {\boldsymbol {U}}={\begin{bmatrix}\cos \theta &\sin \theta &0\\-\sin \theta &\cos \theta &0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\lambda _{1}&0&0\\0&\lambda _{2}&0\\0&0&1\end{bmatrix}}}
where θ is the angle of rotation and λ1, λ2 are the principal stretches.
==== Isochoric plane deformation ====
If the deformation is isochoric (volume preserving) then det(F) = 1 and we have
F
11
F
22
−
F
12
F
21
=
1
{\displaystyle F_{11}F_{22}-F_{12}F_{21}=1}
Alternatively,
λ
1
λ
2
=
1
{\displaystyle \lambda _{1}\lambda _{2}=1}
==== Simple shear ====
A simple shear deformation is defined as an isochoric plane deformation in which there is a set of line elements with a given reference orientation that do not change length and orientation during the deformation.
If e1 is the fixed reference orientation in which line elements do not deform during the deformation then λ1 = 1 and F·e1 = e1.
Therefore,
F
11
e
1
+
F
21
e
2
=
e
1
⟹
F
11
=
1
;
F
21
=
0
{\displaystyle F_{11}\mathbf {e} _{1}+F_{21}\mathbf {e} _{2}=\mathbf {e} _{1}\quad \implies \quad F_{11}=1~;~~F_{21}=0}
Since the deformation is isochoric,
F
11
F
22
−
F
12
F
21
=
1
⟹
F
22
=
1
{\displaystyle F_{11}F_{22}-F_{12}F_{21}=1\quad \implies \quad F_{22}=1}
Define
γ
:=
F
12
{\displaystyle \gamma :=F_{12}}
Then, the deformation gradient in simple shear can be expressed as
F
=
[
1
γ
0
0
1
0
0
0
1
]
{\displaystyle {\boldsymbol {F}}={\begin{bmatrix}1&\gamma &0\\0&1&0\\0&0&1\end{bmatrix}}}
Now,
F
⋅
e
2
=
F
12
e
1
+
F
22
e
2
=
γ
e
1
+
e
2
⟹
F
⋅
(
e
2
⊗
e
2
)
=
γ
e
1
⊗
e
2
+
e
2
⊗
e
2
{\displaystyle {\boldsymbol {F}}\cdot \mathbf {e} _{2}=F_{12}\mathbf {e} _{1}+F_{22}\mathbf {e} _{2}=\gamma \mathbf {e} _{1}+\mathbf {e} _{2}\quad \implies \quad {\boldsymbol {F}}\cdot (\mathbf {e} _{2}\otimes \mathbf {e} _{2})=\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}+\mathbf {e} _{2}\otimes \mathbf {e} _{2}}
Since
e
i
⊗
e
i
=
1
{\displaystyle \mathbf {e} _{i}\otimes \mathbf {e} _{i}={\boldsymbol {\mathit {1}}}}
we can also write the deformation gradient as
F
=
1
+
γ
e
1
⊗
e
2
{\displaystyle {\boldsymbol {F}}={\boldsymbol {\mathit {1}}}+\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}}
== See also ==
The deformation of long elements such as beams or studs due to bending forces is known as deflection.
Euler–Bernoulli beam theory
Deformation (engineering)
Finite strain theory
Infinitesimal strain theory
Moiré pattern
Shear modulus
Shear stress
Shear strength
Strain (mechanics)
Stress (mechanics)
Stress measures
== References ==
== Further reading ==
Bazant, Zdenek P.; Cedolin, Luigi (2010). Three-Dimensional Continuum Instabilities and Effects of Finite Strain Tensor, chapter 11 in "Stability of Structures", 3rd ed. Singapore, New Jersey, London: World Scientific Publishing. ISBN 978-9814317030.
Dill, Ellis Harold (2006). Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity. Germany: CRC Press. ISBN 0-8493-9779-0.
Hutter, Kolumban; Jöhnk, Klaus (2004). Continuum Methods of Physical Modeling. Germany: Springer. ISBN 3-540-20619-1.
Jirasek, M; Bazant, Z.P. (2002). Inelastic Analysis of Structures. London and New York: J. Wiley & Sons. ISBN 0471987166.
Lubarda, Vlado A. (2001). Elastoplasticity Theory. CRC Press. ISBN 0-8493-1138-1.
Macosko, C. W. (1994). Rheology: principles, measurement and applications. VCH Publishers. ISBN 1-56081-579-5.
Mase, George E. (1970). Continuum Mechanics. McGraw-Hill Professional. ISBN 0-07-040663-4.
Mase, G. Thomas; Mase, George E. (1999). Continuum Mechanics for Engineers (2nd ed.). CRC Press. ISBN 0-8493-1855-6.
Nemat-Nasser, Sia (2006). Plasticity: A Treatise on Finite Deformation of Heterogeneous Inelastic Materials. Cambridge: Cambridge University Press. ISBN 0-521-83979-3.
Prager, William (1961). Introduction to Mechanics of Continua. Boston: Ginn and Co. ISBN 0486438090. {{cite book}}: ISBN / Date incompatibility (help) | Wikipedia/Elongation_(materials_science) |
In solid mechanics, a reinforced solid is a brittle material that is reinforced by ductile bars or fibres. A common application is reinforced concrete. When the concrete cracks the tensile force in a crack is not carried any more by the concrete but by the steel reinforcing bars only. The reinforced concrete will continue to carry the load provided that sufficient reinforcement is present. A typical design problem is to find the smallest amount of reinforcement that can carry the stresses on a small cube (Fig. 1). This can be formulated as an optimization problem.
== Optimization problem ==
The reinforcement is directed in the x, y and z direction. The reinforcement ratio is defined in a cross-section of a reinforcing bar as the reinforcement area
A
r
{\displaystyle A_{r}}
over the total area
A
{\displaystyle A}
, which is the brittle material area plus the reinforcement area.
ρ
x
{\displaystyle \rho _{x}}
=
A
r
x
{\displaystyle A_{rx}}
/
A
x
{\displaystyle A_{x}}
ρ
y
{\displaystyle \rho _{y}}
=
A
r
y
{\displaystyle A_{ry}}
/
A
y
{\displaystyle A_{y}}
ρ
z
{\displaystyle \rho _{z}}
=
A
r
z
{\displaystyle A_{rz}}
/
A
z
{\displaystyle A_{z}}
In case of reinforced concrete the reinforcement ratios are usually between 0.1% and 2%. The yield stress of the reinforcement is denoted by
f
y
{\displaystyle f_{y}}
. The stress tensor of the brittle material is
[
σ
x
x
−
ρ
x
f
y
σ
x
y
σ
x
z
σ
x
y
σ
y
y
−
ρ
y
f
y
σ
y
z
σ
x
z
σ
y
z
σ
z
z
−
ρ
z
f
y
]
{\displaystyle \left[{\begin{matrix}\sigma _{xx}-\rho _{x}f_{y}&\sigma _{xy}&\sigma _{xz}\\\sigma _{xy}&\sigma _{yy}-\rho _{y}f_{y}&\sigma _{yz}\\\sigma _{xz}&\sigma _{yz}&\sigma _{zz}-\rho _{z}f_{y}\\\end{matrix}}\right]}
.
This can be interpreted as the stress tensor of the composite material minus the stresses carried by the reinforcement at yielding. This formulation is accurate for reinforcement ratio's smaller than 5%. It is assumed that the brittle material has no tensile strength. (In case of reinforced concrete this assumption is necessary because the concrete has small shrinkage cracks.) Therefore, the principal stresses of the brittle material need to be compression. The principal stresses of a stress tensor are its eigenvalues.
The optimization problem is formulated as follows. Minimize
ρ
x
{\displaystyle \rho _{x}}
+
ρ
y
{\displaystyle \rho _{y}}
+
ρ
z
{\displaystyle \rho _{z}}
subject to all eigenvalues of the brittle material stress tensor are less than or equal to zero (negative-semidefinite). Additional constraints are
ρ
x
{\displaystyle \rho _{x}}
≥ 0,
ρ
y
{\displaystyle \rho _{y}}
≥ 0,
ρ
z
{\displaystyle \rho _{z}}
≥ 0.
== Solution ==
The solution to this problem can be presented in a form most suitable for hand calculations. It can be presented in graphical form. It can also be presented in a form most suitable for computer implementation. In this article the latter method is shown.
There are 12 possible reinforcement solutions to this problem, which are shown in the table below. Every row contains a possible solution. The first column contains the number of a solution. The second column gives conditions for which a solution is valid. Columns 3, 4 and 5 give the formulas for calculating the reinforcement ratios.
I
1
{\displaystyle I_{1}}
,
I
2
{\displaystyle I_{2}}
and
I
3
{\displaystyle I_{3}}
are the stress invariants of the composite material stress tensor.
The algorithm for obtaining the right solution is simple. Compute the reinforcement ratios of each possible solution that fulfills the conditions. Further ignore solutions with a reinforcement ratio less than zero. Compute the values of
ρ
x
{\displaystyle \rho _{x}}
+
ρ
y
{\displaystyle \rho _{y}}
+
ρ
z
{\displaystyle \rho _{z}}
and select the solution for which this value is smallest. The principal stresses in the brittle material can be computed as the eigenvalues of the brittle material stress tensor, for example by Jacobi's method.
The formulas can be simply checked by substituting the reinforcement ratios in the brittle material stress tensor and calculating the invariants. The first invariant needs to be less than or equal to zero. The second invariant needs to be greater than or equal to zero. These provide the conditions in column 2. For solution 2 to 12, the third invariant needs to be zero.
== Examples ==
The table below shows computed reinforcement ratios for 10 stress tensors. The applied reinforcement yield stress is
f
y
{\displaystyle f_{y}}
= 500 N/mm². The mass density of the reinforcing bars is 7800 kg/m3. In the table
σ
m
{\displaystyle \sigma _{m}}
is the computed brittle material stress.
m
r
{\displaystyle m_{r}}
is the optimised amount of reinforcement.
Elaborate contour plots for beams, a corbel, a pile cap and a trunnion girder can be found in the dissertation of Reinaldo Chen.
== Safe approximation ==
The solution to the optimization problem can be approximated conservatively.
ρ
x
f
y
{\displaystyle \rho _{x}f_{y}}
=
σ
x
x
+
|
σ
x
y
|
+
|
σ
x
z
|
{\displaystyle \sigma _{xx}+|\sigma _{xy}|+|\sigma _{xz}|}
ρ
y
f
y
{\displaystyle \rho _{y}f_{y}}
=
σ
y
y
+
|
σ
x
y
|
+
|
σ
y
z
|
{\displaystyle \sigma _{yy}+|\sigma _{xy}|+|\sigma _{yz}|}
ρ
z
f
y
{\displaystyle \rho _{z}f_{y}}
=
σ
z
z
+
|
σ
x
z
|
+
|
σ
y
z
|
{\displaystyle \sigma _{zz}+|\sigma _{xz}|+|\sigma _{yz}|}
This can be proofed as follows. For this upper bound, the characteristic polynomial of the brittle material stress tensor is
λ
3
+
2
(
|
σ
y
z
|
+
|
σ
x
z
|
+
|
σ
x
y
|
)
λ
2
+
3
(
|
σ
x
z
σ
x
y
|
+
|
σ
y
z
σ
x
y
|
+
|
σ
y
z
σ
x
z
|
)
λ
+
2
|
σ
y
z
σ
x
z
σ
x
y
|
−
2
σ
y
z
σ
x
z
σ
x
y
{\displaystyle \lambda ^{3}+2(|\sigma _{yz}|+|\sigma _{xz}|+|\sigma _{xy}|)\lambda ^{2}+3(|\sigma _{xz}\sigma _{xy}|+|\sigma _{yz}\sigma _{xy}|+|\sigma _{yz}\sigma _{xz}|)\lambda +2|\sigma _{yz}\sigma _{xz}\sigma _{xy}|-2\sigma _{yz}\sigma _{xz}\sigma _{xy}}
,
which does not have positive roots, or eigenvalues.
The approximation is easy to remember and can be used to check or replace computation results.
== Extension ==
The above solution can be very useful to design reinforcement; however, it has some practical limitations. The following aspects can be included too, if the problem is solved using convex optimization:
Multiple stress tensors in one point due to multiple loads on the structure instead of only one stress tensor
A constraint imposed to crack widths at the surface of the structure
Shear stress in the crack (aggregate interlock)
Reinforcement in other directions than x, y and z
Reinforcing bars that already have been placed in the reinforcement design process
The whole structure instead of one small material cube in turn
Large reinforcement ratio's
Compression reinforcement
== Bars in any direction ==
Reinforcing bars can have other directions than the x, y and z direction. In case of bars in one direction the stress tensor of the brittle material is computed by
[
σ
x
x
σ
x
y
σ
x
z
σ
x
y
σ
y
y
σ
y
z
σ
x
z
σ
y
z
σ
z
z
]
−
ρ
f
y
[
cos
2
(
α
)
cos
(
α
)
cos
(
β
)
cos
(
α
)
cos
(
γ
)
cos
(
β
)
cos
(
α
)
cos
2
(
β
)
cos
(
β
)
cos
(
γ
)
cos
(
γ
)
cos
(
α
)
cos
(
γ
)
cos
(
β
)
cos
2
(
γ
)
]
{\displaystyle \left[{\begin{matrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{xy}&\sigma _{yy}&\sigma _{yz}\\\sigma _{xz}&\sigma _{yz}&\sigma _{zz}\\\end{matrix}}\right]-\rho f_{y}\left[{\begin{matrix}\cos ^{2}(\alpha )&\cos(\alpha )\cos(\beta )&\cos(\alpha )\cos(\gamma )\\\cos(\beta )\cos(\alpha )&\cos ^{2}(\beta )&\cos(\beta )\cos(\gamma )\\\cos(\gamma )\cos(\alpha )&\cos(\gamma )\cos(\beta )&\cos ^{2}(\gamma )\\\end{matrix}}\right]}
where
α
,
β
,
γ
{\displaystyle \alpha ,\beta ,\gamma }
are the angles of the bars with the x, y and z axis. Bars in other directions can be added in the same way.
== Utilization ==
Often, builders of reinforced concrete structures know, from experience, where to put reinforcing bars. Computer tools can support this by checking whether proposed reinforcement is sufficient. To this end the tension criterion,
The eigenvalues of
[
σ
x
x
−
ρ
x
f
y
σ
x
y
σ
x
z
σ
x
y
σ
y
y
−
ρ
y
f
y
σ
y
z
σ
x
z
σ
y
z
σ
z
z
−
ρ
z
f
y
]
{\displaystyle \left[{\begin{matrix}\sigma _{xx}-\rho _{x}f_{y}&\sigma _{xy}&\sigma _{xz}\\\sigma _{xy}&\sigma _{yy}-\rho _{y}f_{y}&\sigma _{yz}\\\sigma _{xz}&\sigma _{yz}&\sigma _{zz}-\rho _{z}f_{y}\\\end{matrix}}\right]}
shall be less than or equal to zero.
is rewritten into,
The eigenvalues of
[
σ
x
x
ρ
x
f
y
σ
x
y
ρ
x
ρ
y
f
y
σ
x
z
ρ
x
ρ
z
f
y
σ
x
y
ρ
x
ρ
y
f
y
σ
y
y
ρ
y
f
y
σ
y
z
ρ
y
ρ
z
f
y
σ
x
z
ρ
x
ρ
z
f
y
σ
y
z
ρ
y
ρ
z
f
y
σ
z
z
ρ
z
f
y
]
{\displaystyle \left[{\begin{matrix}{\frac {\sigma _{xx}}{\rho _{x}f_{y}}}&{\frac {\sigma _{xy}}{{\sqrt {\rho _{x}\rho _{y}}}f_{y}}}&{\frac {\sigma _{xz}}{{\sqrt {\rho _{x}\rho _{z}}}f_{y}}}\\{\frac {\sigma _{xy}}{{\sqrt {\rho _{x}\rho _{y}}}f_{y}}}&{\frac {\sigma _{yy}}{\rho _{y}f_{y}}}&{\frac {\sigma _{yz}}{{\sqrt {\rho _{y}\rho _{z}}}f_{y}}}\\{\frac {\sigma _{xz}}{{\sqrt {\rho _{x}\rho _{z}}}f_{y}}}&{\frac {\sigma _{yz}}{{\sqrt {\rho _{y}\rho _{z}}}f_{y}}}&{\frac {\sigma _{zz}}{\rho _{z}f_{y}}}\\\end{matrix}}\right]}
shall be less than or equal to one.
The latter matrix is the utilization tensor. The largest eigenvalue of this tensor is the utilization (unity check), which can be displayed in a contour plot of a structure for all load combinations related to the ultimate limit state.
For example, the stress at some location in a structure is
σ
x
x
{\displaystyle \sigma _{xx}}
= 4 N/mm²,
σ
y
y
{\displaystyle \sigma _{yy}}
= -10 N/mm²,
σ
z
z
{\displaystyle \sigma _{zz}}
= 3 N/mm²,
σ
y
z
{\displaystyle \sigma _{yz}}
= 3 N/mm²,
σ
x
z
{\displaystyle \sigma _{xz}}
= -7 N/mm²,
σ
x
y
{\displaystyle \sigma _{xy}}
= 1 N/mm². The reinforcement yield stress is
f
y
{\displaystyle f_{y}}
= 500 N/mm². The proposed reinforcement is
ρ
x
{\displaystyle \rho _{x}}
= 1.4%,
ρ
y
{\displaystyle \rho _{y}}
= 0.1%,
ρ
z
{\displaystyle \rho _{z}}
= 1.9%. The eigenvalues of the utilization tensor are -20.11, -0.33 and 1.32. The utilization is 1.32. This shows that the bars are overloaded and 32% more reinforcement is required.
Combined compression and shear failure of the concrete can be checked with the Mohr-Coulomb criterion applied to the eigenvalues of the stress tensor of the brittle material.
σ
1
f
t
+
σ
3
f
c
{\displaystyle {\frac {\sigma _{1}}{f_{t}}}+{\frac {\sigma _{3}}{f_{c}}}}
≤ 1,
where
σ
1
{\displaystyle \sigma _{1}}
is the largest principal stress,
σ
3
{\displaystyle \sigma _{3}}
is the smallest principal stress,
f
c
{\displaystyle f_{c}}
is the uniaxial compressive strength (negative value) and
f
t
{\displaystyle f_{t}}
is the tensile strength. We can use the tensile strength here because the lumps of concrete that form compression diagonals are not cracked.
Cracks in the concrete can be checked by replacing the yield stress
f
y
{\displaystyle f_{y}}
in the utilization tensor by the bar stress at which the maximum crack width occurs. (This bar stress depends also on the bar diameter, the bar spacing and the bar cover.) Clearly, crack widths need checking only at the surface of a structure for stress states due to load combinations related to the serviceability limit state.
== See also ==
Reinforced concrete
Solid mechanics
Structural engineering
== References == | Wikipedia/Reinforced_solid |
Traction, traction force or tractive force is a force used to generate motion between a body and a tangential surface, through the use of either dry friction or shear force.
It has important applications in vehicles, as in tractive effort.
Traction can also refer to the maximum tractive force between a body and a surface, as limited by available friction; when this is the case, traction is often expressed as the ratio of the maximum tractive force to the normal force and is termed the coefficient of traction (similar to coefficient of friction). It is the force which makes an object move over the surface by overcoming all the resisting forces like friction, normal loads (load acting on the tiers in negative Z axis), air resistance, rolling resistance, etc.
== Definitions ==
Traction can be defined as:
a physical process in which a tangential force is transmitted across an interface between two bodies through dry friction or an intervening fluid film resulting in motion, stoppage or the transmission of power.
In vehicle dynamics, tractive force is closely related to the terms tractive effort and drawbar pull, though all three terms have different definitions.
== Coefficient of traction ==
The coefficient of traction is defined as the usable force for traction divided by the weight on the running gear (wheels, tracks etc.) i.e.:
usable traction = coefficient of traction × normal force.
=== Factors affecting coefficient of traction ===
Traction between two surfaces depends on several factors:
Material composition of each surface.
Macroscopic and microscopic shape (texture; macrotexture and microtexture)
Normal force pressing contact surfaces together.
Contaminants at the material boundary including lubricants and adhesives.
Relative motion of tractive surfaces - a sliding object (one in kinetic friction) has less traction than a non-sliding object (one in static friction).
Direction of traction relative to some coordinate system - e.g., the available traction of a tire often differs between cornering, accelerating, and braking.
For low-friction surfaces, such as off-road or ice, traction can be increased by using traction devices that partially penetrate the surface; these devices use the shear strength of the underlying surface rather than relying solely on dry friction (e.g., aggressive off-road tread or snow chains)....
=== Traction coefficient in engineering design ===
In the design of wheeled or tracked vehicles, high traction between wheel and ground is more desirable than low traction, as it allows for higher acceleration (including cornering and braking) without wheel slippage. One notable exception is in the motorsport technique of drifting, in which rear-wheel traction is purposely lost during high speed cornering.
Other designs dramatically increase surface area to provide more traction than wheels can, for example in continuous track and half-track vehicles. A tank or similar tracked vehicle uses tracks to reduce the pressure on the areas of contact. A 70-ton M1A2 would sink to the point of high centering if it used round tires. The tracks spread the 70 tons over a much larger area of contact than tires would and allow the tank to travel over much softer land.
In some applications, there is a complicated set of trade-offs in choosing materials. For example, soft rubbers often provide better traction but also wear faster and have higher losses when flexed—thus reducing efficiency. Choices in material selection may have a dramatic effect. For example: tires used for track racing cars may have a life of 200 km, while those used on heavy trucks may have a life approaching 100,000 km. The truck tires have less traction and also thicker rubber.
Traction also varies with contaminants. A layer of water in the contact patch can cause a substantial loss of traction. This is one reason for grooves and siping of automotive tires.
The traction of trucks, agricultural tractors, wheeled military vehicles, etc. when driving on soft and/or slippery ground has been found to improve significantly by use of Tire Pressure Control Systems (TPCS). A TPCS makes it possible to reduce and later restore the tire pressure during continuous vehicle operation. Increasing traction by use of a TPCS also reduces tire wear and ride vibration.
== See also ==
== References == | Wikipedia/Traction_(mechanics) |
A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. It may sometimes be used to refer to a single star. A large group of stars bound by gravitation is generally called a star cluster or galaxy, although, broadly speaking, they are also star systems. Star systems are not to be confused with planetary systems, which include planets and similar bodies (such as comets).
== Terminology ==
A star system of two stars is known as a binary star, binary star system or physical double star.
Systems with four or more components are rare, and are much less commonly found than those with 2 or 3. Multiple-star systems are called triple, ternary, or trinary if they contain three stars; quadruple or quaternary if they contain four stars; quintuple or quintenary with five stars; sextuple or sextenary with six stars; septuple or septenary with seven stars; and octuple or octenary with eight stars.
These systems are smaller than open star clusters, which have more complex dynamics and typically have from 100 to 1,000 stars.
== Optical doubles and multiples ==
Binary and multiple star systems are also known as a physical multiple stars, to distinguish them from optical multiple stars, which merely look close together when viewed from Earth. Multiple stars may refer to either optical or physical, but optical multiples do not form a star system.
Triple stars that are not all gravitationally bound (and thus do not form a triple star system) might comprise a physical binary and an optical companion (such as Beta Cephei) or, in rare cases, a purely optical triple star (such as Gamma Serpentis).
== Abundance ==
Research on binary and multiple stars estimates they make up about a third of the star systems in the Milky Way galaxy, with two-thirds of stars being single.
Binary stars are the most common non-single stars. With multiple star systems, the number of known systems decreases exponentially with multiplicity. For example, in the 1999 revision of Tokovinin's catalog of physical multiple stars, 551 out of the 728 systems described are triple. However, because of suspected selection effects, the ability to interpret these statistics is very limited.
== Detection ==
There are various methods to detect star systems and distinguish them from optical binaries multiples. These include:
Make observations six months apart and look for differences caused by parallaxes. (Not feasible for distant stars.)
Directly observe the stars orbiting each other or an apparently empty space (such as a dim star or neutron star). (Not feasible for distant stars or those with long orbital periods.)
Observe a varying Doppler shift.
Observe fluctuations in brightness that result from eclipses. (Relies on the Earth being in the orbital plane.)
Observe fluctuations in brightness that result from stars reflecting each others' light or gravitationally deforming each other.
== Orbital characteristics ==
In systems that satisfy the assumptions of the two-body problem – including having negligible tidal effects, perturbations (from the gravity of other bodies), and transfer of mass between stars – the two stars will trace out a stable elliptical orbit around the barycenter of the system. Examples of binary systems are Sirius, Procyon and Cygnus X-1, the last of which probably consists of a star and a black hole.
Multiple-star systems can be divided into two main dynamical classes:
Hierarchical systems are stable and consist of nested orbits that do not interact much. Each level of the hierarchy can be treated as a two-body problem.
Trapezia have unstable, strongly interacting orbits and are modelled as an n-body problem, exhibiting chaotic behavior. They can have 2, 3, or 4 stars.
=== Hierarchical systems ===
Most multiple-star systems are organized in what is called a hierarchical system: the stars in the system can be divided into two smaller groups, each of which traverses a larger orbit around the system's center of mass. Each of these smaller groups must also be hierarchical, which means that they must be divided into smaller subgroups which themselves are hierarchical, and so on. Each level of the hierarchy can be treated as a two-body problem by considering close pairs as if they were a single star. In these systems there is little interaction between the orbits and the stars' motion will continue to approximate stable Keplerian orbits around the system's center of mass.
For example, stable trinary systems consist of two stars in a close binary system, with a third orbiting this pair at a distance much larger than that of the binary orbit. If the inner and outer orbits are comparable in size, the system may become dynamically unstable, leading to a star being ejected from the system. EZ Aquarii is an example of a physical hierarchical triple system, which has an outer star orbiting an inner binary composed of two more red dwarf stars.
==== Mobile diagrams ====
Hierarchical arrangements can be organized by what Evans (1968) called mobile diagrams, which look similar to ornamental mobiles hung from the ceiling. Each level of the mobile illustrates the decomposition of the system into two or more systems with smaller size. Evans calls a diagram multiplex if there is a node with more than two children, i.e. if the decomposition of some subsystem involves two or more orbits with comparable size. Because multiplexes may be unstable, multiple stars are expected to be simplex, meaning that at each level there are exactly two children. Evans calls the number of levels in the diagram its hierarchy.
A simplex diagram of hierarchy 1, as in (b), describes a binary system.
A simplex diagram of hierarchy 2 may describe a triple system, as in (c), or a quadruple system, as in (d).
A simplex diagram of hierarchy 3 may describe a system with anywhere from four to eight components. The mobile diagram in (e) shows an example of a quadruple system with hierarchy 3, consisting of a single distant component orbiting a close binary system, with one of the components of the close binary being an even closer binary.
A real example of a system with hierarchy 3 is Castor, also known as Alpha Geminorum or α Gem. It consists of what appears to be a visual binary star which, upon closer inspection, can be seen to consist of two spectroscopic binary stars. By itself, this would be a quadruple hierarchy 2 system as in (d), but it is orbited by a fainter more distant component, which is also a close red dwarf binary. This forms a sextuple system of hierarchy 3.
The maximum hierarchy occurring in A. A. Tokovinin's Multiple Star Catalogue, as of 1999, is 4. For example, the stars Gliese 644A and Gliese 644B form what appears to be a close visual binary star; because Gliese 644B is a spectroscopic binary, this is actually a triple system. The triple system has the more distant visual companion Gliese 643 and the still more distant visual companion Gliese 644C, which, because of their common motion with Gliese 644AB, are thought to be gravitationally bound to the triple system. This forms a quintuple system whose mobile diagram would be the diagram of level 4 appearing in (f).
Higher hierarchies are also possible. Most of these higher hierarchies either are stable or suffer from internal perturbations. Others consider complex multiple stars will in time theoretically disintegrate into less complex multiple stars, like more common observed triples or quadruples.
=== Trapezia ===
Trapezia are usually very young, unstable systems. These are thought to form in stellar nurseries, and quickly fragment into stable multiple stars, which in the process may eject components as galactic high-velocity stars. They are named after the multiple star system known as the Trapezium Cluster in the heart of the Orion Nebula. Such systems are not rare, and commonly appear close to or within bright nebulae. These stars have no standard hierarchical arrangements, but compete for stable orbits. This relationship is called interplay. Such stars eventually settle down to a close binary with a distant companion, with the other star(s) previously in the system ejected into interstellar space at high velocities. This dynamic may explain the runaway stars that might have been ejected during a collision of two binary star groups or a multiple system. This event is credited with ejecting AE Aurigae, Mu Columbae and 53 Arietis at above 200 km·s−1 and has been traced to the Trapezium cluster in the Orion Nebula some two million years ago.
== Designations and nomenclature ==
=== Multiple star designations ===
The components of multiple stars can be specified by appending the suffixes A, B, C, etc., to the system's designation. Suffixes such as AB may be used to denote the pair consisting of A and B. The sequence of letters B, C, etc. may be assigned in order of separation from the component A. Components discovered close to an already known component may be assigned suffixes such as Aa, Ba, and so forth.
=== Nomenclature in the Multiple Star Catalogue ===
A. A. Tokovinin's Multiple Star Catalogue uses a system in which each subsystem in a mobile diagram is encoded by a sequence of digits. In the mobile diagram (d) above, for example, the widest system would be given the number 1, while the subsystem containing its primary component would be numbered 11 and the subsystem containing its secondary component would be numbered 12. Subsystems which would appear below this in the mobile diagram will be given numbers with three, four, or more digits. When describing a non-hierarchical system by this method, the same subsystem number will be used more than once; for example, a system with three visual components, A, B, and C, no two of which can be grouped into a subsystem, would have two subsystems numbered 1 denoting the two binaries AB and AC. In this case, if B and C were subsequently resolved into binaries, they would be given the subsystem numbers 12 and 13.
=== Future multiple star system nomenclature ===
The current nomenclature for double and multiple stars can cause confusion as binary stars discovered in different ways are given different designations (for example, discoverer designations for visual binary stars and variable star designations for eclipsing binary stars), and, worse, component letters may be assigned differently by different authors, so that, for example, one person's A can be another's C. Discussion starting in 1999 resulted in four proposed schemes to address this problem:
KoMa, a hierarchical scheme using upper- and lower-case letters and Arabic and Roman numerals;
The Urban/Corbin Designation Method, a hierarchical numeric scheme similar to the Dewey Decimal Classification system;
The Sequential Designation Method, a non-hierarchical scheme in which components and subsystems are assigned numbers in order of discovery; and
WMC, the Washington Multiplicity Catalog, a hierarchical scheme in which the suffixes used in the Washington Double Star Catalog are extended with additional suffixed letters and numbers.
For a designation system, identifying the hierarchy within the system has the advantage that it makes identifying subsystems and computing their properties easier. However, it causes problems when new components are discovered at a level above or intermediate to the existing hierarchy. In this case, part of the hierarchy will shift inwards. Components which are found to be nonexistent, or are later reassigned to a different subsystem, also cause problems.
During the 24th General Assembly of the International Astronomical Union in 2000, the WMC scheme was endorsed and it was resolved by Commissions 5, 8, 26, 42, and 45 that it should be expanded into a usable uniform designation scheme. A sample of a catalog using the WMC scheme, covering half an hour of right ascension, was later prepared. The issue was discussed again at the 25th General Assembly in 2003, and it was again resolved by commissions 5, 8, 26, 42, and 45, as well as the Working Group on Interferometry, that the WMC scheme should be expanded and further developed.
The sample WMC is hierarchically organized; the hierarchy used is based on observed orbital periods or separations. Since it contains many visual double stars, which may be optical rather than physical, this hierarchy may be only apparent. It uses upper-case letters (A, B, ...) for the first level of the hierarchy, lower-case letters (a, b, ...) for the second level, and numbers (1, 2, ...) for the third. Subsequent levels would use alternating lower-case letters and numbers, but no examples of this were found in the sample.
== Examples ==
=== Binary ===
Sirius, a binary consisting of a main-sequence type A star and a white dwarf
Procyon, which is similar to Sirius
Mira, a variable consisting of a red giant and a white dwarf
Delta Cephei, a Cepheid variable
Almaaz, an eclipsing binary
Spica
=== Triple ===
Alpha Centauri is a triple star composed of a main binary Yellow dwarf and an Orange dwarf pair (Rigil Kentaurus and Toliman), and an outlying red dwarf, Proxima Centauri. Together, Rigil Kentaurus and Toliman form a physical binary star, designated as Alpha Centauri AB, α Cen AB, or RHD 1 AB, where the AB denotes this is a binary system. The moderately eccentric orbit of the binary can make the components be as close as 11 AU or as far away as 36 AU. Proxima Centauri, also (though less frequently) called Alpha Centauri C, is much farther away (between 4300 and 13,000 AU) from α Cen AB, and orbits the central pair with a period of 547,000 (+66,000/-40,000) years.
Polaris or Alpha Ursae Minoris (α UMi), the north star, is a triple star system in which the closer companion star is extremely close to the main star—so close that it was only known from its gravitational tug on Polaris A (α UMi A) until it was imaged by the Hubble Space Telescope in 2006.
Gliese 667 is a triple star system with two K-type main sequence stars and a red dwarf. The red dwarf, C, hosts between two and seven planets, of which one, Cc, alongside the unconfirmed Cf and Ce, are potentially habitable.
HD 188753 is a triple star system located approximately 149 light-years away from Earth in the constellation Cygnus. The system is composed of HD 188753A, a yellow dwarf; HD 188753B, an orange dwarf; and HD 188753C, a red dwarf. B and C orbit each other every 156 days, and, as a group, orbit A every 25.7 years.
Fomalhaut (α PsA, α Piscis Austrini) is a triple star system in the constellation Piscis Austrinus. It was discovered to be a triple system in 2013, when the K type flare star TW Piscis Austrini and the red dwarf LP 876-10 were all confirmed to share proper motion through space. The primary has a massive dust disk similar to that of the early Solar System, but much more massive. It also contains a gas giant, Fomalhaut b. That same year, the tertiary star, LP 876-10 was also confirmed to house a dust disk.
HD 181068 is a unique triple system, consisting of a red giant and two main-sequence stars. The orbits of the stars are oriented in such a way that all three stars eclipse each other.
=== Quadruple ===
Capella, a pair of giant stars orbited by a pair of red dwarfs, around 42 light years away from the Solar System. It has an apparent magnitude of around 0.08, making Capella one of the brightest stars in the night sky.
4 Centauri
Mizar is often said to have been the first binary star discovered when it was observed in 1650 by Giovanni Battista Riccioli, p. 1 but it was probably observed earlier, by Benedetto Castelli and Galileo. Later, spectroscopy of its components Mizar A and B revealed that they are both binary stars themselves.
HD 98800
The PH1 system has the planet PH1 b (discovered in 2012 by the Planet Hunters group, a part of the Zooniverse) orbiting two of the four stars, making it the first known planet to be in a quadruple star system.
KOI-2626 is the first quadruple star system with an Earth-sized planet.
Xi Tauri (ξ Tau, ξ Tauri), located about 222 light years away, is a spectroscopic and eclipsing quadruple star consisting of three blue-white B-type main-sequence stars, along with an F-type star. Two of the stars are in a close orbit and revolve around each other once every 7.15 days. These in turn orbit the third star once every 145 days. The fourth star orbits the other three stars roughly every fifty years.
=== Quintuple ===
Dabih
Mintaka
HD 155448
KIC 4150611
1SWASP J093010.78+533859.5
=== Sextuple ===
Beta Tucanae
Castor
HD 139691
TYC 7037-89-1
If Alcor is considered part of the Mizar system, the system can be considered a sextuple.
=== Septuple ===
Jabbah
AR Cassiopeiae
V871 Centauri
=== Octuple ===
Gamma Cassiopeiae
=== Nonuple ===
QZ Carinae
== See also ==
Exoplanet
Solar System
== Footnotes ==
== References ==
== External links ==
NASA Astronomy Picture of the Day: Triple star system (11 September 2002)
NASA Astronomy Picture of the Day: Alpha Centauri system (23 March 2003)
Alpha Centauri, APOD, 2002 April 25
General news on triple star systems, TSN, 2008 April 22 Archived 3 April 2019 at the Wayback Machine
The Double Star Library Archived 15 December 2008 at the Wayback Machine is located at the U.S. Naval Observatory
Naming New Extrasolar Planets
=== Individual specimens ===
NASA Astronomy Picture of the Day: Triple star system (11 September 2002)
NASA Astronomy Picture of the Day: Alpha Centauri system (23 March 2003)
Alpha Centauri, APOD, 2002 April 25 | Wikipedia/Stellar_systems |
Chromatography software is called also Chromatography Data System. It is located in the data station of the modern liquid, gas or supercritical fluid chromatographic systems. This is a dedicated software connected to an hardware interface within the chromatographic system, which serves as a central hub for collecting, analyzing, and managing the data generated during the chromatographic analysis.
The data station is connected to the entire instrument in modern systems, especially the detectors, allowing real-time monitoring of the runs, exhibiting them as chromatograms. A chromatogram is a graphical representation of the results obtained from the chromatographic system. In a chromatogram, each component of the mixture appears as a peak or band at a specific retention time, which is related to its characteristics, such as molecular weight, polarity, and affinity for the stationary phase. The height, width, and area of the peaks in a chromatogram provide information about the amount and purity of the components in the sample. Analyzing a chromatogram helps identify and quantify the substances present in the mixture being analyzed.
== Integration & Processing ==
The major tool of the chromatographic software is peaks "integration". A series of articles describes it: Peak Integration Part 1, Peak Integration Part 2, Peak Integration Part 3. The parameters inside the chromatography software which affect the integration are called the Integration events.
Peak integration in any chromatographic software refers to the process of quantifying the areas under the peak's curve in the chromatogram. The area under the peak is proportional to the amount of that particular component in the sample.
Here are the basics of peak integration in a chromatographic system:
Peak Identification: Before integration, the peaks corresponding to different components in the sample need to be identified, based on their retention times. This is typically done by comparing the observed peaks with known standards or reference data.
Baseline Correction: Establish a baseline for the chromatogram, which represents the lowest signal level along the time axis next to the peak. The baseline represents the noise and background signal. Taking into account the baseline level allows an accurate integration, because it takes into account any drift or fluctuations in the baseline.
Peak Integration parameters and settings: Use appropriate algorithms to integrate the peaks in the chromatogram. Adjust integration parameters and settings as needed, such as noting peak width, noise threshold, and baseline correction method, which determine where the peak starts and ends and its maximum point. Optimizing these parameters helps obtain accurate and precise integration results.
Quantification: Once the areas under the peaks are determined through integration, the quantification of each component is performed. The integrated areas are compared to a calibration curve, created using standards' concentrations to calculate the concentration of each component in the unknown sample.
Data Interpretation: The software analyzes the integrated data to draw conclusions about the composition, concentration, and purity of the sample. The integrated areas provide valuable information for various applications, including quality control, research, and analysis.
Validation and Quality Control: It is important to ensure the accuracy and reliability of the integration process, by performing validation and quality control checks to the software itself. This may involve comparing integration results with known standards, replicating analyses, and assessing precision and accuracy
Applications are also available for simulation of chromatography, for example for teaching, demonstration, or for method development &/or optimization.
== Software Packages ==
Many chromatography software packages are provided by manufacturers, and many of them only provide a simple interface to acquire data. They also provide different tools to analyze this data.
The following is a list of software and the (unexplained) tools that each provides. Please note that some of them were discontinued with the years.
== See also ==
Laboratory informatics
== References == | Wikipedia/Chromatography_software |
Chiral column chromatography is a variant of column chromatography that is employed for the separation of chiral compounds, i.e. enantiomers, in mixtures such as racemates or related compounds. The chiral stationary phase (CSP) is made of a support, usually silica based, on which a chiral reagent or a macromolecule with numerous chiral centers is bonded or immobilized.
The chiral stationary phase can be prepared by attaching a chiral compound to the surface of an achiral support such as silica gel. For example, one class of the most commonly used chiral stationary phases both in liquid chromatography and supercritical fluid chromatography is based on oligosaccharides such as Amylose Cellulose or Cyclodextrin (in particular with β-cyclodextrin, a seven sugar ring molecule) immobilized on silica gel.
The principle can be also applied to the fabrication of Monolithic HPLC columns or Gas Chromatography columns. or Supercritical Fluid Chromatography columns.
== Principle of Chiral Column Chromatography ==
The chiral stationary phase, CSP, can interact differently with two enantiomers, by a process known as chiral recognition. Chiral recognition depends on various interactions such as hydrogen bonding, π-π interaction, dipole stacking, inclusion complexation, steric, hydrophobic and electrostatic interaction, charge-transfer interactions, ionic interactions etc, between the analyte and the CSP, to form in-situ transient-diastereomeric complexes.
Most of the types of stationary phases can be classified as Pirkle type (Brush type), Protein-based, Cyclodextrins based, Polymer-based carbohydrates (polysaccharide-based CSPs), Macrocyclic antibiotic, Chiral crown ethers, imprinted polymers, etc.
=== Brush type columns (Pirkle Type) ===
The brush type, or Pirkle type chiral stationary phases are also called π-π Donnor-Acceptor columns. According to some theoretical models separation on these CSPs are based on a three-point attachment between the solute and the bonded chiral ligand on the surface of the stationary phase. These interactions may be attractive or repulsive in nature, depending on the mutual properties. Pirkle columns discriminate enantiomers by binding of one enantiomer with the chiral stationary phase, thereby forming a diastereomeric complex through π-π bonding, hydrogen bonding, steric interactions, and/or dipole stacking. Pirkle CSP can be categorized into three classes:
(i) π-electron acceptor
(ii) π-electron donor
(iii) π-electron donor-π-electron acceptor.
=== Protein-based chiral stationary phases ===
A protein-based chiral stationary phase is based on silica-gel, on which a protein is immobilized or bonded. The protein is based on many chiral centers, therefore the mechanism of chiral interaction between the protein and the analytes involves many interactions, such as hydrophobic and electrostatic interactions, hydrogen bonding and charge-transfer interactions, which may contribute to chiral recognition. Hydrophobic interactions between the protein and the analyte are affected by percent organic in the mobile phase. As the organic content increases, retention on protein-based columns decreases.
=== Polysaccharide chiral stationary phases ===
The naturally occurring polysaccharide form the basis for an important group of columns designed for chiral separation. The main polysaccharides are cellulose, amylose, chitosan, dextran, xylan, curdlan, and inulin. Polysaccharide-based stationary phase have a high loading capacity, many chiral centers and complicated stereochemistry, and can be used for the separation of a wide range of compounds.
Polysaccharide-based chiral stationary phases have a wide application due to their high separation efficiency, selectivity, sensitivity and reproducibility under normal and reversed-phase conditions, as well as their broad applicability for structurally diversified compounds. The mechanism of chiral interaction on the polysaccharide-based chiral stationary phase has not yet been elucidated. However, the following interactions are believed to play a role in the retention:
(i) Hydrogen bonding interactions of the polar chiral analyte with carbamate groups on the CSP;
(ii) π-π interactions between phenyl groups on the CSP and aromatic groups of the solute;
(i) Dipole-dipole interactions
(ii) Steric interactions due to the helical structure of the CSP.
These effects on the retention process originate also from the functionality of the derivatives of the polysaccharide, its average molecular weight, and size distribution, the solvent used to immobilize it on the macroporous silica support, and the nature of the macroporous silica support itself.
=== Cyclodextrin (CD) chiral stationary phases ===
Cyclodextrin (CD) chiral stationary phase is produced by partial degradation of starch by the enzyme cyclodextrin glycosyltransferase, followed by enzymatic coupling of the glucose units, forming a toroidal structure. CDs are cyclic oligosaccharides consisting of six (α CDs), seven (β CDs) and eight (γ CDs) glucopyranose units. The chiral recognition mechanism is based on a sort of inclusion complexation. Complexation involves the interaction of the hydrophobic portion of an analyte enantiomer with the non-polar interior of the cavity, while the polar functional groups can form a hydrogen bond with the polar hydroxyl chiral cavity space. The most important factor that determines whether the analyte molecule will fit into the cyclodextrin cavity is its size. The α-CD consists of 30 stereo-selective centers, β-CD consists of 35 stereo-selective centers and γ-CD consists of 40 stereo-selective centers. When the hydrophobic portion of the analyte is larger or smaller than the toroid's cavity size, inclusion will not occur.
=== Macrocyclic chiral stationary phases ===
Macrocyclic chiral stationary phases consist of a silica support, on which macrocyclic antibiotic molecules are bonded. The commonly used macrocyclic antibiotics include rifamycin, glycopeptides (for example, avoparcin, teicoplanin, ristocetin A, vancomycin, and their analogs), polypeptide antibiotic thiostrepton, and aminoglycosides (for example, fradiomycin, kanamycin, and streptomycin). The macrocyclic antibiotics interact with the analyte through hydrogen bonds, dipole-dipole interactions with the polar groups of the analyte, ionic interactions and π-π interactions.
=== Chiral crown ether ===
Chiral crown stationary phases consist Crown ethers, immobilized or bonded to the support particles, are polyethers with a macrocyclic structure that can create host-guest complexes with alkali, earth-alkali metal ions, and ammonium cations. The skeleton of the cyclic structure is composed of oxygen and methylene groups arranged alternately. The electron-donating ether oxygens are positioned within the inner wall of the crown cavity, and are encircled by methylene groups in a collar-like arrangement. The chiral recognition is based on two distinct diastereomeric inclusion complexes that can be generated. The primary interactions facilitating complexation involve hydrogen bonds, formed between the three amine hydrogens and the oxygens of the macrocyclic ether, arranged in a tripod configuration. Additionally, ionic interactions, dipole-dipole interactions, or hydrogen bonds can occur between the carbocyclic groups and polar groups of the analytes, providing further support for the complexes.
=== Method Development ===
Method development of chiral chromatography is still done by screening of columns from the various classes of chiral columns. While chiral separation mechanisms are understandable in certain scenarios, and the retention characteristics of analytes within the chromatographic columns can occasionally be elucidated, the precise combination of chiral stationary phases (CSPs) and mobile-phase compositions that required to effectively resolve a specific enantiomeric pair often remains elusive.
The chemistry of CSP ligands significantly influences the creation of in-situ diastereomeric complexes upon the stationary phase surface. However, other method's conditions, such as mobile-phase solvents, their composition, mobile phase additives and column temperature can play equally critical roles. The final resolution of the enantiomers is the outcome of combination of intermolecular forces, and even a subtle change in them can determine the success or failure of separation. This complexity prevents from establishing routine method-development protocols that are universally applicable to a diverse range of enantiomers. In fact, sometimes the outcome of previous unsuccessful experiments do not provide any clue for the subsequent steps. Therefore, in practice, a chiral method development laboratory settings, acts like a high-throughput screening protocol, of conducting a systematic screening of various CSP's by advanced column switching devices, trying automatically and systematically various mobile-phase combinations, effectively employing a trial-and-error strategy.
Because of the highly complex retention mechanism of a chiral stationary-phase due to chiral recognition, whose principles have not been deciphered, it is often difficult, if not impossible to predict in advance the steps that can be successfully applied to the enantiomers at hand as part of method development. That's why the standard approach in the method development is high throughput screening, to evaluate or examine a series of stationary phases, using various mobile-phase combinations, to increase the chance of finding a suitable separation condition.
== See also ==
Chiral thin-layer chromatography
== References ==
This article incorporates text by Celina Nazareth and Sanelly Pereira available under the CC BY 4.0 license. | Wikipedia/Chiral_column_chromatography |
Countercurrent chromatography (CCC, also counter-current chromatography) is a form of liquid–liquid chromatography that uses a liquid stationary phase that is held in place by inertia of the molecules composing the stationary phase accelerating toward the center of a centrifuge due to centripetal force and is used to separate, identify, and quantify the chemical components of a mixture. In its broadest sense, countercurrent chromatography encompasses a collection of related liquid chromatography techniques that employ two immiscible liquid phases without a solid support. The two liquid phases come in contact with each other as at least one phase is pumped through a column, a hollow tube or a series of chambers connected with channels, which contains both phases. The resulting dynamic mixing and settling action allows the components to be separated by their respective solubilities in the two phases. A wide variety of two-phase solvent systems consisting of at least two immiscible liquids may be employed to provide the proper selectivity for the desired separation.
Some types of countercurrent chromatography, such as dual flow CCC, feature a true countercurrent process where the two immiscible phases flow past each other and exit at opposite ends of the column. More often, however, one liquid acts as the stationary phase and is retained in the column while the mobile phase is pumped through it. The liquid stationary phase is held in place by gravity or inertia of the molecules composing the stationary phase accelerating toward the center of a centrifuge due to centripetal force. An example of a gravity method is called droplet counter current chromatography (DCCC). There are two modes by which the stationary phase is retained by centripetal force: hydrostatic and hydrodynamic. In the hydrostatic method, the column is rotated about a central axis. Hydrostatic instruments are marketed under the name centrifugal partition chromatography (CPC). Hydrodynamic instruments are often marketed as high-speed or high-performance countercurrent chromatography (HSCCC and HPCCC respectively) instruments which rely on the Archimedes' screw force in a helical coil to retain the stationary phase in the column.
The components of a CCC system are similar to most liquid chromatography configurations, such as high-performance liquid chromatography (HPLC). One or more pumps deliver the phases to the column which is the CCC instrument itself. Samples are introduced into the column through a sample loop filled with an automated or manual syringe. The outflow is monitored with various detectors such as ultraviolet–visible spectroscopy or mass spectrometry. The operation of the pumps, CCC instrument, sample injection, and detection may be controlled manually or with a microprocessor.
== History ==
The predecessor of modern countercurrent chromatography theory and practice was countercurrent distribution (CCD). The theory of CCD was described in the 1930s by Randall and Longtin. Archer Martin and Richard Laurence Millington Synge developed the methodology further during the 1940s. Finally, Lyman C. Craig introduced the Craig countercurrent distribution apparatus in 1944 which made CCD practical for laboratory work. CCD was used to separate a wide variety of useful compounds for several decades.
== Support-free liquid chromatography ==
Standard column chromatography consists of a solid stationary phase and a liquid mobile phase, while gas chromatography (GC) uses a solid or liquid stationary phase on a solid support and a gaseous mobile phase. By contrast, in liquid-liquid chromatography, both the mobile and stationary phases are liquid. The contrast is, however, not as stark as it first appears. In reversed-phase chromatography, for example, the stationary phase can be regarded as a liquid which is immobilized by chemical bonding to a micro-porous silica solid support. In countercurrent chromatography centripetal or gravitational forces immobilize the stationary liquid layer. By eliminating solid supports, permanent adsorption of the analyte onto the column is avoided, and a high recovery of the analyte can be achieved. The countercurrent chromatography instrument is easily switched between normal phase chromatography and reversed-phase chromatography simply by changing the mobile and stationary phases. With column chromatography, the separation potential is limited by the commercially available stationary phase media and its particular characteristics. Nearly any pair of immiscible solutions can be used in countercurrent chromatography provided that the stationary phase can be successfully retained.
Solvent costs are also generally lower than for HPLC. In comparison to column chromatography, flows and total solvent usage can in most countercurrent chromatography separations may be reduced by half and even up to a tenth. Also, the cost of purchasing and disposing of stationary phase media is eliminated. Another advantage of countercurrent chromatography is that experiments conducted in the laboratory can be scaled to industrial volumes. When gas chromatography or HPLC is carried out with large volumes, resolution is lost due to issues with surface-to-volume ratios and flow dynamics; this is avoided when both phases are liquid.
The CCC separation process can be thought of as occurring in three stages: mixing, settling, and separation of the two phases (although they often occur continuously). Vigorous mixing of the phases is critical in order to maximize the interfacial area between them and enhance mass transfer. The analyte will distribute between the phases according to its partition coefficient which is also called the distribution coefficient, distribution constant, or partition ratio and is represented by P, K, D, Kc, or KD. The partition coefficient for an analyte in a particular biphasic solvent system is independent of the volume of the instrument, flow rate, stationary phase retention volume ratio and the g-force required to immobilize the stationary phase. The degree of stationary phase retention is a crucial parameter. Common factors that influence stationary phase retention are flow rate, solvent composition of the biphasic solvent system, and the g-force. The stationary phase retention is represented by the stationary phase volume retention ratio (Sf) which is the volume of the stationary phase divided by the total volume of the instrument. The settling time is a property of the solvent system and the sample matrix, both of which greatly influence stationary phase retention.
To most process chemists, the term "countercurrent" implies two immiscible liquids moving in opposing directions, as typically occurs in large centrifugal extractor units. With the exception of dual flow (see below) CCC, most countercurrent chromatography modes of operation have a stationary phase and a mobile phase. Even in this situation, countercurrent flows occur within the instrument column. Several researchers have proposed renaming both CCC & CPC to liquid-liquid chromatography, but others feel the term "countercurrent" itself is a misnomer.
Unlike column chromatography and HPLC, countercurrent chromatography operators can inject large volumes relative to column volume. Typically 5 to 10% of coil volume can be injected. In some cases this can be increased to as high as 15 to 20% of the coil volume. Typically, most modern commercial CCC and CPC can inject 5 to 40 g/L capacity. The range is so large, even for a specific instrument, let alone all instrument options, as the type of target, matrix and available biphasic solvent vary so much. Approximately 10 g/L would be a more typical value, that the majority of applications could use as a base value.
The countercurrent separation starts with choosing an appropriate biphasic solvent system for the desired separation. A wide array of biphasic solvent mixtures are available to the CCC practitioner including the combination n-hexane (or heptane), ethyl acetate, methanol and water in different proportions. This basic solvent system is sometimes referred to as the HEMWat solvent system. The choice of solvent system may be guided by perusal of the CCC literature. The familiar technique of thin layer chromatography may also be employed to determine an optimal solvent system. The organization of solvent systems into "families" has greatly facilitated the choice of solvent systems as well. A solvent system can be tested with a one-flask partitioning experiment. The measured partition coefficient from the partitioning experiment will indicate the elution behavior of the compound. Typically, it is desirable to choose a solvent system where the target compound(s) have a partition coefficient between 0.25 and 8. Historically, it was thought that no commercial countercurrent chromatograph could cope with the high viscosities of ionic liquids. However, modern instruments that can accommodate 30 to 70+ % ionic liquids (and potentially 100% ionic liquid, if both phases are suitably customized ionic liquids) have become available. Ionic liquids can be customized for polar / non-polar organic, achiral and chiral compounds, bio-molecule, and inorganic separations, as ionic liquids can be customized to have extraordinary solvency and specificity.
After the biphasic solvent system has been chosen a batch of is formulated and equilibrated in a separatory funnel. This step is called pre-equilibration of the solvent system. The two phases are separated. Then the column is filled with stationary with a pump. Next, the column is set an equilibration conditions, such as the desired rotation speed, and the mobile phase is pumped through the column. The mobile phase displaces the a portion of the stationary phase until column equilibration is achieved and the mobile phase elutes from the column. The sample may be introduced into the column at any time during the column equilibration step or after equilibration has been accomplished. After the volume of eluant surpasses the volume of the mobile phase in the column, the sample components will begin to elute. Compounds with a partition coefficient of unity will elute when one column volume of mobile phase has passed through the column since the time of injection. The compound can then be introduced to another stationary phase to help increase the resolution of results. The flow is stopped after the target compound(s) are eluted or the column is extruded by pumping the stationary phase through the column. An example of a major application of countercurrent chromatography is to take an extremely complex matrix such as a plant extract, perform the countercurrent chromatography separation with a carefully selected solvent system, and extrude the column to recover all of the sample. The original complex matrix will have been fractionated into discrete narrow polarity bands, which may then be assayed for chemical composition or bioactivity. Performing one or more countercurrent chromatography separations in conjunction with other chromatographic and non chromatographic techniques has the potential for rapid advances in compositional recognition of extremely complex matrices.
== Droplet CCC ==
Droplet countercurrent chromatography (DCCC) was introduced in 1970 by Tanimura, Pisano, Ito, and Bowman. DCCC uses only gravity to move the mobile phase through the stationary phase which is held in long vertical tubes connected in series. In the descending mode, droplets of the denser mobile phase and sample are allowed to fall through the columns of the lighter stationary phase using only gravity. If a less-dense mobile phase is used it will rise through the stationary phase; this is called ascending mode. The eluent from one column is transferred to another; the more columns that are used, the more theoretical plates can be achieved. DCCC enjoyed some success with natural product separations but was largely eclipsed by the rapid development of high-speed countercurrent chromatography. The main limitation of DCCC is that flow rates are low, and poor mixing is achieved for most binary solvent systems.
== Hydrodynamic CCC ==
The modern era of CCC began with the development of the planetary centrifuge by Dr. Yoichiro Ito which was first introduced in 1966 as a closed helical tube which was rotated on a "planetary" axis as is turned on a "sun" axis. A flow-through model was subsequently developed and the new technique was called countercurrent chromatography in 1970. The technique was further developed by employing test mixtures of DNP amino acids in a chloroform:glacial acetic acid:0.1 M aqueous hydrochloric acid (2:2:1 v/v) solvent system. Much development was needed to engineer the instrument so that required planetary motion could be sustained while the phases were being pumped through the coil(s). Parameters such as the relative rotation of the two axes (synchronous or non-synchronous), the direction of flow through the coil, and the rotor angles were investigated.
=== High-speed ===
By 1982 the technology was sufficiently advanced for the technique to be called "high-speed" countercurrent chromatography (HSCCC). Peter Carmeci initially commercialized the PC Inc. Ito Multilayer Coil Separator/Extractor which utilized a single bobbin (onto which the coil is wound) and a counterbalance, plus a set of "flying leads" which are tubing that connect the bobbins. Dr. Walter Conway & others later evolved the bobbin design such that multiple coils, even coils of different tubing sizes, could be placed on the single bobbin. Edward Chou later evolved and commercialized a triple bobbin design as the Pharmatech CCC which had a de-twist mechanism for leads between the three bobbins. The Quattro CCC released in 1993 further evolved the commercially available instruments by utilizing a novel mirror image, twin bobbin design that did not need the de-twist mechanism of the Pharmatech between the multiple bobbins, so could still accommodate multiple bobbins on the same instrument. Hydrodynamic CCC are now available with up to 4 coils per instrument. These coils can be in PTFE, PEEK, PVDF, or stainless steel tubing. The 2, 3 or 4 coils can all be of the same bore to facilitate "2D" CCC (see below). The coils may be connected in series to lengthen the coil and increase the capacity, or the coils may be linked in parallel so that 2, 3, or 4 separations may be done simultaneously. The coils can also be of different sizes, on one instrument, ranging from 1 to 6 mm on one instrument, thus allowing a single instrument to optimize from mg to kilos per day. More recently instrument derivatives have been offered with rotating seals for various hydrodynamic CCC designs, instead of flying leads, either as custom or standard options.
=== High-performance ===
The operating principle of CCC equipment requires a column consisting of a tube coiled around a bobbin. The bobbin is rotated in a double-axis gyratory motion (a cardioid), which causes a variable g-force to act on the column during each rotation. This motion causes the column to see one partitioning step per revolution and components of the sample separate in the column due to their partitioning coefficient between the two immiscible liquid phases. "High-performance" countercurrent chromatography (HPCCC) works in much the same way as HSCCC. A seven-year research and development process produced HPCCC instruments that generated 240 g's, compared to the 80 g's of the HSCCC machines. This increase in g-force and larger bore of the column has enabled a ten-fold increase in throughput, due to improved mobile phase flow rates and a higher stationary phase retention. Countercurrent chromatography is a preparative liquid chromatography technique, however with the advent of the higher-g HPCCC instruments it is now possible to operate instruments with sample loadings as low as a few milligrams, whereas in the past hundreds of milligrams had been necessary. Major application areas for this technique include natural product purification and drug development.
== Hydrostatic CCC ==
Hydrostatic CCC or centrifugal partition chromatography (CPC) was invented in the 1980s by the Japanese company Sanki Engineering Ltd, whose president was Kanichi Nunogaki. CPC has been extensively developed in France starting from the late 1990s. In France, they initially optimized the stacked disc concept initiated by Sanki. More recently, in France and UK, non-stacked disc CPC configurations have been developed with PTFE, stainless steel or titanium rotors. These have been designed to overcome possible leakages between the stacked discs of the original concept, and to allow steam cleaning for good manufacturing practice. The volumes ranging from a 100 ml to 12 liters are available in different rotor materials. The 25-liter rotor CPC has a titanium rotor. This technique is sometimes sold under the name "fast" CPC or "high-performance" CPC.
=== Realization ===
The centrifugal partition chromatograph instrument is constituted with a unique rotor which contains the column. This rotor rotates on its central axis (while HSCCC column rotates on its planetary axis and simultaneously rotates eccentrically about another solar axis). With less vibrations and noise, the CPC offers a typical rotation speed range from 500 to 2000 rpm. Contrary to hydrodynamic CCC, the rotation speed is not directly proportional to the retention volume ratio of the stationary phase. Like DCCC, CPC can be operated in either descending or ascending mode, where the direction is relative to the force generated by the rotor rather than gravity. A redesigned CPC column with larger chambers and channels has been named centrifugal partition extraction (CPE). In the CPE design, faster flow rates and increased column loading can be achieved.
=== Advantages ===
CPC offers direct scale-up from analytical apparatuses (few milliliters) to industrial apparatuses (several liters) for fast batch-production. CPC seems particularly suited to accommodate aqueous two-phase solvent systems. Generally, CPC instruments can retain solvent systems that are not well-retained in a hydrodynamic instrument due to small differences in density between the phases. It has been very helpful for the development of CPC instrumentation to visualize the flow patterns which give rise to the mixing and settling in the CPC chamber with an asynchronous camera and a stroboscope triggered by the CPC rotor.
== Modes of operation ==
The aforementioned hydrodynamic and hydrostatic instruments may be employed in a variety of ways, or modes of operation, in order to address the particular separation needs of the scientist. Many modes of operation have been devised to take advantage of the strengths and potentialities of the countercurrent chromatography technique. Generally, the following modes may be performed with commercially available instruments.
=== Normal-phase ===
Normal phase elution is achieved by pumping the non-aqueous or phase of a biphasic solvent system through the column as the mobile phase, with a more polar stationary phase being retained in the column. The cause of original nomenclature of is relevant. As original stationary phases of paper chromatography were superseded by more efficient materials such as diatomaceous earths (natural micro-porous silica) and followed by modern silica gel, the thin-layer chromatography stationary phase was polar (hydroxy groups attached to silica) and maximum retention was achieved with non-polar solvents such as n-hexane. Progressively more polar eluents were then used to move polar compounds up the plate. Various alkane bonded phases were tried with C18 becoming the most popular. Alkane chains were chemically bonded to the silica, and a reversal of the elution trend occurred. Thus a polar stationary became "normal" phase chromatography, and the non-polar stationary phase chromatography became "reversed" phase chromatography.
=== Reversed-phase ===
In reversed-phase (e.g. aqueous mobile phase) elution, the aqueous phase is used as the mobile phase with a less polar stationary phase. In countercurrent chromatography the same solvent system may be used in either normal or reversed phase mode simply by switching the direction of mobile phase flow through the column.
=== Elution-extrusion ===
The extrusion of stationary phase from the column at the end of a separation experiment by stopping rotation and pumping solvent or gas through the column was used by CCC practitioners before the term EECCC was suggested. In elution-extrusion mode (EECCC), The mobile phase is extruded after a certain point by switching the phase being pumped into the system whilst maintaining rotation. For example, if the separation has been initiated with the aqueous phase as the mobile phase at a certain point the organic phase is pumped through the column which effectively pushes out both phases that are present in the column at the time of switching. The complete sample is eluted in the order of polarity (either normal or reversed) without loss of resolution by diffusion. It requires only one column volume of solvent phase and leaves the column full of fresh stationary phase for the subsequent separation.
=== Gradient ===
The use of a solvent gradient is very well developed in column chromatography but is less common in CCC. A solvent gradient is produced by increasing (or decreasing) the polarity of the mobile phase during the separation to achieve optimal resolution across a wider range of polarities. For example, a methanol-water mobile phase gradient may be employed using heptane as the stationary phase. This is not possible with all biphasic solvent systems, due to excessive loss of stationary phase created by disruption the equilibrium conditions within the column. Gradients may either be produced in steps, or continuously.
=== Dual-mode ===
In dual-mode, the mobile and stationary phases are reversed part way through the separation experiment. This requires changing the phase being pumped through the column as well as the direction of flow. Dual-mode operation is likely to elute the entire sample from the column but the order of elution is disrupted by switching the phase and direction of flow.
=== Dual-flow ===
Dual-flow, also known as dual, countercurrent chromatography occurs when both phases are flowing in opposite directions inside the column. Instruments are available for dual-flow operation for both Hydrodynamic and hydrostatic CCC. Dual-flow countercurrent chromatography was first described by Yoichiro Ito in 1985 for foam CCC where gas-liquid separations were performed. Liquid–liquid separations soon followed. The countercurrent chromatography instrument must be modified so that both ends of the column have both inlet and outlet capabilities. This mode may accommodate continuous or sequential separations with the sample being introduced in the middle of the column or between two bobbins in a hydrodynamic instrument. A technique called intermittent countercurrent
extraction (ICcE) is a quasi-continuous method where the flow of the phases is alternated "intermittently" between normal and reversed-phase elution so that the stationary phase also alternates.
=== Recycling and Sequential ===
Recycling chromatography is mode practiced in both HPLC and CCC. In recycling chromatography, the target compounds are reintroduced into the column after they elute. Each pass through the column increases the number of theoretical plates the compounds experience and enhances chromatographic resolution. Direct recycling must be done with an isocratic solvent system. With this mode, the eluant can be selectively re-chromatographed on the same or a different column in order to facilitate the separation. This process of selective recycling has been termed a "heart-cut" and is especially effective in purifying selected target compounds with some sacrificial loss of recovery. The process of re-separating selected fractions from one chromatography experiment with another chromatographic method has long been practiced by scientists. Recycling and sequential chromatography is a streamlined version of this process. In CCC, the separation characteristics of the column may be modified simply by changing the composition of the biphasic solvent system.
=== Ion-exchange and pH-Zone-refining ===
In an conventional CCC experiment the biphasic solvent system is pre-equilibrated before the instrument is filled with the stationary phase and equilibrated with the mobile phase. An ion-exchange mode has been created by modifying both of the phases after pre-equilibration. Generally, an ionic displacer (or eluter) is added to mobile phase and an ionic retainer is added to the stationary phase. For example, the aqueous mobile phase may contain NaI as a displacer and the organic stationary phase may be modified with the quaternary ammonium salt called Aliquat 336 as a retainer. The mode known a pH-zone-refining is a type of ion-exchange mode that utilizes acids and/or bases as solvent modifiers. Typically, the analytes are eluted in an order determined by their pKa values. For example, 6 oxindole alkaloids were isolated from a 4.5g sample of Gelsemium elegans stem extract with a biphasic solvent system composed of hexane–ethyl acetate–methanol–water (3:7:1:9, v/v) where 10 mM triethylamine (TEA) was added to the upper organic stationary phase as a retainer and 10 mM hydrochloric acid (HCl) to the aqueous mobile phase as an eluter. Ion-exchange modes such as pH-zone-refining have tremendous potential because high sample loads can be achieved without sacrificing separation power. It works best with ionizable compounds such as nitrogen containing alkaloids or carboxylic acid containing fatty acids.
== Applications ==
Countercurrent chromatography and related liquid-liquid separation techniques have been used on both industrial and laboratory scale to purify a wide variety of chemical substances. Separation realizations include proteins, DNA, Cannabidiol (CBD) from Cannabis Sativa antibiotics, vitamins, natural products, pharmaceuticals, metal ions, pesticides, enantiomers, polyaromatic hydrocarbons from environmental samples, active enzymes, and carbon nanotubes. Countercurrent chromatography is known for its high dynamic range of scalability: milligram to kilogram quantities purified chemical components may be obtained with this technique. It also has the advantage of accommodating chemically complex samples with undissolved particulates.
== See also ==
History of chromatography
Supercritical fluid chromatography
== References ==
== External links == | Wikipedia/Countercurrent_chromatography |
Liquid chromatography–mass spectrometry (LC–MS) is an analytical chemistry technique that combines the physical separation capabilities of liquid chromatography (or HPLC) with the mass analysis capabilities of mass spectrometry (MS). Coupled chromatography – MS systems are popular in chemical analysis because the individual capabilities of each technique are enhanced synergistically. While liquid chromatography separates mixtures with multiple components, mass spectrometry provides spectral information that may help to identify (or confirm the suspected identity of) each separated component. MS is not only sensitive, but provides selective detection, relieving the need for complete chromatographic separation. LC–MS is also appropriate for metabolomics because of its good coverage of a wide range of chemicals. This tandem technique can be used to analyze biochemical, organic, and inorganic compounds commonly found in complex samples of environmental and biological origin. Therefore, LC–MS may be applied in a wide range of sectors including biotechnology, environment monitoring, food processing, and pharmaceutical, agrochemical, and cosmetic industries. Since the early 2000s, LC–MS (or more specifically LC–MS/MS) has also begun to be used in clinical applications.
In addition to the liquid chromatography and mass spectrometry devices, an LC–MS system contains an interface that efficiently transfers the separated components from the LC column into the MS ion source. The interface is necessary because the LC and MS devices are fundamentally incompatible. While the mobile phase in a LC system is a pressurized liquid, the MS analyzers commonly operate under high vacuum. Thus, it is not possible to directly pump the eluate from the LC column into the MS source. Overall, the interface is a mechanically simple part of the LC–MS system that transfers the maximum amount of analyte, removes a significant portion of the mobile phase used in LC and preserves the chemical identity of the chromatography products (chemically inert). As a requirement, the interface should not interfere with the ionizing efficiency and vacuum conditions of the MS system. Nowadays, most extensively applied LC–MS interfaces are based on atmospheric pressure ionization (API) strategies like electrospray ionization (ESI), atmospheric-pressure chemical ionization (APCI), and atmospheric pressure photoionization (APPI). These interfaces became available in the 1990s after a two decade long research and development process.
== History ==
The coupling of chromatography with MS is a well developed chemical analysis strategy dating back from the 1950s. Gas chromatography (GC)–MS was originally introduced in 1952, when A. T. James and A. J. P. Martin were trying to develop tandem separation – mass analysis techniques. In GC, the analytes are eluted from the separation column as a gas and the connection with electron ionization (EI) or chemical ionization (CI) ion sources in the MS system was a technically simpler challenge. Because of this, the development of GC-MS systems was faster than LC–MS and such systems were first commercialized in the 1970s. The development of LC–MS systems took longer than GC-MS and was directly related to the development of proper interfaces. Victor Talrose and his collaborators in Russia started the development of LC–MS in the late 1960s, when they first used capillaries to connect an LC column to an EI source. A similar strategy was investigated by McLafferty and collaborators in 1973 who coupled the LC column to a CI source, which allowed a higher liquid flow into the source. This was the first and most obvious way of coupling LC with MS, and was known as the capillary inlet interface. This pioneer interface for LC–MS had the same analysis capabilities of GC-MS and was limited to rather volatile analytes and non-polar compounds with low molecular mass (below 400 Da). In the capillary inlet interface, the evaporation of the mobile phase inside the capillary was one of the main issues. Within the first years of development of LC–MS, on-line and off-line alternatives were proposed as coupling alternatives. In general, off-line coupling involved fraction collection, evaporation of solvent, and transfer of analytes to the MS using probes. Off-line analyte treatment process was time-consuming and there was an inherent risk of sample contamination. Rapidly, it was realized that the analysis of complex mixtures would require the development of a fully automated on-line coupling solution in LC–MS.
The key to the success and widespread adoption of LC–MS as a routine analytical tool lies in the interface and ion source between the liquid-based LC and the vacuum-base MS. The following interfaces were stepping-stones on the way to the modern atmospheric-pressure ionization interfaces, and are described for historical interest.
=== Moving-belt interface ===
The moving-belt interface (MBI) was developed by McFadden et al. in 1977 and commercialized by Finnigan. This interface consisted of an endless moving belt onto which the LC column effluent was deposited in a band. On the belt, the solvent was evaporated by gently heating and efficiently exhausting the solvent vapours under reduced pressure in two vacuum chambers. After the liquid phase was removed, the belt passed over a heater which flash desorbed the analytes into the MS ion source. One of the significant advantages of the MBI was its compatibility with a wide range of chromatographic conditions. MBI was successfully used for LC–MS applications between 1978 and 1990 because it allowed coupling of LC to MS devices using EI, CI, and fast-atom bombardment (FAB) ion sources. The most common MS systems connected by MBI interfaces to LC columns were magnetic sector and quadrupole instruments. MBI interfaces for LC–MS allowed MS to be widely applied in the analysis of drugs, pesticides, steroids, alkaloids, and polycyclic aromatic hydrocarbons. This interface is no longer used because of its mechanical complexity and the difficulties associated with belt renewal (or cleaning) as well as its inability to handle very labile biomolecules.
=== Direct liquid-introduction interface ===
The direct liquid-introduction (DLI) interface was developed in 1980. This interface was intended to solve the problem of evaporation of liquid inside the capillary inlet interface. In DLI, a small portion of the LC flow was forced through a small aperture or diaphragm (typically 10 μm in diameter) to form a liquid jet composed of small droplets that were subsequently dried in a desolvation chamber. The analytes were ionized using a solvent-assisted chemical ionization source, where the LC solvents acted as reagent gases. To use this interface, it was necessary to split the flow coming out of the LC column because only a small portion of the effluent (10 to 50 μl/min out of 1 ml/min) could be introduced into the source without raising the vacuum pressure of the MS system too high. Alternately, Henion at Cornell University had success with using micro-bore LC methods so that the entire (low) flow of the LC could be used. One of the main operational problems of the DLI interface was the frequent clogging of the diaphragm orifices. The DLI interface was used between 1982 and 1985 for the analysis of pesticides, corticosteroids, metabolites in horse urine, erythromycin, and vitamin B12. However, this interface was replaced by the thermospray interface, which removed the flow rate limitations and the issues with the clogging diaphragms.
A related device was the particle beam interface (PBI), developed by Willoughby and Browner in 1984. Particle beam interfaces took over the wide applications of MBI for LC–MS in 1988. The PBI operated by using a helium gas nebulizer to spray the eluant into the vacuum, drying the droplets and pumping away the solvent vapour (using a jet separator) while the stream of monodisperse dried particles containing the analyte entered the source. Drying the droplets outside of the source volume, and using a jet separator to pump away the solvent vapour, allowed the particles to enter and be vapourized in a low-pressure EI source. As with the MBI, the ability to generate library-searchable EI spectra was a distinct advantage for many applications. Commercialized by Hewlett Packard, and later by VG and Extrel, it enjoyed moderate success, but has been largely supplanted by the atmospheric pressure interfaces such as electrospray and APCI which provide a broader range of compound coverage and applications.
=== Thermospray interface ===
The thermospray (TSP) interface was developed in 1980 by Marvin Vestal and co-workers at the University of Houston. It was commercialized by Vestec and several of the major mass spectrometer manufacturers. The interface resulted from a long-term research project intended to find a LC–MS interface capable of handling high flow rates (1 ml/min) and avoiding the flow split in DLI interfaces. The TSP interface was composed of a heated probe, a desolvation chamber, and an ion focusing skimmer. The LC effluent passed through the heated probe and emerged as a jet of vapor and small droplets flowing into the desolvation chamber at low pressure. Initially operated with a filament or discharge as the source of ions (thereby acting as a CI source for vapourized analyte), it was soon discovered that ions were also observed when the filament or discharge was off. This could be attributed to either direct emission of ions from the liquid droplets as they evaporated in a process related to electrospray ionization or ion evaporation, or to chemical ionization of vapourized analyte molecules from buffer ions (such as ammonium acetate). The fact that multiply-charged ions were observed from some larger analytes suggests that direct analyte ion emission was occurring under at least some conditions. The interface was able to handle up to 2 ml/min of eluate from the LC column and would efficiently introduce it into the MS vacuum system. TSP was also more suitable for LC–MS applications involving reversed phase liquid chromatography (RT-LC). With time, the mechanical complexity of TSP was simplified, and this interface became popular as the first ideal LC–MS interface for pharmaceutical applications comprising the analysis of drugs, metabolites, conjugates, nucleosides, peptides, natural products, and pesticides. The introduction of TSP marked a significant improvement for LC–MS systems and was the most widely applied interface until the beginning of the 1990s, when it began to be replaced by interfaces involving atmospheric pressure ionization (API).
=== FAB based interfaces ===
The first fast atom bombardment (FAB) and continuous flow-FAB (CF-FAB) interfaces were developed in 1985 and 1986 respectively. Both interfaces were similar, but they differed in that the first used a porous frit probe as connecting channel, while CF-FAB used a probe tip. From these, the CF-FAB was more successful as a LC–MS interface and was useful to analyze non-volatile and thermally labile compounds. In these interfaces, the LC effluent passed through the frit or CF-FAB channels to form a uniform liquid film at the tip. There, the liquid was bombarded with ion beams or high energy atoms (fast atoms). For stable operation, the FAB based interfaces were able to handle liquid flow rates of only 1–15 μl and were also restricted to microbore and capillary columns. In order to be used in FAB MS ionization sources, the analytes of interest had to be mixed with a matrix (e.g., glycerol) that could be added before or after the separation in the LC column. FAB based interfaces were extensively used to characterize peptides, but lost applicability with the advent of electrospray based interfaces in 1988.
== Liquid chromatography ==
Liquid chromatography is a method of physical separation in which the components of a liquid mixture are distributed between two immiscible phases, i.e., stationary and mobile. The practice of LC can be divided into five categories, i.e., adsorption chromatography, partition chromatography, ion-exchange chromatography, size-exclusion chromatography, and affinity chromatography. Among these, the most widely used variant is the reverse-phase (RP) mode of the partition chromatography technique, which makes use of a nonpolar (hydrophobic) stationary phase and a polar mobile phase. In common applications, the mobile phase is a mixture of water and other polar solvents (e.g., methanol, isopropanol, and acetonitrile), and the stationary matrix is prepared by attaching long-chain alkyl groups (e.g., n-octadecyl or C18) to the external and internal surfaces of irregularly or spherically shaped 5 μm diameter porous silica particles.
In HPLC, typically 20 μl of the sample of interest are injected into the mobile phase stream delivered by a high pressure pump. The mobile phase containing the analytes permeates through the stationary phase bed in a definite direction. The components of the mixture are separated depending on their chemical affinity with the mobile and stationary phases. The separation occurs after repeated sorption and desorption steps occurring when the liquid interacts with the stationary bed. The liquid solvent (mobile phase) is delivered under high pressure (up to 400 bar or 5800 psi) into a packed column containing the stationary phase. The high pressure is necessary to achieve a constant flow rate for reproducible chromatography experiments. Depending on the partitioning between the mobile and stationary phases, the components of the sample will flow out of the column at different times. The column is the most important component of the LC system and is designed to withstand the high pressure of the liquid. Conventional LC columns are 100–300 mm long with outer diameter of 6.4 mm (1/4 inch) and internal diameter of 3.0–4.6 mm. For applications involving LC–MS, the length of chromatography columns can be shorter (30–50 mm) with 3–5 μm diameter packing particles. In addition to the conventional model, other LC columns are the narrow bore, microbore, microcapillary, and nano-LC models. These columns have smaller internal diameters, allow for a more efficient separation, and handle liquid flows under 1 ml/min (the conventional flow-rate). In order to improve separation efficiency and peak resolution, ultra performance liquid chromatography (UHPLC) can be used instead of HPLC. This LC variant uses columns packed with smaller silica particles (~1.7 μm diameter) and requires higher operating pressures in the range of 310000 to 775000 torr (6000 to 15000 psi, 400 to 1034 bar).
== Mass spectrometry ==
Mass spectrometry (MS) is an analytical technique that measures the mass-to-charge ratio (m/z) of charged particles (ions). Although there are many different kinds of mass spectrometers, all of them make use of electric or magnetic fields to manipulate the motion of ions produced from an analyte of interest and determine their m/z. The basic components of a mass spectrometer are the ion source, the mass analyzer, the detector, and the data and vacuum systems. The ion source is where the components of a sample introduced in a MS system are ionized by means of electron beams, photon beams (UV lights), laser beams or corona discharge. In the case of electrospray ionization, the ion source moves ions that exist in liquid solution into the gas phase. The ion source converts and fragments the neutral sample molecules into gas-phase ions that are sent to the mass analyzer. While the mass analyzer applies the electric and magnetic fields to sort the ions by their masses, the detector measures and amplifies the ion current to calculate the abundances of each mass-resolved ion. In order to generate a mass spectrum that a human eye can easily recognize, the data system records, processes, stores, and displays data in a computer.
The mass spectrum can be used to determine the mass of the analytes, their elemental and isotopic composition, or to elucidate the chemical structure of the sample. MS is an experiment that must take place in gas phase and under vacuum (1.33 * 10−2 to 1.33 * 10−6 pascal). Therefore, the development of devices facilitating the transition from samples at higher pressure and in condensed phase (solid or liquid) into a vacuum system has been essential to develop MS as a potent tool for identification and quantification of organic compounds like peptides. MS is now in very common use in analytical laboratories that study physical, chemical, or biological properties of a great variety of compounds. Among the many different kinds of mass analyzers, the ones that find application in LC–MS systems are the quadrupole, time-of-flight (TOF), ion traps, and hybrid quadrupole-TOF (QTOF) analyzers.
== Interfaces ==
The interface between a liquid phase technique (HPLC) with a continuously flowing eluate, and a gas phase technique carried out in a vacuum was difficult for a long time. The advent of electrospray ionization changed this. Currently, the most common LC–MS interfaces are electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI), and atmospheric pressure photo-ionization (APPI). These are newer MS ion sources that facilitate the transition from a high pressure environment (HPLC) to high vacuum conditions needed at the MS analyzer. Although these interfaces are described individually, they can also be commercially available as dual ESI/APCI, ESI/APPI, or APCI/APPI ion sources. Various deposition and drying techniques were used in the past (e.g., moving belts) but the most common of these was the off-line MALDI deposition. A new approach still under development called direct-EI LC–MS interface, couples a nano HPLC system and an electron ionization equipped mass spectrometer.
=== Electrospray ionization (ESI) ===
ESI interface for LC–MS systems was developed by Fenn and collaborators in 1988. This ion source/ interface can be used for the analysis of moderately polar and even very polar molecules (e.g., metabolites, xenobiotics, peptides, nucleotides, polysaccharides). The liquid eluate coming out of the LC column is directed into a metal capillary kept at 3 to 5 kV and is nebulized by a high-velocity coaxial flow of gas at the tip of the capillary, creating a fine spray of charged droplets in front of the entrance to the vacuum chamber. To avoid contamination of the vacuum system by buffers and salts, this capillary is usually perpendicularly located at the inlet of the MS system, in some cases with a counter-current of dry nitrogen in front of the entrance through which ions are directed by the electric field. In some sources, rapid droplet evaporation and thus maximum ion emission is achieved by mixing an additional stream of hot gas with the spray plume in front of the vacuum entrance. In other sources, the droplets are drawn through a heated capillary tube as they enter the vacuum, promoting droplet evaporation and ion emission. These methods of increasing droplet evaporation now allow the use of liquid flow rates of 1 - 2 mL/min to be used while still achieving efficient ionisation and high sensitivity. Thus while the use of 1 – 3 mm microbore columns and lower flow rates of 50 - 200 μl/min was commonly considered necessary for optimum operation, this limitation is no longer as important, and the higher column capacity of larger bore columns can now be advantageously employed with ESI LC–MS systems. Positively and negatively charged ions can be created by switching polarities, and it is possible to acquire alternate positive and negative mode spectra rapidly within the same LC run . While most large molecules (greater than MW 1500–2000) produce multiply charged ions in the ESI source, the majority of smaller molecules produce singly charged ions.
=== Atmospheric pressure chemical ionization (APCI) ===
The development of the APCI interface for LC–MS started with Horning and collaborators in the early 1973. However, its commercial application was introduced at the beginning of the 1990s after Henion and collaborators improved the LC–APCI–MS interface in 1986. The APCI ion source/ interface can be used to analyze small, neutral, relatively non-polar, and thermally stable molecules (e.g., steroids, lipids, and fat soluble vitamins). These compounds are not well ionized using ESI. In addition, APCI can also handle mobile phase streams containing buffering agents. The liquid from the LC system is pumped through a capillary and there is also nebulization at the tip, where a corona discharge takes place. First, the ionizing gas surrounding the interface and the mobile phase solvent are subject to chemical ionization at the ion source. Later, these ions react with the analyte and transfer their charge. The sample ions then pass through small orifice skimmers by means of or ion-focusing lenses. Once inside the high vacuum region, the ions are subject to mass analysis. This interface can be operated in positive and negative charge modes and singly-charged ions are mainly produced. APCI ion source can also handle flow rates between 500 and 2000 μl/min and it can be directly connected to conventional 4.6 mm ID columns.
=== Atmospheric pressure photoionization (APPI) ===
The APPI interface for LC–MS was developed simultaneously by Bruins and Syage in 2000. APPI is another LC–MS ion source/ interface for the analysis of neutral compounds that cannot be ionized using ESI. This interface is similar to the APCI ion source, but instead of a corona discharge, the ionization occurs by using photons coming from a discharge lamp. In the direct-APPI mode, singly charged analyte molecular ions are formed by absorption of a photon and ejection of an electron. In the dopant-APPI mode, an easily ionizable compound (Dopant) is added to the mobile phase or the nebulizing gas to promote a reaction of charge-exchange between the dopant molecular ion and the analyte. The ionized sample is later transferred to the mass analyzer at high vacuum as it passes through small orifice skimmers.
== Applications ==
The coupling of MS with LC systems is attractive because liquid chromatography can separate delicate and complex natural mixtures, which chemical composition needs to be well established (e.g., biological fluids, environmental samples, and drugs). Further, LC–MS has applications in volatile explosive residue analysis. Nowadays, LC–MS has become one of the most widely used chemical analysis techniques because more than 85% of natural chemical compounds are polar and thermally labile and GC-MS cannot process these samples. As an example, HPLC–MS is regarded as the leading analytical technique for proteomics and pharmaceutical laboratories. Other important applications of LC–MS include the analysis of food, pesticides, and plant phenols.
=== Pharmacokinetics ===
LC–MS is widely used in the field of bioanalysis and is specially involved in pharmacokinetic studies of pharmaceuticals. Pharmacokinetic studies are needed to determine how quickly a drug will be cleared from the body organs and the hepatic blood flow. MS analyzers are useful in these studies because of their shorter analysis time, and higher sensitivity and specificity compared to UV detectors commonly attached to HPLC systems. One major advantage is the use of tandem MS–MS, where the detector may be programmed to select certain ions to fragment. The measured quantity is the sum of molecule fragments chosen by the operator. As long as there are no interferences or ion suppression in LC–MS, the LC separation can be quite quick.
=== Proteomics/metabolomics ===
LC–MS is used in proteomics as a method to detect and identify the components of a complex mixture. The bottom-up proteomics LC–MS approach generally involves protease digestion and denaturation using trypsin as a protease, urea to denature the tertiary structure, and iodoacetamide to modify the cysteine residues. After digestion, LC–MS is used for peptide mass fingerprinting, or LC–MS/MS (tandem MS) is used to derive the sequences of individual peptides. LC–MS/MS is most commonly used for proteomic analysis of complex samples where peptide masses may overlap even with a high-resolution mass spectrometry. Samples of complex biological (e.g., human serum) may be analyzed in modern LC–MS/MS systems, which can identify over 1000 proteins. However, this high level of protein identification is possible only after separating the sample by means of SDS-PAGE gel or HPLC-SCX. Recently, LC–MS/MS has been applied to search peptide biomarkers. Examples are the recent discovery and validation of peptide biomarkers for four major bacterial respiratory tract pathogens (Staphylococcus aureus, Moraxella catarrhalis; Haemophilus influenzae and Streptococcus pneumoniae) and the SARS-CoV-2 virus.
LC–MS has emerged as one of the most commonly used techniques in global metabolite profiling of biological tissue (e.g., blood plasma, serum, urine). LC–MS is also used for the analysis of natural products and the profiling of secondary metabolites in plants. In this regard, MS-based systems are useful to acquire more detailed information about the wide spectrum of compounds from a complex biological samples. LC–nuclear magnetic resonance (NMR) is also used in plant metabolomics, but this technique can only detect and quantify the most abundant metabolites. LC–MS has been useful to advance the field of plant metabolomics, which aims to study the plant system at molecular level providing a non-biased characterization of the plant metabolome in response to its environment. The first application of LC–MS in plant metabolomics was the detection of a wide range of highly polar metabolites, oligosaccharides, amino acids, amino sugars, and sugar nucleotides from Cucurbita maxima phloem tissues. Another example of LC–MS in plant metabolomics is the efficient separation and identification of glucose, sucrose, raffinose, stachyose, and verbascose from leaf extracts of Arabidopsis thaliana.
=== Drug development ===
LC–MS is frequently used in drug development because it allows quick molecular weight confirmation and structure identification. These features speed up the process of generating, testing, and validating a discovery starting from a vast array of products with potential application. LC–MS applications for drug development are highly automated methods used for peptide mapping, glycoprotein mapping, lipodomics, natural products dereplication, bioaffinity screening, in vivo drug screening, metabolic stability screening, metabolite identification, impurity identification, quantitative bioanalysis, and quality control.
== See also ==
Gas chromatography–mass spectrometry
Capillary electrophoresis–mass spectrometry
Ion-mobility spectrometry–mass spectrometry
== References ==
== Further reading == | Wikipedia/Liquid_chromatography–mass_spectrometry |
Size-exclusion chromatography, also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their shape, and in some cases size. It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers. Typically, when an aqueous solution is used to transport the sample through the column, the technique is known as gel filtration chromatography, versus the name gel permeation chromatography, which is used when an organic solvent is used as a mobile phase. The chromatography column is packed with fine, porous beads which are commonly composed of dextran, agarose, or polyacrylamide polymers. The pore sizes of these beads are used to estimate the dimensions of macromolecules. SEC is a widely used polymer characterization method because of its ability to provide good molar mass distribution (Mw) results for polymers.
Size-exclusion chromatography (SEC) is fundamentally different from all other chromatographic techniques in that separation is based on a simple procedure of classifying molecule sizes rather than any type of interaction.
== Applications ==
The main application of size-exclusion chromatography is the fractionation of proteins and other water-soluble polymers, while gel permeation chromatography is used to analyze the molecular weight distribution of organic-soluble polymers. Either technique should not be confused with gel electrophoresis, where an electric field is used to "pull" molecules through the gel depending on their electrical charges. The amount of time a solute remains within a pore is dependent on the size of the pore. Larger solutes will have access to a smaller volume and vice versa. Therefore, a smaller solute will remain within the pore for a longer period of time compared to a larger solute.
Even though size exclusion chromatography is widely utilized to study natural organic material, there are limitations. One of these limitations include that there is no standard molecular weight marker; thus, there is nothing to compare the results back to. If precise molecular weight is required, other methods should be used.
== Advantages ==
The advantages of this method include good separation of large molecules from the small molecules with a minimal volume of eluate, and that various solutions can be applied without interfering with the filtration process, all while preserving the biological activity of the particles to separate. The technique is generally combined with others that further separate molecules by other characteristics, such as acidity, basicity, charge, and affinity for certain compounds. With size exclusion chromatography, there are short and well-defined separation times and narrow bands, which lead to good sensitivity. There is also no sample loss because solutes do not interact with the stationary phase.
The other advantage to this experimental method is that in certain cases, it is feasible to determine the approximate molecular weight of a compound. The shape and size of the compound (eluent) determine how the compound interacts with the gel (stationary phase). To determine approximate molecular weight, the elution volumes of compounds with their corresponding molecular weights are obtained and then a plot of “Kav” vs “log(Mw)” is made, where
K
a
v
=
(
V
e
−
V
o
)
/
(
V
t
−
V
o
)
{\displaystyle K_{av}=(V_{e}-V_{o})/(V_{t}-V_{o})}
and Mw is the molecular mass. This plot acts as a calibration curve, which is used to approximate the desired compound's molecular weight. The Ve component represents the volume at which the intermediate molecules elute such as molecules that have partial access to the beads of the column. In addition, Vt is the sum of the total volume between the beads and the volume within the beads. The Vo component represents the volume at which the larger molecules elute, which elute in the beginning. Disadvantages are, for example, that only a limited number of bands can be accommodated because the time scale of the chromatogram is short, and, in general, there must be a 10% difference in molecular mass to have a good resolution.
== Discovery ==
The technique was invented in 1955 by Grant Henry Lathe and Colin R Ruthven, working at Queen Charlotte's Hospital, London. They later received the John Scott Award for this invention. While Lathe and Ruthven used starch gels as the matrix, Jerker Porath and Per Flodin later introduced dextran gels; other gels with size fractionation properties include agarose and polyacrylamide. A short review of these developments has appeared.
There were also attempts to fractionate synthetic high polymers; however, it was not until 1964, when J. C. Moore of the Dow Chemical Company published his work on the preparation of gel permeation chromatography (GPC) columns based on cross-linked polystyrene with controlled pore size, that a rapid increase of research activity in this field began. It was recognized almost immediately that with proper calibration, GPC was capable to provide molar mass and molar mass distribution information for synthetic polymers. Because the latter information was difficult to obtain by other methods, GPC came rapidly into extensive use.
== Theory and method ==
SEC is used primarily for the analysis of large molecules such as proteins or polymers. SEC works by trapping smaller molecules in the pores of the adsorbent ("stationary phase"). This process is usually performed within a column, which typically consists of a hollow tube tightly packed with micron-scale polymer beads containing pores of different sizes. These pores may be depressions on the surface or channels through the bead. As the solution travels down the column some particles enter into the pores. Larger particles cannot enter into as many pores. The larger the particles, the faster the elution. The larger molecules simply pass by the pores because those molecules are too large to enter the pores. Larger molecules therefore flow through the column more quickly than smaller molecules, that is, the smaller the molecule, the longer the retention time.
One requirement for SEC is that the analyte does not interact with the surface of the stationary phases, with differences in elution time between analytes ideally being based solely on the solute volume the analytes can enter, rather than chemical or electrostatic interactions with the stationary phases. Thus, a small molecule that can penetrate every region of the stationary phase pore system can enter a total volume equal to the sum of the entire pore volume and the interparticle volume. This small molecule elutes late (after the molecule has penetrated all of the pore- and interparticle volume—approximately 80% of the column volume). At the other extreme, a very large molecule that cannot penetrate any the smaller pores can enter only the interparticle volume (~35% of the column volume) and elutes earlier when this volume of mobile phase has passed through the column. The underlying principle of SEC is that particles of different sizes elute (filter) through a stationary phase at different rates. This results in the separation of a solution of particles based on size. Provided that all the particles are loaded simultaneously or near-simultaneously, particles of the same size should elute together.
However, as there are various measures of the size of a macromolecule (for instance, the radius of gyration and the hydrodynamic radius), a fundamental problem in the theory of SEC has been the choice of a proper molecular size parameter by which molecules of different kinds are separated. Experimentally, Benoit and co-workers found an excellent correlation between elution volume and a dynamically based molecular size, the hydrodynamic volume, for several different chain architecture and chemical compositions. The observed correlation based on the hydrodynamic volume became accepted as the basis of universal SEC calibration.
Still, the use of the hydrodynamic volume, a size based on dynamical properties, in the interpretation of SEC data is not fully understood. This is because SEC is typically run under low flow rate conditions where hydrodynamic factor should have little effect on the separation. In fact, both theory and computer simulations assume a thermodynamic separation principle: the separation process is determined by the equilibrium distribution (partitioning) of solute macromolecules between two phases: a dilute bulk solution phase located at the interstitial space and confined solution phases within the pores of column packing material. Based on this theory, it has been shown that the relevant size parameter to the partitioning of polymers in pores is the mean span dimension (mean maximal projection onto a line). Although this issue has not been fully resolved, it is likely that the mean span dimension and the hydrodynamic volume are strongly correlated.
Each size exclusion column has a range of molecular weights that can be separated. The exclusion limit defines the molecular weight at the upper end of the column 'working' range and is where molecules are too large to get trapped in the stationary phase. The lower end of the range is defined by the permeation limit, which defines the molecular weight of a molecule that is small enough to penetrate all pores of the stationary phase. All molecules below this molecular mass are so small that they elute as a single band.
The filtered solution that is collected at the end is known as the eluate. The void volume includes any particles too large to enter the medium, and the solvent volume is known as the column volume.
Following are the materials which are commonly used for porous gel beads in size exclusion chromatography
== Factors affecting filtration ==
In real-life situations, particles in solution do not have a fixed size, resulting in the probability that a particle that would otherwise be hampered by a pore passing right by it. Also, the stationary-phase particles are not ideally defined; both particles and pores may vary in size. Elution curves, therefore, resemble Gaussian distributions. The stationary phase may also interact in undesirable ways with a particle and influence retention times, though great care is taken by column manufacturers to use stationary phases that are inert and minimize this issue.
Like other forms of chromatography, increasing the column length enhances resolution, and increasing the column diameter increases column capacity. Proper column packing is important for maximum resolution: An over-packed column can collapse the pores in the beads, resulting in a loss of resolution. An under-packed column can reduce the relative surface area of the stationary phase accessible to smaller species, resulting in those species spending less time trapped in pores. Unlike affinity chromatography techniques, a solvent head at the top of the column can drastically diminish resolution as the sample diffuses prior to loading, broadening the downstream elution.
== Analysis ==
In simple manual columns, the eluent is collected in constant volumes, known as fractions. The more similar the particles are in size the more likely they are in the same fraction and not detected separately. More advanced columns overcome this problem by constantly monitoring the eluent.
The collected fractions are often examined by spectroscopic techniques to determine the concentration of the particles eluted. Common spectroscopy detection techniques are refractive index (RI) and ultraviolet (UV). When eluting spectroscopically similar species (such as during biological purification), other techniques may be necessary to identify the contents of each fraction. It is also possible to analyze the eluent flow continuously with RI, LALLS, Multi-Angle Laser Light Scattering MALS, UV, and/or viscosity measurements.
The elution volume (Ve) decreases roughly linear with the logarithm of the molecular hydrodynamic volume. Columns are often calibrated using 4-5 standard samples (e.g., folded proteins of known molecular weight), and a sample containing a very large molecule such as thyroglobulin to determine the void volume. (Blue dextran is not recommended for Vo determination because it is heterogeneous and may give variable results) The elution volumes of the standards are divided by the elution volume of the thyroglobulin (Ve/Vo) and plotted against the log of the standards' molecular weights.
== Applications ==
=== Biochemical applications ===
In general, SEC is considered a low-resolution chromatography as it does not discern similar species very well, and is therefore often reserved for the final step of a purification. The technique can determine the quaternary structure of purified proteins that have slow exchange times, since it can be carried out under native solution conditions, preserving macromolecular interactions. SEC can also assay protein tertiary structure, as it measures the hydrodynamic volume (not molecular weight), allowing folded and unfolded versions of the same protein to be distinguished. For example, the apparent hydrodynamic radius of a typical protein domain might be 14 Å and 36 Å for the folded and unfolded forms, respectively. SEC allows the separation of these two forms, as the folded form elutes much later due to its smaller size.
=== Polymer synthesis ===
SEC can be used as a measure of both the size and the polydispersity of a synthesized polymer, that is, the ability to find the distribution of the sizes of polymer molecules. If standards of a known size are run previously, then a calibration curve can be created to determine the sizes of polymer molecules of interest in the solvent chosen for analysis (often THF). In alternative fashion, techniques such as light scattering and/or viscometry can be used online with SEC to yield absolute molecular weights that do not rely on calibration with standards of known molecular weight. Due to the difference in size of two polymers with identical molecular weights, the absolute determination methods are, in general, more desirable. A typical SEC system can quickly (in about half an hour) give polymer chemists information on the size and polydispersity of the sample. The preparative SEC can be used for polymer fractionation on an analytical scale.
== Drawbacks ==
In SEC, mass is not measured so much as the hydrodynamic volume of the polymer molecules, that is, how much space a particular polymer molecule takes up when it is in solution. However, the approximate molecular weight can be calculated from SEC data because the exact relationship between molecular weight and hydrodynamic volume for polystyrene can be found. For this, polystyrene is used as a standard. But the relationship between hydrodynamic volume and molecular weight is not the same for all polymers, so only an approximate measurement can be obtained.
Another drawback is the possibility of interaction between the stationary phase and the analyte. Any interaction leads to a later elution time and thus mimics a smaller analyte size.
When performing this method, the bands of the eluting molecules may be broadened. This can occur by turbulence caused by the flow of the mobile phase molecules passing through the molecules of the stationary phase. In addition, molecular thermal diffusion and friction between the molecules of the glass walls and the molecules of the eluent contribute to the broadening of the bands. Besides broadening, the bands also overlap with each other. As a result, the eluent usually gets considerably diluted. A few precautions can be taken to prevent the likelihood of the bands broadening. For instance, one can apply the sample in a narrow, highly concentrated band on the top of the column. The more concentrated the eluent is, the more efficient the procedure would be. However, it is not always possible to concentrate the eluent, which can be considered as one more disadvantage.
== Absolute size-exclusion chromatography ==
Absolute size-exclusion chromatography (ASEC) is a technique that couples a light scattering instrument, most commonly multi-angle light scattering (MALS) or another form of static light scattering (SLS), but possibly a dynamic light scattering (DLS) instrument, to a size-exclusion chromatography system for absolute molar mass and/or size measurements of proteins and macromolecules as they elute from the chromatography system.
The definition of “absolute” in this case is that calibration of retention time on the column with a set of reference standards is not required to obtain molar mass or the hydrodynamic size, often referred to as hydrodynamic diameter (DH in units of nm). Non-ideal column interactions, such as electrostatic or hydrophobic surface interactions that modulate retention time relative to standards, do not impact the final result. Likewise, differences between conformation of the analyte and the standard have no effect on an absolute measurement; for example, with MALS analysis, the molar mass of inherently disordered proteins are characterized accurately even though they elute at much earlier times than globular proteins with the same molar mass, and the same is true of branched polymers which elute late compared to linear reference standards with the same molar mass. Another benefit of ASEC is that the molar mass and/or size is determined at each point in an eluting peak, and therefore indicates homogeneity or polydispersity within the peak. For example, SEC-MALS analysis of a monodisperse protein will show that the entire peak consists of molecules with the same molar mass, something that is not possible with standard SEC analysis.
Determination of molar mass with SLS requires combining the light scattering measurements with concentration measurements. Therefore SEC-MALS typically includes the light scattering detector and either a differential refractometer or UV/Vis absorbance detector. In addition, MALS determines the rms radius Rg of molecules above a certain size limit, typically 10 nm. SEC-MALS can therefore analyze the conformation of polymers via the relationship of molar mass to Rg. For smaller molecules, either DLS or, more commonly, a differential viscometer is added to determine hydrodynamic radius and evaluate molecular conformation in the same manner.
In SEC-DLS, the sizes of the macromolecules are measured as they elute into the flow cell of the DLS instrument from the size exclusion column set. The hydrodynamic size of the molecules or particles are measured and not their molecular weights. For proteins a Mark-Houwink type of calculation can be used to estimate the molecular weight from the hydrodynamic size.
A major advantage of DLS coupled with SEC is the ability to obtain enhanced DLS resolution. Batch DLS is quick and simple and provides a direct measure of the average size, but the baseline resolution of DLS is a ratio of 3:1 in diameter. Using SEC, the proteins and protein oligomers are separated, allowing oligomeric resolution. Aggregation studies can also be done using ASEC. Though the aggregate concentration may not be calculated with light scattering (an online concentration detector such as that used in SEC-MALS for molar mass measurement also determines aggregate concentration), the size of the aggregate can be measured, only limited by the maximum size eluting from the SEC columns.
Limitations of ASEC with DLS detection include flow-rate, concentration, and precision. Because a correlation function requires anywhere from 3–7 seconds to properly build, a limited number of data points can be collected across the peak. ASEC with SLS detection is not limited by flow rate and measurement time is essentially instantaneous, and the range of concentration is several orders of magnitude larger than for DLS. However, molar mass analysis with SEC-MALS does require accurate concentration measurements. MALS and DLS detectors are often combined in a single instrument for more comprehensive absolute analysis following separation by SEC.
== See also ==
PEGylation
Gel permeation chromatography
Protein purification
== References ==
== External links == | Wikipedia/Size-exclusion_chromatography |
Fast protein liquid chromatography (FPLC) is a form of liquid chromatography that is often used to analyze or purify mixtures of proteins. As in other forms of chromatography, separation is possible because the different components of a mixture have different affinities for two materials, a moving fluid (the mobile phase) and a porous solid (the stationary phase). In FPLC the mobile phase is an aqueous buffer solution. The buffer flow rate is controlled by a positive-displacement pump and is normally kept constant, while the composition of the buffer can be varied by drawing fluids in different proportions from two or more external reservoirs. The stationary phase is a resin composed of beads, usually of cross-linked agarose, packed into a cylindrical glass or plastic column. FPLC resins are available in a wide range of bead sizes and surface ligands depending on the application.
FPLC was developed and marketed in Sweden by Pharmacia in 1982, and was originally called fast performance liquid chromatography to contrast it with high-performance liquid chromatography (HPLC). FPLC is generally applied only to proteins; however, because of the wide choice of resins and buffers it has broad applications. In contrast to HPLC, the buffer pressure used is relatively low, typically less than 5 bar, but the flow rate is relatively high, typically 1–5 ml/min.
FPLC can be readily scaled from analysis of milligrams of mixtures in columns with a total volume of 5 ml or less to industrial production of kilograms of purified protein in columns with volumes of many liters. When used for analysis of mixtures, the eluant is usually collected in fractions of 1–5 ml which can be further analyzed. When used for protein purification there may be only two collection containers: one for the purified product and one for waste.
== General principles ==
In a common FPLC strategy, a resin is chosen that the protein of interest will bind to by a charge interaction while in buffer A (the running buffer) but become dissociated and return to solution in buffer B (the elution buffer). A mixture containing one or more proteins of interest is dissolved in 100% buffer A and pumped into the column. The proteins of interest bind to the resin while other components are carried out in the buffer. The total flow rate of the buffer is kept constant; however, the proportion of buffer B (the "elution" buffer) is gradually increased from 0% to 100% according to a programmed change in concentration (the "gradient"). At some point during this process each of the bound proteins dissociates and appears in the eluant. The eluant passes through two detectors which measure salt concentration (by conductivity) and protein concentration (by absorption of ultraviolet light at a wavelength of 280 nm). As each protein is eluted, it appears in the eluant as a "peak" in protein concentration, and can be collected for further use.
== System components ==
A typical laboratory FPLC consist of one or two high-precision pumps, a control unit, a column, a detection system and a fraction collector. Although it is possible to operate the system manually, the components are normally linked to a personal computer or, in older units, a microcontroller.
=== Pumps ===
The majority of systems utilize two two-cylinder piston pumps, one for each buffer, combining the output of both in a mixing chamber. Some simpler systems use a single peristaltic pump which draws both buffers from separate reservoirs through a proportioning valve and mixing chamber. In either case the system allows the fraction of each buffer entering the column to be continuously varied. The flow rate can go from a few milliliters per minute in bench-top systems to liters per minute for industrial scale purifications. The wide flow range makes it suitable both for analytical and preparative chromatography.
=== Injection loop ===
The injection loop is a segment of tubing of known volume which is filled with the sample solution before it is injected into the column. Loop volume can range from a few microliters to 50 ml or more.
=== Injection valve ===
The injection valve is a motorized valve which links the mixer and sample loop to the column. Typically the valve has three positions for loading the sample loop, for injecting the sample from the loop into the column, and for connecting the pumps directly to the waste line to wash them or change buffer solutions. The injection valve has a sample loading port through which the sample can be loaded into the injection loop, usually from a hypodermic syringe using a Luer-lock connection.
=== Column ===
The column is a glass or plastic cylinder packed with beads of resin and filled with buffer solution. It is normally mounted vertically with the buffer flowing downward from top to bottom. A glass frit at the bottom of the column retains the resin beads in the column while allowing the buffer and dissolved proteins to exit.
=== Flow cell ===
The eluant from the column passes through one or more flow cells to measure the concentration of protein in the eluant (by UV light absorption at 280 nm). The conductivity cell measures the buffer conductivity, usually in millisiemens/cm, which indicates the concentration of salt in the buffer. A flow cell which measures pH of the buffer is also commonly included. Usually each flow cell is connected to a separate electronics module which provides power and amplifies the signal.
=== Monitor/recorder ===
The flow cells are connected to a display and/or recorder. On older systems this was a simple chart recorder, on modern systems a computer with hardware interface and display is used. This permits the experimenter to identify when peaks in protein concentration occur, indicating that specific components of the mixture are being eluted.
=== Fraction collector ===
The fraction collector is typically a rotating rack that can be filled with test tubes or similar containers. Distribution of the eluate into separate containers are determined by fixed volumes or specific fractions detected at peaks of protein concentration.
Many systems include various optional components. A filter may be added between the mixer and column to minimize clogging. In large FPLC columns the sample may be loaded into the column directly using a small peristaltic pump rather than an injection loop. When the buffer contains dissolved gas, bubbles may form as pressure drops where the buffer exits the column; these bubbles create artifacts if they pass through the flow cells. This may be prevented by degassing the buffers, e.g. with a degasser, or by adding a flow restrictor downstream of the flow cells to maintain a pressure of 1-5 bar in the eluant line.
== Columns ==
The columns used in FPLC are large (inner diameters on the order of millimeters) tubes that contain small (micrometer-scale) particles or gel beads as the stationary phase. The chromatographic bed is composed of gel beads inside the column and the sample is introduced into the injector and carried into the column by the flowing solvent. As a result of different components adhering to or diffusing through the gel, the sample mixture gets separated.
Columns used with an FPLC can separate macromolecules based on size (size-exclusion chromatography), charge distribution (ion exchange), hydrophobicity, reverse-phase or biorecognition (as with affinity chromatography). For easy use, a wide range of pre-packed columns for techniques such as ion exchange, gel filtration (size exclusion), hydrophobic interaction, and affinity chromatography are available. FPLC differs from HPLC in that the columns used for FPLC can only be used up to maximum pressure of 3-4 MPa (435-580 psi). Thus, if the pressure of HPLC can be limited, each FPLC column may also be used in an HPLC machine.
== Optimizing protein purification ==
Combinations of chromatographic methods can be used to purify a target molecule. The purpose of purifying proteins with FPLC is to deliver quantities of the target at sufficient purity in a biologically active state to suit its further use. The quality of the end product varies depending the type and amount of starting material, efficiency of separation, and selectivity of the purification resin. The ultimate goal of a given purification protocol is to deliver the required yield and purity of the target molecule in the quickest, cheapest, and safest way for acceptable results. The range of purity required can be from that required for basic analysis (SDS-PAGE or ELISA, for example), with only bulk impurities removed, to pure enough for structural analysis (NMR or X-ray crystallography), approaching >99% target molecule. Purity required can also mean pure enough that the biological activity of the target is retained. These demands can be used to determine the amount of starting material required to reach the experimental goal. If the starting material is limited and full optimization of purification protocol cannot be performed, then a safe standard protocol that requires a minimum adjustment and optimization steps are expected. This may not be optimal with respect to experimental time, yield, and economy but it will achieve the experimental goal. On the other hand, if the starting material is enough to develop more complete protocol, the amount of work to reach the separation goal depends on the available sample information and target molecule properties. Limits to development of purification protocols many times depends on the source of the substance to be purified, whether from natural sources (harvested tissues or organisms, for example), recombinant sources (such as using prokaryotic or eukaryotic vectors in their respective expression systems), or totally synthetic sources.
No chromatographic techniques provide 100% yield of active material and overall yields depend on the number of steps in the purification protocol. By optimizing each step for the intended purpose and arranging them that minimizes inter step treatments, the number of steps will be minimized.
A typical multistep purification protocol starts with a preliminary capture step which often utilizes ion exchange chromatography (IEC). The media (stationary phase) resin consists of beads, which range in size from being large (good for fast flow rates and little to no sample clarification at the expense of resolution) to small (for best possible resolution with all other factors being equal). Short and wide column geometries are amenable to high flow rates also at the expense of resolution, typically because of lateral diffusion of sample on the column. For techniques such as size exclusion chromatography to be useful, very long, thin columns and minimal sample volumes (maximum 5% of column volume) are required. Hydrophobic interaction chromatography (HIC) can also be used for first and/ or intermediate steps. Selectivity in HIC is independent of running pH and descending salt gradients are used. For HIC, conditioning involves adding ammonium sulfate to the sample to match the buffer A concentration. If HIC is used before IEC, the ionic strength would have to be lowered to match that of buffer A for IEC step by dilution, dialysis or buffer exchange by gel filtration. This is why IEC is usually performed prior to HIC as the high salt elution conditions for IEC are ideal for binding to HIC resins in the next purification step. Polishing is used to achieve the final level of purification required and is commonly performed on a gel filtration column. An extra intermediate purification step can be added or optimization of the different steps is performed for improving purity. This extra step usually involves another round of IEC under completely different conditions.
Although this is an example of a common purification protocol for proteins, the buffer conditions, flow rates, and resins used to achieve final goals can be chosen to cover a broad range of target proteins. This flexibility is imperative for a functional purification system as all proteins behave differently and often deviate from predictions.
== References ==
== External links ==
Example FPLC risk assessment (Leeper Group, University of Cambridge) | Wikipedia/Fast_protein_liquid_chromatography |
Centrifugal partition chromatography is a special chromatographic technique where both stationary and mobile phase are liquid, and the stationary phase is immobilized by a strong centrifugal force. Centrifugal partition chromatography consists of a series-connected network of extraction cells, which operates as elemental extractors, and the efficiency is guaranteed by the cascade.
== History ==
In the 1940s Craig invented the first apparatus to conduct countercurrent partitioning; he called this the countercurrent distribution Craig apparatus. The apparatus consists of a series of glass tubes that are designed and arranged such that the lighter liquid phase is transferred from one tube to the next. The next major milestone was droplet countercurrent chromatography (DCCC). It uses only gravity to move the mobile phase through the stationary phase which is held in long vertical tubes connected in series. The modern era of CCC began with the development of the planetary centrifuge by Ito which was first introduced in 1966 as a closed helical tube which was rotated on a "planetary" axis as is turned on a "sun" axis.
Centrifugal partition chromatography was introduced in Japan in 1982; the first instrument was built at Sanki Eng. Ltd. in Kyoto. The first instrument consisted of twelve cartridges arranged around the rotor of a centrifuge; the inner volume of each cartridge was about 15 mL for 50 channels. In 1999 Kromaton developed the first FCPC with radial cells. During cell development, the Z cell was completed in 2005 and the twin cell in 2009. In 2017 RotaChrom designed its top performing CPC cells through computed fluid dynamic simulation software. After thousands of simulations, this tool revealed the drawbacks of conventional CPC cell designs and highlighted the unparallel load capacity and scalable cell design of RotaChrom.
== Operation ==
The extraction cells consist of hollow bodies with inlets and outlets of liquid connection. The cells are first filled with the liquid chosen to be the stationary phase. Under rotation, the pumping of the mobile phase is started, which enters the cells from the inlet. When entering the flow of mobiles phase forms small droplets according to the Stokes' law, which is called atomization. These droplets fall through the stationary phase, creating a high interface area, which is called the extraction. At the end of the cells, these droplets unite due to the surface tension, which is called settling.
When a sample mixture is injected as a plug into the flow of mobile phase the compounds of the mixtures elute according to their partition coefficients:
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Centrifugal partition chromatography requires only a biphasic mixture of solvents, so by varying the constitution of the solvent system it is possible to tune the partition coefficients of different compounds so that separation is guaranteed by the high selectivity.
=== Comparison with countercurrent chromatography ===
Countercurrent chromatography and centrifugal partition chromatography are two different instrumental realization of the same liquid–liquid chromatographic theory. Countercurrent chromatography usually uses a planetary gear motion without rotary seals, while centrifugal partition chromatography uses circular rotation with rotary seals for liquid connection. CCC has interchanging mixing and settling zones in the coil tube, so atomization, extraction and settling are time and zone separated. Inside centrifugal partition chromatography, all three steps happen continuously in one time, inside the cells.
Advantages of centrifugal partition chromatography:
Higher flow rate for same volume size Laboratory scale example: 250 mL centrifugal partition chromatography has optimal flow rate of 5–15 mL/min, 250 mL countercurrent chromatography has optimal flow rate of 1–3 mL/min. Process scale example: 25 L countercurrent chromatography has optimal flow rate of 100–300 ml/min, 25 L centrifugal partition chromatography has optimal flow rate of 1000–3000 ml/min.
Higher productivity (due to higher flow rate and faster separation time)
Scalable up to tonnes per month
Better stationary phase retention for most phases
Disadvantages of centrifugal partition chromatography:
Higher pressure than CCC (typical operation pressures of 40–160 bar vs 5–25 bar)
Rotary seal wear over time
== Laboratory scale ==
Centrifugal partition chromatography has been extensively used for isolation and purification of natural products for 40 years. Due to the ability to get very high selectivity, and the ability to tolerate samples containing particulated matter, it is possible to work with direct extracts of biomass, opposed to traditional liquid chromatography, where impurities degrade the solid stationary phase so that separation become impossible.
There are numerous laboratory scale centrifugal partition chromatography manufacturers around the world, like Gilson (Armen Instrument), Kromaton (Rousselet Robatel), and AECS-QUIKPREP. These instruments operate at flow rates of 1–500 mL/min. with stationary phase retentions of 40–80%.
== Production scale ==
Centrifugal partition chromatography does not use any solid stationary phase, so it guarantees a cost-effective separation for the highest industrial levels. As opposed to countercurrent chromatography, it is possible to get very high flow rates (for example 10 liters / min) with active stationary phase ratio of >80%, which guarantees good separation and high productivity. As in centrifugal partition chromatography, material is dissolved, and loaded the column in mass / volume units, loading capability can be much higher than standard solid-liquid chromatographic techniques, where material is loaded to the active surface area of the stationary phase, which takes up less than 10% of the column.
Industrial instrument like Gilson (Armen Instrument), Kromaton (Rousselet Robatel) and RotaChrom Technologies (RotaChrom) differ from laboratory scale instruments by the applicable flow rate with satisfactory stationary phase retention (70–90%). Industrial instruments have flow rates of multiple liter / minutes, while able to purify materials from 10 kg to tonnes per month.
Operating the production scale equipment requires industrial volume solvent preparation (mixer/settler) and solvent recovery equipment.
== See also ==
Radial chromatography
== References ==
Centrifugal partition Chromatography - Chromatographic Science Series - Volume 68, Editor: Alain P. Foucault, Marcel Dekker Inc | Wikipedia/Centrifugal_partition_chromatography |
Pyrolysis–gas chromatography–mass spectrometry is a method of chemical analysis in which the sample is heated to decomposition to produce smaller molecules that are separated by gas chromatography and detected using mass spectrometry.
== How it works ==
Pyrolysis is the thermal decomposition of materials in an inert atmosphere or a vacuum. The sample is put into direct contact with a platinum wire, or placed in a quartz sample tube, and rapidly heated to 600–1000 °C. Depending on the application even higher temperatures are used. Three different heating techniques are used in actual pyrolyzers: Isothermal furnace, inductive heating (Curie Point filament), and resistive heating using platinum filaments. Large molecules cleave at their weakest bonds, producing smaller, more volatile fragments. These fragments can be separated by gas chromatography. Pyrolysis GC chromatograms are typically complex because a wide range of different decomposition products is formed. The data can either be used as fingerprint to prove material identity or the GC/MS data is used to identify individual fragments to obtain structural information. To increase the volatility of polar fragments, various methylating reagents can be added to a sample before pyrolysis.
Besides the usage of dedicated pyrolyzers, pyrolysis GC of solid and liquid samples can be performed directly inside programmable temperature vaporizer (PTV) injectors that provide quick heating (up to 60 °C/s) and high maximum temperatures of 600-650 °C. This is sufficient for many pyrolysis applications. The main advantage is that no dedicated instrument has to be purchased and pyrolysis can be performed as part of routine GC analysis. In this case quartz GC inlet liners can be used. Quantitative data can be acquired, and good results of derivatization inside the PTV injector are published as well.
== Applications ==
Pyrolysis gas chromatography is useful for the identification of involatile compounds. These materials include polymeric materials, such as acrylics or alkyds. The way in which the polymer fragments, before it is separated in the GC, can help in identification. Pyrolysis gas chromatography is also used for environmental samples, including fossil analysis and microplastic detection. Pyrolysis GC is used in forensic laboratories to analyze evidence found in crime scenes such as paints, adhesives, plastics, synthetic fibres and soil extracts.
== References == | Wikipedia/Pyrolysis–gas_chromatography–mass_spectrometry |
Affinity chromatography is a method of separating a biomolecule from a mixture, based on a highly specific macromolecular binding interaction between the biomolecule and another substance. The specific type of binding interaction depends on the biomolecule of interest; antigen and antibody, enzyme and substrate, receptor and ligand, or protein and nucleic acid binding interactions are frequently exploited for isolation of various biomolecules. Affinity chromatography is useful for its high selectivity and resolution of separation, compared to other chromatographic methods.
== Principle ==
Affinity chromatography has the advantage of specific binding interactions between the analyte of interest (normally dissolved in the mobile phase), and a binding partner or ligand (immobilized on the stationary phase). In a typical affinity chromatography experiment, the ligand is attached to a solid, insoluble matrix—usually a polymer such as agarose or polyacrylamide—chemically modified to introduce reactive functional groups with which the ligand can react, forming stable covalent bonds. The stationary phase is first loaded into a column to which the mobile phase is introduced. Molecules that bind to the ligand will remain associated with the stationary phase. A wash buffer is then applied to remove non-target biomolecules by disrupting their weaker interactions with the stationary phase, while the biomolecules of interest will remain bound. Target biomolecules may then be removed by applying a so-called elution buffer, which disrupts interactions between the bound target biomolecules and the ligand. The target molecule is thus recovered in the eluting solution.
Affinity chromatography does not require the molecular weight, charge, hydrophobicity, or other physical properties of the analyte of interest to be known, although knowledge of its binding properties is useful in the design of a separation protocol. Types of binding interactions commonly exploited in affinity chromatography procedures are summarized in the table below.
== Batch and column setups ==
Binding to the solid phase may be achieved by column chromatography whereby the solid medium is packed onto a column, the initial mixture run through the column to allow settling, a wash buffer run through the column and the elution buffer subsequently applied to the column and collected. These steps are usually done at ambient pressure. Alternatively, binding may be achieved using a batch treatment, for example, by adding the initial mixture to the solid phase in a vessel, mixing, separating the solid phase, removing the liquid phase, washing, re-centrifuging, adding the elution buffer, re-centrifuging and removing the elute.
Sometimes a hybrid method is employed such that the binding is done by the batch method, but the solid phase with the target molecule bound is packed onto a column and washing and elution are done on the column.
The ligands used in affinity chromatography are obtained from both organic and inorganic sources. Examples of biological sources are serum proteins, lectins and antibodies. Inorganic sources are moronic acid, metal chelates and triazine dyes.
A third method, expanded bed absorption, which combines the advantages of the two methods mentioned above, has also been developed. The solid phase particles are placed in a column where liquid phase is pumped in from the bottom and exits at the top. The gravity of the particles ensure that the solid phase does not exit the column with the liquid phase.
Affinity columns can be eluted by changing salt concentrations, pH, pI, charge and ionic strength directly or through a gradient to resolve the particles of interest.
More recently, setups employing more than one column in series have been developed. The advantage compared to single column setups is that the resin material can be fully loaded since non-binding product is directly passed on to a consecutive column with fresh column material. These chromatographic processes are known as periodic counter-current chromatography (PCC). The resin costs per amount of produced product can thus be drastically reduced. Since one column can always be eluted and regenerated while the other column is loaded, already two columns are sufficient to make full use of the advantages. Additional columns can give additional flexibility for elution and regeneration times, at the cost of additional equipment and resin costs.
== Specific uses ==
Affinity chromatography can be used in a number of applications, including nucleic acid purification, protein purification from cell free extracts, and purification from blood.
By using affinity chromatography, one can separate proteins that bind to a certain fragment from proteins that do not bind that specific fragment. Because this technique of purification relies on the biological properties of the protein needed, it is a useful technique and proteins can be purified many folds in one step.
=== Various affinity media ===
Many different affinity media exist for a variety of possible uses.
Briefly, they are (generalized) activated/functionalized that work as a functional spacer, support matrix, and eliminates handling of toxic reagents.
Amino acid media is used with a variety of serum proteins, proteins, peptides, and enzymes, as well as rRNA and dsDNA. Avidin biotin media is used in the purification process of biotin/avidin and their derivatives.
Carbohydrate bonding is most often used with glycoproteins or any other carbohydrate-containing substance; carbohydrate is used with lectins, glycoproteins, or any other carbohydrate metabolite protein. Dye ligand media is nonspecific but mimics biological substrates and proteins. Glutathione is useful for separation of GST tagged recombinant proteins. Heparin is a generalized affinity ligand, and it is most useful for separation of plasma coagulation proteins, along with nucleic acid enzymes and lipases
Hydrophobic interaction media are most commonly used to target free carboxyl groups and proteins.
Immunoaffinity media (detailed below) utilizes antigens' and antibodies' high specificity to separate; immobilized metal affinity chromatography is detailed further below and uses interactions between metal ions and proteins (usually specially tagged) to separate; nucleotide/coenzyme that works to separate dehydrogenases, kinases, and transaminases.
Nucleic acids function to trap mRNA, DNA, rRNA, and other nucleic acids/oligonucleotides. Protein A/G method is used to purify immunoglobulins.
Speciality media are designed for a specific class or type of protein/co enzyme; this type of media will only work to separate a specific protein or coenzyme.
=== Immunoaffinity ===
Another use for the procedure is the affinity purification of antibodies from blood serum. If the serum is known to contain antibodies against a specific antigen (for example if the serum comes from an organism immunized against the antigen concerned) then it can be used for the affinity purification of that antigen. This is also known as Immunoaffinity Chromatography. For example, if an organism is immunised against a GST-fusion protein it will produce antibodies against the fusion-protein, and possibly antibodies against the GST tag as well. The protein can then be covalently coupled to a solid support such as agarose and used as an affinity ligand in purifications of antibody from immune serum.
For thoroughness, the GST protein and the GST-fusion protein can each be coupled separately. The serum is initially allowed to bind to the GST affinity matrix. This will remove antibodies against the GST part of the fusion protein. The serum is then separated from the solid support and allowed to bind to the GST-fusion protein matrix. This allows any antibodies that recognize the antigen to be captured on the solid support. Elution of the antibodies of interest is most often achieved using a low pH buffer such as glycine pH 2.8. The eluate is collected into a neutral tris or phosphate buffer, to neutralize the low pH elution buffer and halt any degradation of the antibody's activity. This is a nice example as affinity purification is used to purify the initial GST-fusion protein, to remove the undesirable anti-GST antibodies from the serum and to purify the target antibody.
Monoclonal antibodies can also be selected to bind proteins with great specificity, where protein is released under fairly gentle conditions. This can become of use for further research in the future.
A simplified strategy is often employed to purify antibodies generated against peptide antigens. When the peptide antigens are produced synthetically, a terminal cysteine residue is added at either the N- or C-terminus of the peptide. This cysteine residue contains a sulfhydryl functional group which allows the peptide to be easily conjugated to a carrier protein (e.g. Keyhole limpet hemocyanin (KLH)). The same cysteine-containing peptide is also immobilized onto an agarose resin through the cysteine residue and is then used to purify the antibody.
Most monoclonal antibodies have been purified using affinity chromatography based on immunoglobulin-specific Protein A or Protein G, derived from bacteria.
Immunoaffinity chromatography with monoclonal antibodies immobilized on monolithic column has been successfully used to capture extracellular vesicles (e.g., exosomes and exomeres) from human blood plasma by targeting tetraspanins and integrins found on the surface of the EVs.
Immunoaffinity chromatography is also the basis for immunochromatographic test (ICT) strips, which provide a rapid means of diagnosis in patient care. Using ICT, a technician can make a determination at a patient's bedside, without the need for a laboratory. ICT detection is highly specific to the microbe causing an infection.
=== Immobilized metal ion affinity chromatography ===
Immobilized metal ion affinity chromatography (IMAC) is based on the specific coordinate covalent bond of amino acids, particularly histidine, to metals. This technique works by allowing proteins with an affinity for metal ions to be retained in a column containing immobilized metal ions, such as cobalt, nickel, or copper for the purification of histidine-containing proteins or peptides, iron, zinc or gallium for the purification of phosphorylated proteins or peptides. Many naturally occurring proteins do not have an affinity for metal ions, therefore recombinant DNA technology can be used to introduce such a protein tag into the relevant gene. Methods used to elute the protein of interest include changing the pH, or adding a competitive molecule, such as imidazole.
=== Recombinant proteins ===
Possibly the most common use of affinity chromatography is for the purification of recombinant proteins. Proteins with a known affinity are protein tagged in order to aid their purification. The protein may have been genetically modified so as to allow it to be selected for affinity binding; this is known as a fusion protein. Protein tags include hexahistidine (His), glutathione-S-transferase (GST), maltose binding protein (MBP), and the Colicin E7 variant CL7 tag. Histidine tags have an affinity for nickel, cobalt, zinc, copper and iron ions which have been immobilized by forming coordinate covalent bonds with a chelator incorporated in the stationary phase. For elution, an excess amount of a compound able to act as a metal ion ligand, such as imidazole, is used. GST has an affinity for glutathione which is commercially available immobilized as glutathione agarose. During elution, excess glutathione is used to displace the tagged protein. CL7 has an affinity and specificity for Immunity Protein 7 (Im7) which is commercially available immobilized as Im7 agarose resin. For elution, an active and site-specific protease is applied to the Im7 resin to release the tag-free protein.
=== Lectins ===
Lectin affinity chromatography is a form of affinity chromatography where lectins are used to separate components within the sample. Lectins, such as concanavalin A are proteins which can bind specific alpha-D-mannose and alpha-D-glucose carbohydrate molecules. Some common carbohydrate molecules that is used in lectin affinity chromatography are Con A-Sepharose and WGA-agarose. Another example of a lectin is wheat germ agglutinin which binds D-N-acetyl-glucosamine. The most common application is to separate glycoproteins from non-glycosylated proteins, or one glycoform from another glycoform. Although there are various ways to perform lectin affinity chromatography, the goal is extract a sugar ligand of the desired protein.
=== Specialty ===
Another use for affinity chromatography is the purification of specific proteins using a gel matrix that is unique to a specific protein. For example, the purification of E. coli β-galactosidase is accomplished by affinity chromatography using p-aminobenyl-1-thio-β-D-galactopyranosyl agarose as the affinity matrix. p-aminobenyl-1-thio-β-D-galactopyranosyl agarose is used as the affinity matrix because it contains a galactopyranosyl group, which serves as a good substrate analog for E. coli β-Galactosidase. This property allows the enzyme to bind to the stationary phase of the affinity matrix and β-Galactosidase is eluted by adding increasing concentrations of salt to the column.
==== Alkaline phosphatase ====
Alkaline phosphatase from E. coli can be purified using a DEAE-Cellulose matrix. A. phosphatase has a slight negative charge, allowing it to weakly bind to the positively charged amine groups in the matrix. The enzyme can then be eluted out by adding buffer with higher salt concentrations.
==== Boronate affinity chromatography ====
Boronate affinity chromatography consists of using boronic acid or boronates to elute and quantify amounts of glycoproteins. Clinical adaptations have applied this type of chromatography for use in determining long term assessment of diabetic patients through analysis of their glycated hemoglobin.
=== Serum albumin purification ===
Affinity purification of albumin and macroglobulin contamination is helpful in removing excess albumin and α2-macroglobulin contamination, when performing mass spectrometry. In affinity purification of serum albumin, the stationary used for collecting or attracting serum proteins can be Cibacron Blue-Sepharose. Then the serum proteins can be eluted from the adsorbent with a buffer containing thiocyanate (SCN−).
== Weak affinity chromatography ==
Weak affinity chromatography (WAC) is an affinity chromatography technique for affinity screening in drug development. WAC is an affinity-based liquid chromatographic technique that separates chemical compounds based on their different weak affinities to an immobilized target. The higher affinity a compound has towards the target, the longer it remains in the separation unit, and this will be expressed as a longer retention time. The affinity measure and ranking of affinity can be achieved by processing the obtained retention times of analyzed compounds. Affinity chromatography is part of a larger suite of techniques used in chemoproteomics based drug target identification.
The WAC technology is demonstrated against a number of different protein targets – proteases, kinases, chaperones and protein–protein interaction (PPI) targets. WAC has been shown to be more effective than established methods for fragment based screening.
== History ==
Affinity chromatography was conceived and first developed by Pedro Cuatrecasas and Meir Wilchek.
== References ==
== External links ==
"Affinity Chromatography Principle, Procedure And Advance Detailed Note – 2020".
"What is affinity chromatography" | Wikipedia/Affinity_chromatography |
Glowmatography is a laboratory technique for the separation of dyes present in solutions contained in glow sticks. The chemical components of such solutions can be chromatographically separated into polar and nonpolar components. Developed as a laboratory class experiment, it can be used to demonstrate chemistry concepts of polarity, chemical kinetics, and chemiluminescence.
== Description ==
In the chromatography of a glow stick solution, a piece of chalk, a highly polar substance, is used as the stationary phase while comparatively less-polar solvents like acetone and 91% isopropyl alcohol can be used as the mobile phase. Chalk is made up of calcium carbonate (CaCO3) or calcium sulfate (CaSO4), and therefore contains ions. This allows it to attract other ions and polar molecules, but not nonpolar molecules. As a result, ionic and more-polar dyes would be attracted to the stationary phase and move relatively slowly or a fairly small distance, while less polar dyes would migrate further as the mobile phase wicks up the chalk. This then allows for the separation of dyes.
== Experiment ==
This experiment can be conducted with glow sticks, chalks, and solutions of acetone or isopropyl alcohol.
Drops of glowing fluid from a glow stick are added to a chalk so that a band is created halfway through it. The chalk is then placed vertically into a beaker filled with a small amount of acetone or alcohol - ensuring the surface of the solvent is below the dye band. The liquid is then allowed to travel up the chalk; polar dyes would tend to stick to the chalk and not travel significantly while non-polar dyes would travel up with the solvent. Once it travels almost to the top of the chalk, it is removed from the beaker. The chalk chromatogram, with separation of colours, can then be observed in a dark room.
Additionally, this glomatographic experiment can be done using other materials. For instance, silica gel can be used as the stationary phase together with a solution of nonpolar hexanes acting as the mobile phase. The polar components would be attracted to the polar silanol (Si-OH) groups on the surface of the silica gel, and the nonpolar components would travel further with the hexanes. Further, dyes in glow sticks can also be extracted using liquid carbon dioxide (CO2) as an environmentally friendly or green solvent. In this case, non polar dyes would dissolve in the liquid CO2 and other dyes would be attracted to cotton.
== See also ==
Retardation factor
== References ==
== External links == | Wikipedia/Glowmatography |
Two-dimensional chromatography is a type of chromatographic technique in which the injected sample is separated by passing through two different separation stages. Two different chromatographic columns are connected in sequence, and the effluent from the first system is transferred onto the second column. Typically the second column has a different separation mechanism, so that bands that are poorly resolved from the first column may be completely separated in the second column. (For instance, a C18 reversed-phase chromatography column may be followed by a phenyl column.) Alternately, the two columns might run at different temperatures. During the second stage of separation the rate at which the separation occurs must be faster than the first stage, since there is still only a single detector. The plane surface is amenable to sequential development in two directions using two different solvents.
== History ==
Modern two-dimensional chromatographic techniques are based on the results of the early developments of paper chromatography and thin-layer chromatography (TLC) which involved liquid mobile phases and solid stationary phases. These techniques would later generate modern gas chromatography (GC) and liquid chromatography (LC) analysis. Different combinations of one-dimensional GC and LC produced the analytical chromatographic technique that is known as two-dimensional chromatography.
The earliest form of 2D-chromatography came in the form of a multi-step TLC separation in which a thin sheet of cellulose is used first with one solvent in one direction, then, after the paper has been dried, another solvent is run in a direction at right angles to the first. This methodology first appeared in the literature with a 1944 publication by A. J. P. Martin and coworkers detailing an efficient method for separating amino acids – "...but the two-dimensional chromatogram is especially convenient, in that it shows at a glance information that can be gained otherwise only as the result of numerous experiments" (Biochem J., 1944, 38, 224).
== Examples ==
Two-dimensional separations can be carried out in gas chromatography or liquid chromatography. Various different coupling strategies have been developed to "resample" from the first column into the second. Some important hardware for two-dimensional separations are Deans' switch and Modulator, which selectively transfer the first dimension eluent to second dimension column.
The chief advantage of two-dimensional techniques is that they offer a large increase in peak capacity, without requiring extremely efficient separations in either column. (For instance, if the first column offers a peak capacity (k1)of 100 for a 10-minute separation, and the second column offers a peak capacity of 5 (k2) in a 5-second separation, then the combined peak capacity may approach k1 × k2=500, with the total separation time still ~ 10 minutes). 2D separations have been applied to the analysis of gasoline and other petroleum mixtures, and more recently to protein mixtures.
=== Tandem mass spectrometry ===
Tandem mass spectrometry (Tandem MS or MS/MS) uses two mass analyzers in sequence to separate more complex mixtures of analytes. The advantage of tandem MS is that it can be much faster than other two-dimensional methods, with times ranging from milliseconds to seconds. Because there is no dilution with solvents in MS, there is less probability of interference, so tandem MS can be more sensitive and have a higher signal-to-noise ratio compared to other two-dimensional methods. The main disadvantage associated with tandem MS is the high cost of the instrumentation needed. Prices can range from $500,000 to over $1 million. Many form of tandem MS involve a mass selection step and a fragmentation step. The first mass analyzer can be programmed to only pass molecules of a specific mass-to-charge ratio. Then the second mass analyzer can fragment the molecule to determine its identity. This can be especially useful for separating molecules of the same mass (i.e. proteins of the same mass or molecular isomers). Different types of mass analyzers can be coupled to achieve varying effects. One example would be a TOF-Quadrupole system. Ions can be sequentially fragmented and/or analyzed in a quadrupole as they leave the TOF in order of increasing m/z. Another prevalent tandem mass spectrometer is the quadrupole-quadrupole-quadrupole (Q-Q-Q) analyzer. The first quadrupole separates by mass, collisions take place in the second quadrupole, and the fragments are separated by mass in the third quadrupole.
=== Gas chromatography-mass spectrometry ===
Gas chromatography-mass spectrometry (GC-MS) is a two-dimensional chromatography technique that combines the separation technique of gas chromatography with the identification technique of mass spectrometry. GC-MS is the single most important analytical tool for the analysis of volatile and semi-volatile organic compounds in complex mixtures. It works by first injecting the sample into the GC inlet where it is vaporized and pushed through a column by a carrier gas, typically helium. The analytes in the sample are separated based upon their interaction with the coating of the column, or the stationary phase, and the carrier gas, or the mobile phase. The compounds eluted from the column are converted into ions via electron impact (EI) or chemical ionization (CI) before traveling through the mass analyzer. The mass analyzer serves to separate the ions on a mass-to-charge basis. Popular choices perform the same function but differ in the way that they accomplish the separation. The analyzers typically used with GC-MS are the time-of-flight mass analyzer and the quadrupole mass analyzer. After leaving the mass analyzer, the analytes reach the detector and produce a signal that is read by a computer and used to create a gas chromatogram and mass spectrum. Sometimes GC-MS utilizes two gas chromatographers in particularly complex samples to obtain considerable separation power and be able to unambiguously assign the specific species to the appropriate peaks in a technique known as GCxGC-(MS). Ultimately, GC-MS is a technique utilized in many analytical laboratories and is a very effective and adaptable analytical tool.
=== Liquid chromatography-mass spectrometry ===
Liquid chromatography-mass spectrometry (LC/MS) couples high resolution chromatographic separation with MS detection. As the system adopts the high separation of HPLC, analytes which are in the liquid mobile phase are often ionized by various soft ionization methods including atmospheric pressure chemical ionization (APCI), electrospray ionization (ESI) or matrix-assisted laser desorption/ionization (MALDI), which attains the gas phase ionization required for the coupling with MS. These ionization methods allow the analysis of a wider range of biological molecules, including those with larger masses, thermally unstable or nonvolatile compounds where GC-MS is typically incapable of analyzing.
LC-MS provides high selectivity as unresolved peaks can be isolated by selecting a specific mass. Furthermore, better identification is also attained by mass spectra and the user does not have to rely solely on the retention time of analytes. As a result, molecular mass and structural information as well as quantitative data can all be obtained via LC-MS. LC-MS can therefore be applied to various fields, such as impurity identification and profiling in drug development and pharmaceutical manufacturing, since LC provides efficient separation of impurities and MS provides structural characterization for impurity profiling.
Common solvents used in normal or reversed phase LC such as water, acetonitrile, and methanol are all compatible with ESI, yet a LC grade solvent may not be suitable for MS. Furthermore, buffers containing inorganic ions should be avoided as they may contaminate the ion source. Nonetheless, the problem can be resolved by 2D LC-MS, as well as other various issues including analyte coelution and UV detection responses.
=== Liquid chromatography-liquid chromatography ===
Two-dimensional liquid chromatography (2D-LC) combines two separate analyses of liquid chromatography into one data analysis. Modern 2D liquid chromatography has its origins in the late 1970s to early 1980s. During this time, the hypothesized principles of 2D-LC were being proven via experiments conducted along with supplementary conceptual and theoretical work. It was shown that 2D-LC could offer quite a bit more resolving power compared to the conventional techniques of one-dimensional liquid chromatography. In the 1990s, the technique of 2D-LC played an important role in the separation of extremely complex substances and materials found in the proteomics and polymer fields of study. Unfortunately, the technique had been shown to have a significant disadvantage when it came to analysis time. Early work with 2D-LC was limited to small portion of liquid phase separations due to the long analysis time of the machinery. Modern 2D-LC techniques tackled that disadvantage head on, and have significantly reduced what was once a damaging feature. Modern 2D-LC has an instrumental capacity for high resolution separations to be completed in an hour or less. Due to the growing need for instrumentation to perform analysis on substances of growing complexity with better detection limits, the development of 2D-LC pushes forward. Instrumental parts have become a mainstream industry focus and are much easier to attain then before. Prior to this, 2D-LC was performed using components from 1D-LC instruments, and would lead to results of varying degrees in both accuracy and precision. The reduced stress on instrumental engineering has allowed for pioneering work in the field and technique of 2D-LC.
The purpose of employing this technique is to separate mixtures that one-dimensional liquid chromatography otherwise cannot separate effectively. Two-dimensional liquid chromatography is better suited to analyzing complex mixtures samples such as urine, environmental substances and forensic evidence such as blood.
Difficulties in separating mixtures can be attributed to the complexity of the mixture in the sense that separation cannot occur due to the number of different effluents in the compound. Another problem associated with one-dimensional liquid chromatography involves the difficulty associated to resolving closely related compounds. Closely related compounds have similar chemical properties that may prove difficult to separate based on polarity, charge, etc. Two-dimensional liquid chromatography provides separation based on more than one chemical or physical property. Using an example from Nagy and Vekey, a mixture of peptides can be separated based on their basicity, but similar peptides may not elute well. Using a subsequent LC technique, the similar basicity between the peptides can be further separated by employing differences in apolar character.
As a result, to be able to separate mixtures more efficiently, a subsequent LC analysis must employ very different separation selectivity relative to the first column. Another requirement to effectively use 2D liquid chromatography, according to Bushey and Jorgenson, is to employ highly orthogonal techniques which means that the two separation techniques must be as different as possible.
There are two major classifications of 2D liquid chromatography. These include: Comprehensive 2D liquid chromatography (LCxLC) and Heart-cutting 2D liquid chromatography (LC-LC). In comprehensive 2D-LC, all the peaks from a column elution are fully sampled, but it has been deemed unnecessary to transfer the entire sample from the first to the second column. A portion of the sample is sent to waste while the rest is sent to the sampling valve. In heart-cutting 2D-LC specific peaks are targeted with only a small portion of the peak being injected onto a second column. Heart-cutting 2D-LC has proven to be quite useful for sample analysis of substances that are not very complex provided they have similar retention behavior. Compared to comprehensive 2D-LC, heart-cutting 2D-LC provides an effective technique with much less system setup and a much lower operating cost. Multiple heart-cutting (mLC-LC) may be utilized to sample multiple peaks from first dimensional analysis without risking temporary overlap of second dimensional analysis. Multiple heart-cutting (mLC-LC) utilizes a setup of multiple sampling loops.
For 2D-LC, peak capacity is a very important issue. This can be generated using gradient elution separation with much greater efficiency than an isocratic separation given a reasonable amount of time. While isocratic elution is much easier on a fast time scale, it is preferable to perform a gradient elution separation in the second dimension. The mobile phase strength is varied from a weak eluent composition to a stronger one. Based on linear solvent strength theory (LSST) of gradient elution for reversed phase chromatography, the relationship between retention time, instrumental variables and solute parameters is shown below.
tR=t0 +tD + t0/b*ln(b*(k0-td/t0) + 1)
While a lot of pioneering work has been completed in the years since 2D-LC became a major analytical chromatographic technique, there are still many modern problems to be considered. Large amounts of experimental variables have yet to be decided on, and the technique is constantly in a state of development.
=== Gas chromatography – gas chromatography ===
Comprehensive two-dimensional gas chromatography is an analytical technique that separates and analyzes complex mixtures. It has been utilized in fields such as: flavor, fragrance, environmental studies, pharmaceuticals, petroleum products and forensic science. GCxGC provides a high range of sensitivity and produces a greater separation power due to the increased peak capacity.
== See also ==
Two-dimensional gel electrophoresis
== References == | Wikipedia/Two-dimensional_chromatography |
The van Deemter equation in chromatography, named for Jan van Deemter, relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation. These properties include pathways within the column, diffusion (axial and longitudinal), and mass transfer kinetics between stationary and mobile phases. In liquid chromatography, the mobile phase velocity is taken as the exit velocity, that is, the ratio of the flow rate in ml/second to the cross-sectional area of the ‘column-exit flow path.’ For a packed column, the cross-sectional area of the column exit flow path is usually taken as 0.6 times the cross-sectional area of the column. Alternatively, the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied. The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates. The van Deemter equation is a hyperbolic function that predicts that there is an optimum velocity at which there will be the minimum variance per unit column length and, thence, a maximum efficiency. The van Deemter equation was the result of the first application of rate theory to the chromatography elution process.
== Van Deemter equation ==
The van Deemter equation relates height equivalent to a theoretical plate (HETP) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening, as follows:
H
E
T
P
=
A
+
B
u
+
(
C
s
+
C
m
)
⋅
u
{\displaystyle HETP=A+{\frac {B}{u}}+(C_{s}+C_{m})\cdot u}
Where
HETP = a measure of the resolving power of the column [m]
A = Eddy-diffusion parameter, related to channeling through a non-ideal packing [m]
B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m2 s−1]
C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s]
u = speed [m s−1]
In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur. In packed columns, however, multiple distinct routes ("channels") exist through the column packing, which results in band spreading. In the latter case, A will not be zero.
The form of the Van Deemter equation is such that HETP achieves a minimum value at a particular flow velocity. At this flow rate, the resolving power of the column is maximized, although in practice, the elution time is likely to be impractical. Differentiating the van Deemter equation with respect to velocity, setting the resulting expression equal to zero, and solving for the optimum velocity yields the following:
u
=
B
C
{\displaystyle u={\sqrt {\frac {B}{C}}}}
== Plate count ==
The plate height given as:
H
=
L
N
{\displaystyle H={\frac {L}{N}}\,}
with
L
{\displaystyle L\,}
the column length and
N
{\displaystyle N\,}
the number of theoretical plates can be estimated from a chromatogram by analysis of the retention time
t
R
{\displaystyle t_{R}\,}
for each component and its standard deviation
σ
{\displaystyle \sigma \,}
as a measure for peak width, provided that the elution curve represents a Gaussian curve.
In this case the plate count is given by:
N
=
(
t
R
σ
)
2
{\displaystyle N=\left({\frac {t_{R}}{\sigma }}\right)^{2}\,}
By using the more practical peak width at half height
W
1
/
2
{\displaystyle W_{1/2}\,}
the equation is:
N
=
8
ln
(
2
)
⋅
(
t
R
W
1
/
2
)
2
{\displaystyle N=8\ln(2)\cdot \left({\frac {t_{R}}{W_{1/2}}}\right)^{2}\,}
or with the width at the base of the peak:
N
=
16
⋅
(
t
R
W
b
a
s
e
)
2
{\displaystyle N=16\cdot \left({\frac {t_{R}}{W_{base}}}\right)^{2}\,}
== Expanded van Deemter ==
The Van Deemter equation can be further expanded to:
H
=
2
λ
d
p
+
2
γ
D
m
u
+
ω
(
d
p
or
d
c
)
2
u
D
m
+
R
d
f
2
u
D
s
{\displaystyle H=2\lambda d_{p}+{2\gamma D_{m} \over u}+{\omega (d_{p}{\mbox{ or }}d_{c})^{2}u \over D_{m}}+{Rd_{f}^{2}u \over D_{s}}}
Where:
H is plate height
λ is particle shape (with regard to the packing)
dp is particle diameter
γ, ω, and R are constants
Dm is the diffusion coefficient of the mobile phase
dc is the capillary diameter
df is the film thickness
Ds is the diffusion coefficient of the stationary phase.
u is the linear velocity
== Rodrigues equation ==
The Rodrigues equation, named for Alírio Rodrigues, is an extension of the Van Deemter equation used to describe the efficiency of a bed of permeable (large-pore) particles.
The equation is:
H
E
T
P
=
A
+
B
u
+
C
⋅
f
(
λ
)
⋅
u
{\displaystyle HETP=A+{\frac {B}{u}}+C\cdot f(\lambda )\cdot u}
where
f
(
λ
)
=
3
λ
[
1
tanh
(
λ
)
−
1
λ
]
{\displaystyle f(\lambda )={\frac {3}{\lambda }}\left[{\frac {1}{\tanh(\lambda )}}-{\frac {1}{\lambda }}\right]}
and
λ
{\displaystyle \lambda }
is the intraparticular Péclet number.
== See also ==
Resolution (chromatography)
Jan van Deemter
== References == | Wikipedia/Van_Deemter_equation |
Biomedical Chromatography is a monthly peer-reviewed scientific journal, published since 1986 by John Wiley & Sons. It covers research on the applications of chromatography and allied techniques in the biological and medical sciences. The editor-in-chief is Michael Bartlett (University of Georgia).
== Abstracting and indexing ==
The journal is abstracted and indexed in:
Chemical Abstracts Service
Scopus
Science Citation Index
According to the Journal Citation Reports, the journal has a 2020 impact factor of 1.902.
== Notable papers ==
The highest cited papers published in this journal are:
'High-throughput quantitative bioanalysis by LC/MS/MS', Volume 14, Issue 6, Oct 2000, Pages: 422 - 429, Jemal M. Cited 178 times
'Analytical Chemistry and Biochemistry of D-Amino Acids', Volume 10, Issue 6, Nov-Dec 1996, Pages: 303–312, Imai K, Fukushima T, Santa T, et al. Cited 79 times
'Fluorogenic and fluorescent labeling reagents with a benzofurazan skeleton', Volume 15, Issue 5, Aug 2001, Pages: 295–318, Uchiyama S, Santa T, Okiyama N, et al. Cited 74 times
== References ==
== External links ==
Official website | Wikipedia/Biomedical_Chromatography |
In chromatography, resolution is a measure of the separation of two peaks of different retention time t in a chromatogram.
== Expression ==
Chromatographic peak resolution is given by
R
s
=
2
t
R
2
−
t
R
1
w
b
1
+
w
b
2
{\displaystyle R_{s}=2{\cfrac {t_{R2}-t_{R1}}{w_{b1}+w_{b2}}}}
where tR is the retention time and wb is the peak width at baseline. The bigger the time-difference and/or the smaller the bandwidths, the better the resolution of the compounds. Here compound 1 elutes before compound 2.
If the peaks have the same width
R
s
=
t
R
2
−
t
R
1
w
b
{\displaystyle R_{s}={\cfrac {t_{R2}-t_{R1}}{w_{b}}}}
.
== Plate number ==
The theoretical plate height is given by
H
=
L
N
{\displaystyle H={\frac {L}{N}}}
where L is the column length and N the number of theoretical plates. The relation between plate number and peak width at the base is given by
N
=
16
⋅
(
t
R
W
b
)
2
{\displaystyle N=16\cdot \left({\frac {t_{R}}{W_{b}}}\right)^{2}\,}
.
== See also ==
Image resolution
Resolution (mass spectrometry)
Van Deemter equation
== References ==
== External links ==
IUPAC Nomenclature for Chromatography | Wikipedia/Resolution_(chromatography) |
Displacement chromatography is a chromatography technique in which a sample is placed onto the head of the column and is then displaced by a solute that is more strongly sorbed than the components of the original mixture. The result is that the components are resolved into consecutive "rectangular" zones of highly concentrated pure substances rather than solvent-separated "peaks". It is primarily a preparative technique; higher product concentration, higher purity, and increased throughput may be obtained compared to other modes of chromatography.
== Discovery ==
The advent of displacement chromatography can be attributed to Arne Tiselius, who in 1943 first classified the modes of chromatography as frontal, elution, and displacement. Displacement chromatography found a variety of applications including isolation of transuranic elements and biochemical entities.
The technique was redeveloped by Csaba Horváth, who employed modern high-pressure columns and equipment. It has since found many applications, particularly in the realm of biological macromolecule purification.
== Principle ==
The basic principle of displacement chromatography is: there are only a finite number of binding sites for solutes on the matrix (the stationary phase), and if a site is occupied by one molecule, it is unavailable to others. As in any chromatography, equilibrium is established between molecules of a given kind bound to the matrix and those of the same kind free in solution. Because the number of binding sites is finite, when the concentration of molecules free in solution is large relative to the dissociation constant for the sites, those sites will mostly be filled. This results in a downward-curvature in the plot of bound vs free solute, in the simplest case giving a Langmuir isotherm. A molecule with a high affinity for the matrix (the displacer) will compete more effectively for binding sites, leaving the mobile phase enriched in the lower-affinity solute. Flow of mobile phase through the column preferentially carries off the lower-affinity solute and thus at high concentration the higher-affinity solute will eventually displace all molecules with lesser affinities.
== Mode of operation ==
=== Loading ===
At the beginning of the run, a mixture of solutes to be separated is applied to the column, under conditions selected to promote high retention. The higher-affinity solutes are preferentially retained near the head of the column, with the lower-affinity solutes moving farther downstream. The fastest moving component begins to form a pure zone downstream. The other components also begin to form zones, but the continued supply of the mixed feed at head of the column prevents full resolution.
=== Displacement ===
After the entire sample is loaded, the feed is switched to the displacer, chosen to have higher affinity than any sample component. The displacer forms a sharp-edged zone at the head of the column, pushing the other components downstream. Each sample component now acts as a displacer for the lower-affinity solutes, and the solutes sort themselves out into a series of contiguous bands (a "displacement train"), all moving downstream at the rate set by the displacer. The size and loading of the column are chosen to let this sorting process reach completion before the components reach the bottom of the column. The solutes appear at the bottom of the column as a series of contiguous zones, each consisting of one purified component, with the concentration within each individual zone effectively uniform.
=== Regeneration ===
After the last solute has been eluted, it is necessary to strip the displacer from the column. Since the displacer was chosen for high affinity, this can pose a challenge. On reverse-phase materials, a wash with a high percentage of organic solvent may suffice. Large pH shifts are also often employed. One effective strategy is to remove the displacer by chemical reaction; for instance if hydrogen ion was used as displacer it can be removed by reaction with hydroxide, or a polyvalent metal ion can be removed by reaction with a chelating agent. For some matrices, reactive groups on the stationary phase can be titrated to temporarily eliminate the binding sites, for instance weak-acid ion exchangers or chelating resins can be converted to the protonated form. For gel-type ion exchangers, selectivity reversal at very high ionic strength can also provide a solution. Sometimes the displacer is specifically designed with a titratable functional group to shift its affinity. After the displacer is washed out, the column is washed as needed to restore it to its initial state for the next run.
== Comparison with elution chromatography ==
=== Common fundamentals ===
In any form of chromatography, the rate at which the solute moves down the column is a direct reflection of the percentage of time the solute spends in the mobile phase. To achieve separation in either elution or displacement chromatography, there must be appreciable differences in the affinity of the respective solutes for the stationary phase. Both methods rely on movement down the column to amplify the effect of small differences in distribution between the two phases. Distribution between the mobile and stationary phases is described by the binding isotherm, a plot of solute bound to (or partitioned into) the stationary phase as a function of concentration in the mobile phase. The isotherm is often linear, or approximately so, at low concentrations, but commonly curves (concave-downward) at higher concentrations as the stationary phase becomes saturated.
=== Characteristics of elution mode ===
In elution mode, solutes are applied to the column as narrow bands and, at low concentration, move down the column as approximately Gaussian peaks. These peaks continue to broaden as they travel, in proportion to the square root of the distance traveled. For two substances to be resolved, they must migrate down the column at sufficiently different rates to overcome the effects of band spreading. Operating at high concentration, where the isotherm is curved, is disadvantageous in elution chromatography because the rate of travel then depends on concentration, causing the peaks to spread and distort.
Retention in elution chromatography is usually controlled by adjusting the composition of the mobile phase (in terms of solvent composition, pH, ionic strength, and so forth) according to the type of stationary phase employed and the particular solutes to be separated. The mobile phase components generally have lower affinity for the stationary phase than do the solutes being separated, but are present at higher concentration and achieve their effects due to mass action. Resolution in elution chromatography is generally better when peaks are strongly retained, but conditions that give good resolution of early peaks lead to long run-times and excessive broadening of later peaks unless gradient elution is employed. Gradient equipment adds complexity and expense, particularly at large scale.
=== Advantages and disadvantages of displacement mode ===
In contrast to elution chromatography, solutes separated in displacement mode form sharp-edged zones rather than spreading peaks. Zone boundaries in displacement chromatography are self-sharpening: if a molecule for some reason gets ahead of its band, it enters a zone in which it is more strongly retained, and will then run more slowly until its zone catches up. Furthermore, because displacement chromatography takes advantage of the non-linearity of the isotherms, loadings are deliberately high; more material can be separated on a given column, in a given time, with the purified components recovered at significantly higher concentrations. Retention conditions can still be adjusted, but the displacer controls the migration rate of the solutes. The displacer is selected to have higher affinity for the stationary phase than does any of the solutes being separated, and its concentration is set to approach saturation of the stationary phase and to give the desired migration rate of the concentration wave. High-retention conditions can be employed without gradient operation, because the displacer ensures removal of all solutes of interest in the designed run time.
Because of the concentrating effect of loading the column under high-retention conditions, displacement chromatography is well suited to purify components from dilute feed streams. However, it is also possible to concentrate material from a dilute stream at the head of a chromatographic column and then switch conditions to elute the adsorbed material in conventional isocratic or gradient modes. Therefore, this approach is not unique to displacement chromatography, although the higher loading capacity and less dilution allow greater concentration in displacement mode.
A disadvantage of displacement chromatography is that non-idealities always give rise to an overlap zone between each pair of components; this mixed zone must be collected separately for recycle or discard to preserve the purity of the separated materials. The strategy of adding spacer molecules to form zones between the components (sometimes termed "carrier displacement chromatography") has been investigated and can be useful when suitable, readily removable spacers are found. Another disadvantage is that the raw chromatogram, for instance a plot of absorbance or refractive index vs elution volume, can be difficult to interpret for contiguous zones, especially if the displacement train is not fully developed. Documentation and troubleshooting may require additional chemical analysis to establish the distribution of a given component. Another disadvantage is that the time required for regeneration limits throughput.
According to John C. Ford's article in the Encyclopedia of Chromatography, theoretical studies indicate that at least for some systems, optimized overloaded elution chromatography offers higher throughput than displacement chromatography, though limited experimental tests suggest that displacement chromatography is superior (at least before consideration of regeneration time).
== Applications ==
Historically, displacement chromatography was applied to preparative separations of amino acids and rare earth elements and has also been investigated for isotope separation.
=== Proteins ===
The chromatographic purification of proteins from complex mixtures can be quite challenging, particularly when the mixtures contain similarly retained proteins or when it is desired to enrich trace components in the feed. Further, column loading is often limited when high resolutions are required using traditional modes of chromatography (e.g. linear gradient, isocratic chromatography). In these cases, displacement chromatography is an efficient technique for the purification of proteins from complex mixtures at high column loadings in a variety of applications.
An important advance in the state of the art of displacement chromatography was the development of low molecular mass displacers for protein purification in ion exchange systems. This research was significant in that it represented a major departure from the conventional wisdom that large polyelectrolyte polymers are required to displace proteins in ion exchange systems.
Low molecular mass displacers have significant operational advantages as compared to large polyelectrolyte displacers. For example, if there is any overlap between the displacer and the protein of interest, these low molecular mass materials can be readily separated from the purified protein during post-displacement processing using standard size-based purification methods (e.g. size exclusion chromatography, ultrafiltration). In addition, the salt-dependent adsorption behavior of these low MW displacers greatly facilitates column regeneration. These displacers have been employed for a wide variety of high resolution separations in ion exchange systems. In addition, the utility of displacement chromatography for the purification of recombinant growth factors, antigenic vaccine proteins and antisense oligonucleotides has also been demonstrated. There are several examples in which displacement chromatography has been applied to the purification of proteins using ion exchange, hydrophobic interaction, as well as reversed-phase chromatography.
Displacement chromatography is well suited for obtaining mg quantities of purified proteins from complex mixtures using standard analytical chromatography columns at the bench scale. It is also particularly well suited for enriching trace components in the feed. Displacement chromatography can be readily carried out using a variety of resin systems including, ion exchange, HIC and RPLC.
=== Two-dimensional chromatography ===
Two-dimensional chromatography represents the most thorough and rigorous approach to evaluation of the proteome. While previously accepted approaches have utilized elution mode chromatographic approaches such as cation exchange to reversed phase HPLC, yields are typically very low requiring analytical sensitivities in the picomolar to femtomolar range. As displacement chromatography offers the advantage of concentration of trace components, two dimensional chromatography utilizing displacement rather than elution mode in the upstream chromatography step represents a potentially powerful tool for analysis of trace components, modifications, and identification of minor expressed components of the proteome.
== Notes ==
== References == | Wikipedia/Displacement_chromatography |
In chemical analysis, capillary electrochromatography (CEC) is a chromatographic technique in which the mobile phase is driven through the chromatographic bed by electro-osmosis. Capillary electrochromatography is a combination of two analytical techniques, high-performance liquid chromatography and capillary electrophoresis. Capillary electrophoresis aims to separate analytes on the basis of their mass-to-charge ratio by passing a high voltage across ends of a capillary tube, which is filled with the analyte. High-performance liquid chromatography separates analytes by passing them, under high pressure, through a column filled with stationary phase. The interactions between the analytes and the stationary phase and mobile phase lead to the separation of the analytes. In capillary electrochromatography capillaries, packed with HPLC stationary phase, are subjected to a high voltage. Separation is achieved by electrophoretic migration of solutes and differential partitioning.
== Principle ==
Capillary electrochromatography (CEC) combines the principles used in HPLC and CE. The mobile phase is driven across the chromatographic bed using electroosmosis instead of pressure (as in HPLC). Electroosmosis is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane or any other fluid conduit. Electroosmotic flow is caused by the Coulomb force induced by an electric field on net mobile electric charge in a solution. Under alkaline conditions, the surface silanol groups of the fused silica will become ionised leading to a negatively charged surface. This surface will have a layer of positively charged ions in close proximity which are relatively immobilised. This layer of ions is called the Stern layer. The thickness of the double layer is given by the formula:
δ
=
ϵ
r
ϵ
0
R
T
2
c
F
2
{\displaystyle \delta ={\sqrt {\frac {\epsilon _{r}\epsilon _{0}RT}{2cF^{2}}}}}
where εr is the relative permittivity of the medium, εo is the permittivity of vacuum, R is the universal gas constant, T is the absolute temperature, c is the molar concentration, and F is the Faraday constant
When an electric field is applied to the fluid (usually via electrodes placed at inlets and outlets), the net charge in the electrical double layer is induced to move by the resulting Coulomb force. The resulting flow is termed electroosmotic flow. In CEC positive ions of the electrolyte added along with the analyte accumulate in the electrical double layer of the particles of the column packing on application of an electric field they move towards the cathode and drag the liquid mobile phase with them.
The relationship between the linear velocity u of the liquid in the capillary and the applied electric field is given by the Smoluchowski equation as
u
=
ϵ
r
ϵ
0
ζ
E
η
{\displaystyle u=\epsilon _{r}\epsilon _{0}\zeta E\eta }
where ζ is the potential across the Stern layer (zeta potential), E is the electric field strength, and η is the viscosity of the solvent.
Separation of components in CEC is based on interactions between the stationary phase and differential electrophoretic migration of solutes.
== Instrumentation ==
The components of a capillary electrochromatograph are a sample vial, source and destination vials, a packed capillary, electrodes, a high voltage power supply, a detector, and a data output and handling device. The source vial, destination vial and capillary are filled with an electrolyte such as an aqueous buffer solution. The capillary is packed with stationary phase. To introduce the sample, the capillary inlet is placed into a vial containing the sample and then returned to the source vial (sample is introduced into the capillary via capillary action, pressure, or siphoning). The migration of the analytes is then initiated by an electric field that is applied between the source and destination vials and is supplied to the electrodes by the high-voltage power supply. The analytes separate as they migrate due to their electrophoretic mobility, and are detected near the outlet end of the capillary. The output of the detector is sent to a data output and handling device such as an integrator or computer. The data is then displayed as an electropherogram, which reports detector response as a function of time. Separated chemical compounds appear as peaks with different migration times in an electropherogram.
== Advantages ==
Avoiding the use of pressure to introduce the mobile phase into the column, results in a number of important advantages. Firstly, the pressure driven flow rate across a column depends directly on the square of the particle diameter and inversely on the length of the column. This restricts the length of the column and size of the particle, particle size is seldom less than 3 micrometer and the length of the column is restricted to 25 cm. Electrically driven flow rate is independent of length of column and size. A second advantage of using electroosmosis to pass the mobile phase into the column is the plug-like flow velocity profile of EOF, which reduces the solute dispersion in the column, increasing column efficiency.
== See also ==
Capillary electrophoresis
Chromatography
Electrochromatography
Electrophoresis
High-performance liquid chromatography
== References ==
== Further reading ==
Smith, N. "Capillary ElectroChromatography" Available at:https://www.beckmancoulter.com/wsrportal/bibliography?docname=AP8508ACECPrimer.pdf
Bartle, K. D. Capillary ElectroChromatography Published by The Royal Society of Chemistry, Cambridge. ISBN 0-85404-530-9 | Wikipedia/Capillary_electrochromatography |
Supercritical fluid chromatography (SFC) is a form of normal phase chromatography that uses a supercritical fluid such as carbon dioxide as the mobile phase. It is used for the analysis and purification of low to moderate molecular weight, thermally labile molecules and can also be used for the separation of chiral compounds. Principles are similar to those of high performance liquid chromatography (HPLC); however, SFC typically utilizes carbon dioxide as the mobile phase. Therefore, the entire chromatographic flow path must be pressurized. Because the supercritical phase represents a state whereby bulk liquid and gas properties converge, supercritical fluid chromatography is sometimes called convergence chromatography. The idea of liquid and gas properties convergence was first envisioned by Giddings.
== Applications ==
SFC has been used primarily for separation of chiral molecules, mainly those which required normal phase conditions. While the mobile phase is a fluid in the supercritical state, the stationary phase is packed inside columns similar to those used in liquid chromatography. Since the use of normal phase mode of chromatography remained less common, so did SFC; therefore it is now commonly used for selected chiral and achiral separations and purification in the pharmaceutical industry.
== Apparatus ==
Instrumentation of supercritical fluid chromatography SFC has a similar setup to an HPLC instrument. The stationary phases are similar, and are packed inside similar column types. However, there are special features in these systems, because of the need to keep the mobile phase at supercritical fluidic state over the entire system. Temperature is critical to keep the fluids in a supercritical state, so there should be a heat control tool in the system, similar to that of GC. Also, there should be a precise pressure control mechanism, a restrictor to keep the pressure above a certain point, because pressure is another essential parameter to keep the mobile phase in a supercritical fluid state, so it is kept at the required minimal level. A microprocessor mechanism is placed in the instrument for SFC. This unit collects data for pressure, oven temperature, and detector performance to control the related pieces of the instrument.
CO2 utilized in carbon dioxide dedicated pumps, which require that the incoming CO2 and pump heads be kept cold, in order to maintain the carbon dioxide at a temperature and pressure fit for supercritical fluidic state, where it can be effectively metered at a specified flow rate range. The CO2 subsequently becomes supercritical fluid throughout the injector and the column oven, when the temperature and pressure it is subjected to, are raised above the critical point of the liquid, thus the supercritical state is achieved.
Supercritical fluids combine useful properties of gas and liquid phases, as it can behave like both a gas and a liquid in various aspects. A supercritical fluid provides a gas-like characteristic when it fills a container and it takes the shape of the container. The motion and kinetics of the molecules are quite similar to gas molecules. On the other hand, a supercritical fluid behaves like a liquid because its density property is near liquid; thus, a supercritical fluid shows a similarity to the dissolving effect of a liquid. The result is that one can load masses, similar to those used in HPLC, on column per injection, and still maintain a high chromatographic efficiency similar to those attained in GC. Typically, gradient elution is employed in analytical SFC using a polar co-solvent such as methanol, possibly with a weak acid or base at low concentrations ~1%. The apparent plate count per analysis can be observed to exceed 500K plates per meter routinely with 5 um stationary phases. The operator uses software to set mobile phase flow rate, co-solvent composition, system back pressure and column oven temperature, which must exceed 40 °C for supercritical conditions needed to be achieved with CO2. In addition, SFC provides an additional control parameter – pressure – by using an automated static and dynamic back pressure regulator. From an operational standpoint, SFC is as simple and robust as HPLC, but fraction collection is more convenient because the primary mobile phase evaporates leaving only the analyte and a small volume of polar co-solvent. If the outlet CO2 is captured, it can be re-compressed and recycled, allowing for >90% reuse of CO2.
Similar to HPLC, SFC uses a variety of detection methods including UV/VIS, mass spectrometry, FID (unlike HPLC) and evaporative light scattering.
== Sample preparation ==
A rule-of-thumb is that any molecule that will dissolve in methanol or a less polar solvent is compatible with SFC, including non-volatile polar solutes. CO2 has polarity similar to n-heptane at its critical point. The solvent's elution strength can be increased just by increasing density or alternatively, using a polar co-solvent. In practice, when the fraction of the co-solvent is high, the mobile phase might not be truly at supercritical fluid state, but this terminology is used regardless, and the chromatograms show better elution and higher efficiency nevertheless.
== Mobile phase ==
The mobile phase is composed primarily of supercritical carbon dioxide, but since CO2 on its own is too non-polar to effectively elute many analytes, cosolvents are added to modify the mobile phase polarity. Cosolvents are typically simple alcohols like methanol, ethanol, or isopropyl alcohol. Other solvents such as acetonitrile, chloroform, or ethyl acetate can be used as modifiers. For food-grade materials, the selected cosolvent is often ethanol or ethyl acetate, both of which are generally recognized as safe (GRAS). The solvent limitations are system and column based.
== Drawbacks ==
There have been a few technical issues that have limited adoption of SFC technology in the past. First of all, is the need to keep a high gas pressure in the operating conditions. High-pressure vessels are expensive and bulky, and special materials are often needed to avoid dissolving gaskets and O-rings in the supercritical fluid. A second drawback is difficulty in maintaining pressure constant (by back-pressure regulation). Whereas liquids are nearly incompressible, so their densities are constant regardless of pressure, supercritical fluids are highly compressible and their physical properties change with pressure – such as the pressure drop across a packed-bed column. Currently, automated backpressure regulators can maintain a constant pressure in the column even if flow rate varies, mitigating this problem. A third drawback is difficulty in gas/liquid separation during collection of product. Upon depressurization, the CO2 rapidly turns into gas and aerosolizes any dissolved analyte in the process. Cyclone separators have lessened difficulties in gas/liquid separations.
== References == | Wikipedia/Supercritical_fluid_chromatography |
Fusion proteins or chimeric (kī-ˈmir-ik) proteins (literally, made of parts from different sources) are proteins created through the joining of two or more genes that originally coded for separate proteins. Translation of this fusion gene results in a single or multiple polypeptides with functional properties derived from each of the original proteins. Recombinant fusion proteins are created artificially by recombinant DNA technology for use in biological research or therapeutics. Chimeric or chimera usually designate hybrid proteins made of polypeptides having different functions or physico-chemical patterns. Chimeric mutant proteins occur naturally when a complex mutation, such as a chromosomal translocation, tandem duplication, or retrotransposition creates a novel coding sequence containing parts of the coding sequences from two different genes. Naturally occurring fusion proteins are commonly found in cancer cells, where they may function as oncoproteins. The bcr-abl fusion protein is a well-known example of an oncogenic fusion protein, and is considered to be the primary oncogenic driver of chronic myelogenous leukemia.
== Functions ==
Some fusion proteins combine whole peptides and therefore contain all functional domains of the original proteins. However, other fusion proteins, especially those that occur naturally, combine only portions of coding sequences and therefore do not maintain the original functions of the parental genes that formed them.
Many whole gene fusions are fully functional and can still act to replace the original peptides. Some, however, experience interactions between the two proteins that can modify their functions. Beyond these effects, some gene fusions may cause regulatory changes that alter when and where these genes act. For partial gene fusions, the shuffling of different active sites and binding domains have the potential to result in new proteins with novel functions.
=== Fluorescent protein tags ===
The fusion of fluorescent tags to proteins in a host cell is a widely popular technique used in experimental cell and biology research in order to track protein interactions in real time. The first fluorescent tag, green fluorescent protein (GFP), was isolated from Aequorea victoria and is still used frequently in modern research. More recent derivations include photoconvertible fluorescent proteins (PCFPs), which were first isolated from Anthozoa. The most commonly used PCFP is the Kaede fluorescent tag, but the development of Kikume green-red (KikGR) in 2005 offers a brighter signal and more efficient photoconversion. The advantage of using PCFP fluorescent tags is the ability to track the interaction of overlapping biochemical pathways in real time. The tag will change color from green to red once the protein reaches a point of interest in the pathway, and the alternate colored protein can be monitored through the duration of pathway. This technique is especially useful when studying G-protein coupled receptor (GPCR) recycling pathways. The fates of recycled G-protein receptors may either be sent to the plasma membrane to be recycled, marked by a green fluorescent tag, or may be sent to a lysosome for degradation, marked by a red fluorescent tag.
=== Chimeric protein drugs ===
The purpose of creating fusion proteins in drug development is to impart properties from each of the "parent" proteins to the resulting chimeric protein. Several chimeric protein drugs are currently available for medical use.
Many chimeric protein drugs are monoclonal antibodies whose specificity for a target molecule was developed using mice and hence were initially "mouse" antibodies. As non-human proteins, mouse antibodies tend to evoke an immune reaction if administered to humans. The chimerization process involves engineering the replacement of segments of the antibody molecule that distinguish it from a human antibody. For example, human constant domains can be introduced, thereby eliminating most of the potentially immunogenic portions of the drug without altering its specificity for the intended therapeutic target. Antibody nomenclature indicates this type of modification by inserting -xi- into the non-proprietary name (e.g., abci-xi-mab). If parts of the variable domains are also replaced by human portions, humanized antibodies are obtained. Although not conceptually distinct from chimeras, this type is indicated using -zu- such as in dacli-zu-mab. See the list of monoclonal antibodies for more examples.
In addition to chimeric and humanized antibodies, there are other pharmaceutical purposes for the creation of chimeric constructs. Etanercept, for example, is a TNFα blocker created through the combination of a tumor necrosis factor receptor (TNFR) with the immunoglobulin G1 Fc segment. TNFR provides specificity for the drug target and the antibody Fc segment is believed to add stability and deliverability of the drug. Additional chimeric proteins used for therapeutic applications include:
Aflibercept: A human recombinant protein that aids in the treatment of oxaliplatin-resistant metastatic colorectal cancer, neo-vascular macular degeneration, and macular edema.
Rilonacept: Reduces inflammation by preventing activation of IL-1 receptors to treat cryopyrin-associated periodic syndromes (CAPS).
Alefacept: Regulated T-cell responses by selectively targeting effector memory T-cells to treat psoriasis vulgaris.
Romiplostim: A peptibody that treats immune thrombocytopenia.
Abatacept/Belatacept: Interferes with T-cell co-stimulation to treat autoimmune disorders like rheumatoid arthritis, psoriatic arthritis, and psoriasis.
Denileukin-diftitox: Treats cutaneous lymphoma.
== Recombinant technology ==
A recombinant fusion protein is a protein created through genetic engineering of a fusion gene. This typically involves removing the stop codon from a cDNA sequence coding for the first protein, then appending the cDNA sequence of the second protein in frame through ligation or overlap extension PCR. That DNA sequence will then be expressed by a cell as a single protein. The protein can be engineered to include the full sequence of both original proteins, or only a portion of either.
If the two entities are proteins, often linker (or "spacer") peptides are also added, which make it more likely that the proteins fold independently and behave as expected. Especially in the case where the linkers enable protein purification, linkers in protein or peptide fusions are sometimes engineered with cleavage sites for proteases or chemical agents that enable the liberation of the two separate proteins. This technique is often used for identification and purification of proteins, by fusing a GST protein, FLAG peptide, or a hexa-his peptide (6xHis-tag), which can be isolated using affinity chromatography with nickel or cobalt resins. Di- or multimeric chimeric proteins can be manufactured through genetic engineering by fusion to the original proteins of peptide domains that induce artificial protein di- or multimerization (e.g., streptavidin or leucine zippers). Fusion proteins can also be manufactured with toxins or antibodies attached to them in order to study disease development. Hydrogenase promoter, PSH, was studied constructing a PSH promoter-gfp fusion by using green fluorescent protein (gfp) reporter gene.
=== Recombinant functionality ===
Novel recombinant technologies have made it possible to improve fusion protein design for use in fields as diverse as biodetection, paper and food industries, and biopharmaceuticals. Recent improvements have involved the fusion of single peptides or protein fragments to regions of existing proteins, such as N and C termini, and are known to increase the following properties:
Catalytic efficiency: Fusion of certain peptides allow for greater catalytic efficiency by altering the tertiary and quaternary structure of the target protein.
Solubility: A common challenge in fusion protein design is the issue of insolubility of newly synthesized fusion proteins in the recombinant host, leading to an over-aggregation of the target protein in the cell. Molecular chaperones that are able to aid in protein folding may be added, thereby better segregating hydrophobic and hydrophilic interactions in the solute to increase protein solubility.
Thermostability: Singular peptides or protein fragments are typically added to reduce flexibility of either the N or C terminus of the target protein, which reinforces thermostability and stabilizes pH range.
Enzyme activity: Fusion that involves the introduction of hydrogen bonds may be used to expand overall enzyme activity.
Expression levels: Addition of numerous fusion fragments, such as maltose binding protein (MBP) or small ubiquitin-like molecule (SUMO), serve to enhance enzyme expression and secretion of the target protein.
Immobilization: PHA synthase, an enzyme that allows for the immobilization of proteins of interest, is an important fusion tag in industrial research.
Crystal quality: Crystal quality can be improved by adding covalent links between proteins, aiding in structure determination techniques.
== Recombinant protein design ==
The earliest applications of recombinant protein design can be documented in the use of single peptide tags for purification of proteins in affinity chromatography. Since then, a variety of fusion protein design techniques have been developed for applications as diverse as fluorescent protein tags to recombinant fusion protein drugs. Three commonly used design techniques include tandem fusion, domain insertion, and post-translational conjugation.
=== Tandem fusion ===
The proteins of interest are simply connected end-to-end via fusion of N or C termini between the proteins. This provides a flexible bridge structure allowing enough space between fusion partners to ensure proper folding. However, the N or C termini of the peptide are often crucial components in obtaining the desired folding pattern for the recombinant protein, making simple end-to-end conjoining of domains ineffective in this case. For this reason, a protein linker is often needed to maintain the functionality of the protein domains of interest.
=== Domain insertion ===
This technique involves the fusion of consecutive protein domains by encoding desired structures into a single polypeptide chain, but sometimes may require insertion of a domain within another domain. This technique is typically regarding as more difficult to carry out than tandem fusion, due to difficulty finding an appropriate ligation site in the gene of interest.
=== Post-translational conjugation ===
This technique fuses protein domains following ribosomal translation of the proteins of interest, in contrast to genetic fusion prior to translation used in other recombinant technologies.
=== Protein linkers ===
Protein linkers aid fusion protein design by providing appropriate spacing between domains, supporting correct protein folding in the case that N or C termini interactions are crucial to folding. Commonly, protein linkers permit important domain interactions, reinforce stability, and reduce steric hindrance, making them preferred for use in fusion protein design even when N and C termini can be fused. Three major types of linkers are flexible, rigid, and in vivo cleavable.
Flexible linkers may consist of many small glycine residues, giving them the ability curl into a dynamic, adaptable shape.
Rigid linkers may be formed of large, cyclic proline residues, which can be helpful when highly specific spacing between domains must be maintained.
In vivo cleavable linkers are unique in that they are designed to allow the release of one or more fused domains under certain reaction conditions, such as a specific pH gradient, or when coming in contact with another biomolecule in the cell.
== Natural occurrence ==
Naturally occurring fusion genes are most commonly created when a chromosomal translocation replaces the terminal exons of one gene with intact exons from a second gene. This creates a single gene that can be transcribed, spliced, and translated to produce a functional fusion protein. Many important cancer-promoting oncogenes are fusion genes produced in this way.
Examples include:
Gag-onc fusion protein
Bcr-abl fusion protein
Tpr-met fusion protein
Antibodies are fusion proteins produced by V(D)J recombination.
There are also rare examples of naturally occurring polypeptides that appear to be a fusion of two clearly defined modules, in which each module displays its characteristic activity or function, independent of the other. Two major examples are: double PP2C chimera in Plasmodium falciparum (the malaria parasite), in which each PP2C module exhibits protein phosphatase 2C enzymatic activity, and the dual-family immunophilins that occur in a number of unicellular organisms (such as protozoan parasites and Flavobacteria) and contain full-length cyclophilin and FKBP chaperone modules. The evolutionary origin of such chimera remains unclear.
== See also ==
Genetic engineering
Protein engineering
Cell–cell fusogens
== References ==
== External links ==
Mutant+Chimeric+Proteins at the U.S. National Library of Medicine Medical Subject Headings (MeSH)
ChiPPI Archived 2021-11-10 at the Wayback Machine: The Server Protein–Protein Interaction of Chimeric Proteins. | Wikipedia/Fusion_protein |
The Journal of Chromatography A is a peer-reviewed scientific journal publishing research papers in analytical chemistry, with a focus on techniques and methods used for the separation and identification of mixtures. The major difference between Journal of Chromatography A and Journal of Chromatography B is the focus being on preparative chromatography instead of analytical chromatography. The split of the Journal of Chromatography into two journals occurred in late 1993, with volume 652 being the first for Journal of Chromatography A.
Indexed by ISI the journal received an impact factor of 4.169 as reported in the 2014 Journal Citation Reports by Thomson Reuters, ranking it 15th out of 79 journals in the category "Biochemical Research Methods" and ranking it sixth out of 74 journals in the category "Chemistry, analytical".
== See also ==
Journal of Chromatography B
== References ==
== External links ==
Official website | Wikipedia/Journal_of_Chromatography_A |
The physical process of sedimentation (the act of depositing sediment) has applications in water treatment, whereby gravity acts to remove suspended solids from water. Solid particles entrained by the turbulence of moving water may be removed naturally by sedimentation in the still water of lakes and oceans. Settling basins are ponds constructed for the purpose of removing entrained solids by sedimentation. Clarifiers are tanks built with mechanical means for continuous removal of solids being deposited by sedimentation; however, clarification does not remove dissolved solids.
== Basics ==
Suspended solids (or SS), is the mass of dry solids retained by a filter of a given porosity related to the volume of the water sample. This includes particles 10 μm and greater.
Colloids are particles of a size between 1 nm (0.001 μm) and 1 μm depending on the method of quantification. Because of Brownian motion and electrostatic forces balancing the gravity, they are not likely to settle naturally.
The limit sedimentation velocity of a particle is its theoretical descending speed in clear and still water. In settling process theory, a particle will settle only if:
In a vertical ascending flow, the ascending water velocity is lower than the limit sedimentation velocity.
In a longitudinal flow, the ratio of the length of the tank to the height of the tank is higher than the ratio of the water velocity to the limit sedimentation velocity.
Removal of suspended particles by sedimentation depends upon the size, zeta potential and specific gravity of those particles. Suspended solids retained on a filter may remain in suspension if their specific gravity is similar to water while very dense particles passing through the filter may settle. Settleable solids are measured as the visible volume accumulated at the bottom of an Imhoff cone after water has settled for one hour.
Gravitational theory is employed, alongside the derivation from Newton's second law and the Navier–Stokes equations.
Stokes' law explains the relationship between the settling rate and the particle diameter. Under specific conditions, the particle settling rate is directly proportional to the square of particle diameter and inversely proportional to liquid viscosity.
The settling velocity, defined as the residence time taken for the particles to settle in the tank, enables the calculation of tank volume. Precise design and operation of a sedimentation tank is of high importance in order to keep the amount of sediment entering the diversion system to a minimum threshold by maintaining the transport system and stream stability to remove the sediment diverted from the system. This is achieved by reducing stream velocity as low as possible for the longest period of time possible. This is feasible by widening the approach channel and lowering its floor to reduce flow velocity thus allowing sediment to settle out of suspension due to gravity. The settling behavior of heavier particulates is also affected by the turbulence.
== Designs ==
Although sedimentation might occur in tanks of other shapes, removal of accumulated solids is easiest with conveyor belts in rectangular tanks or with scrapers rotating around the central axis of circular tanks. Settling basins and clarifiers should be designed based on the settling velocity (vs) of the smallest particle to be theoretically 100% removed. The overflow rate is defined as:
Overflow rate (vo ) = Flow of water (Q (m3/s)) /(Surface area of settling basin (A(m2))
In many countries this value is named as surface loading in m3/h per m2. Overflow rate is often used for flow over an edge (for example a weir) in the unit m3/h per m.
The unit of overflow rate is usually meters (or feet) per second, a velocity. Any particle with settling velocity (vs) greater than the overflow rate will settle out, while other particles will settle in the ratio vs/vo.
There are recommendations on the overflow rates for each design that ideally take into account the change in particle size as the solids move through the operation:
Quiescent zones: 9.4 mm (0.031 ft) per second
Full-flow basins: 4.0 mm (0.013 ft) per second
Off-line basins: 0.46 mm (0.0015 ft) per second
However, factors such as flow surges, wind shear, scour, and turbulence reduce the effectiveness of settling. To compensate for these less than ideal conditions, it is recommended doubling the area calculated by the previous equation.
It is also important to equalize flow distribution at each point across the cross-section of the basin. Poor inlet and outlet designs can produce extremely poor flow characteristics for sedimentation.
Settling basins and clarifiers can be designed as long rectangles (Figure 1.a), that are hydraulically more stable and easier to control for large volumes. Circular clarifiers (Fig. 1.b) work as a common thickener (without the usage of rakes), or as upflow tanks (Fig. 1.c).
Sedimentation efficiency does not depend on the tank depth. If the forward velocity is low enough so that the settled material does not re-suspend from the tank floor, the area is still the main parameter when designing a settling basin or clarifier, taking care that the depth is not too low.
== Assessment of main process characteristics ==
Settling basins and clarifiers are designed to retain water so that suspended solids can settle. By sedimentation principles, the suitable treatment technologies should be chosen depending on the specific gravity, size and shear resistance of particles. Depending on the size and density of particles, and physical properties of the solids, there are four types of sedimentation processes:
Type 1 – Dilutes, non-flocculent, free-settling (every particle settles independently.)
Type 2 – Dilute, flocculent (particles can flocculate as they settle).
Type 3 – Concentrated suspensions, zone settling, hindered settling (sludge thickening).
Type 4 – Concentrated suspensions, compression (sludge thickening).
Different factors control the sedimentation rate in each.
=== Settling of discrete particles ===
Unhindered settling is a process that removes the discrete particles in a very low concentration without interference from nearby particles. In general, if the concentration of the solutions is lower than 500 mg/L total suspended solids, sedimentation will be considered discrete. Concentrations of raceway effluent total suspended solids (TSS) in the west are usually less than 5 mg/L net. TSS concentrations of off-line settling basin effluent are less than 100 mg/L net. The particles keep their size and shape during discrete settling, with an independent velocity. With such low concentrations of suspended particles, the probability of particle collisions is very low and consequently the rate of flocculation is small enough to be neglected for most calculations. Thus the surface area of the settling basin becomes the main factor of sedimentation rate. All continuous flow settling basins are divided into four parts: inlet zone, settling zone, sludge zone and outlet zone (Figure 2).
In the inlet zone, flow is established in a same forward direction. Sedimentation occurs in the settling zone as the water flow towards to outlet zone. The clarified liquid is then flow out from outlet zone.
Sludge zone: settled will be collected here and usually we assume that it is removed from water flow once the particles arrives the sludge zone.
In an ideal rectangular sedimentation tank, in the settling zone, the critical particle enters at the top of the settling zone, and the settle velocity would be the smallest value to reach the sludge zone, and at the end of outlet zone, the velocity component of this critical particle are the settling velocity in vertical direction (vs) and in horizontal direction (vh).
From Figure 1, the time needed for the particle to settle;
to =H/vh=L/vs (3)
Since the surface area of the tank is WL, and vs = Q/WL, vh = Q/WH, where Q is the flow rate and W, L, H is the width, length, depth of the tank.
According to Eq. 1, this also is a basic factor that can control the sedimentation tank performance which called overflow rate.
Eq. 2 also shows that the depth of sedimentation tank is independent to the sedimentation efficiency, only if the forward velocity is low enough to make sure the settled mass would not suspended again from the tank floor.
=== Settlement of flocculent particles ===
In a horizontal sedimentation tank, some particles may not follow the diagonal line in Fig. 1, while settling faster as they grow. So this says that particles can grow and develop a higher settling velocity if a greater depth with longer retention time. However, the collision chance would be even greater if the same retention time were spread over a longer, shallower tank. In fact, in order to avoid hydraulic short-circuiting, tanks usually are made 3–6 m deep with retention times of a few hours.
=== Zone-settling behaviour ===
As the concentration of particles in a suspension is increased, a point is reached where particles are so close together that they no longer settle independently of one another and the velocity fields of the fluid displaced by adjacent particles, overlap. There is also a net upward flow of liquid displaced by the settling particles. This results in a reduced particle-settling velocity and the effect is known as hindered settling.
There is a common case for hindered settling occurs. the whole suspension tends to settle as a ‘blanket’ due to its extremely high particle concentration. This is known as zone settling, because it is easy to make a distinction between several different zones which separated by concentration discontinuities. Fig. 3 represents a typical batch-settling column tests on a suspension exhibiting zone-settling characteristics. There is a clear interface near the top of the column would be formed to separating the settling sludge mass from the clarified supernatant as long as leaving such a suspension to stand in a settling column. As the suspension settles, this interface will move down at the same speed. At the same time, there is an interface near the bottom between that settled suspension and the suspended blanket. After settling of suspension is complete, the bottom interface would move upwards and meet the top interface which moves downwards.
=== Compression settling ===
The settling particles can contact each other and arise when approaching the floor of the sedimentation tanks at very high particle concentration. So that further settling will only occur in adjust matrix as the sedimentation rate decreasing. This is can be illustrated by the lower region of the zone-settling diagram (Figure 3). In Compression zone, the settled solids are compressed by gravity (the weight of solids), as the settled solids are compressed under the weight of overlying solids, and water is squeezed out while the space gets smaller.
== Applications ==
=== Potable water treatment ===
Sedimentation in potable water treatment generally follows a step of chemical coagulation and flocculation, which allows grouping particles together into flocs of a bigger size. This increases the settling speed of suspended solids and allows settling colloids.
=== Wastewater treatment ===
Sedimentation has been used to treat wastewater for millennia.
Primary treatment of sewage is removal of floating and settleable solids through sedimentation. Primary clarifiers reduce the content of suspended solids as well as the pollutant embedded in the suspended solids.: 5–9 Because of the large amount of reagent necessary to treat domestic wastewater, preliminary chemical coagulation and flocculation are generally not used, remaining suspended solids being reduced by following stages of the system. However, coagulation and flocculation can be used for building a compact treatment plant (also called a "package treatment plant"), or for further polishing of the treated water.
Sedimentation tanks called "secondary clarifiers" remove flocs of biological growth created in some methods of secondary treatment including activated sludge, trickling filters and rotating biological contactors.: 13
== See also ==
API oil-water separator
Dissolved air flotation
List of waste-water treatment technologies
Sewage treatment
Total suspended solids
== References ==
== Bibliography == | Wikipedia/Sedimentation_(water_treatment) |
Reversed-phase liquid chromatography (RP-LC) is a mode of liquid chromatography in which non-polar stationary phase and polar mobile phases are used for the separation of organic compounds. The vast majority of separations and analyses using high-performance liquid chromatography (HPLC) in recent years are done using the reversed phase mode. In the reversed phase mode, the sample components are retained in the system the more hydrophobic they are.
The factors affecting the retention and separation of solutes in the reversed phase chromatographic system are as follows:
a. The chemical nature of the stationary phase, i.e., the ligands bonded on its surface, as well as their bonding density, namely the extent of their coverage.
b. The composition of the mobile phase. Type of the bulk solvents whose mixtures affect the polarity of the mobile phase, hence the name modifier for a solvent added to affect the polarity of the mobile phase.
c. Additives, such as buffers, affect the pH of the mobile phase, which affect the ionization state of the solutes and their polarity.
In order to retain the organic components in mixtures, the stationary phases, packed within columns, consist of a hydrophobic substrates, bonded to the surface of porous silica-gel particles in various geometries (spheric, irregular), at different diameters (sub-2, 3, 5, 7, 10 um), with varying pore diameters (60, 100, 150, 300, A). The particle's surface is covered by chemically bonded hydrocarbons, such as C3, C4, C8, C18 and more. The longer the hydrocarbon associated with the stationary phase, the longer the sample components will be retained. Some stationary phases are also made of hydrophobic polymeric particles, or hybridized silica-organic groups particles, for method in which mobile phases at extreme pH are used. Most current methods of separation of biomedical materials use C-18 columns, sometimes called by trade names, such as ODS (octadecylsilane) or RP-18.
The mobile phases are mixtures of water and polar organic solvents, the vast majority of which are methanol and acetonitrile. These mixtures usually contain various additives such as buffers (acetate, phosphate, citrate), surfactants (alkyl amines or alkyl sulfonates) and special additives (EDTA). The goal of using supplements of one kind or another is to increase efficiency, selectivity, and control solute retention.
== Stationary phases ==
The history and evolution of reversed phase stationary phases in described in detail in an article by Majors, Dolan, Carr and Snyder.
In the 1970s, most liquid chromatography runs were performed using solid particles as the stationary phases, made of unmodified silica gel or alumina. This type of technique is now referred to as normal-phase chromatography. Since the stationary phase is hydrophilic in this technique, and the mobile phase is non-polar (consisting of organic solvents such as hexane and heptane), biomolecules with hydrophilic properties in the sample adsorb to the stationary phase strongly. Moreover, they were not dissolved easily in the mobile phase solvents. At the same time hydrophobic molecules experience less affinity to the polar stationary phase, and elute through it early with not enough retention. This was the reasons why during the 1970s the silica based particles were treated with hydrocarbons, immobilized or bonded on their surface, and the mobile phases were switched to aqueous and polar in nature, to accommodate biomedical substances.
The use of a hydrophobic stationary phase and polar mobile phases is essentially the reverse of normal phase chromatography, since the polarity of the mobile and stationary phases have been inverted – hence the term reversed-phase chromatography. As a result, hydrophobic molecules in the polar mobile phase tend to adsorb to the hydrophobic stationary phase, and hydrophilic molecules in the sample pass through the column and are eluted first. Hydrophobic molecules can be eluted from the column by decreasing the polarity of the mobile phase using an organic (non-polar) solvent, which reduces hydrophobic interactions. The more hydrophobic the molecule, the more strongly it will bind to the stationary phase, and the higher the concentration of organic solvent that will be required to elute the molecule.
Many of the mathematical parameters of the theory of chromatography and experimental considerations used in other chromatographic methods apply to RP-LC as well (for example, the selectivity factor, chromatographic resolution, plate count, etc. It can be used for the separation of a wide variety of molecules. It is typically used for separation of proteins, because the organic solvents used in normal-phase chromatography can denature many proteins.
Today, RP-LC is a frequently used analytical technique. There are huge variety of stationary phases available for use in RP-LC, allowing great flexibility in the development of the separation methods.
=== Silica-based stationary phases ===
Silica gel particles are commonly used as a stationary phase in high-performance liquid chromatography (HPLC) for several reasons, including:
High surface area: Silica gel particles have a high surface area, allowing direct interactions with solutes or after bonding of variety of ligands for versatile interactions with the sample molecules, leading to better separations.
Chemical and thermal stability and inertness: Silica gel is chemically stable, as it usually does not react with either the solvents of the mobile phase nor the compounds being separated, resulting in accurate, repeatable and reliable analyses.
Wide applicability: Silica gel is versatile and can be modified with various functional groups, making it suitable for a wide range of analytes and applications.
Efficient separation: The unique properties of silica gel particles, combined with their high surface area and controlled average particle diameter pore size, facilitate efficient and precise separation of compounds in HPLC.
Reproducibility: Silica gel particles can offer high batch-to-batch reproducibility, which is crucial for consistent and reliable HPLC analyses throughout decades.
Particle diameter and pore size control: Silica gel can be engineered to have specific pore sizes, enabling precise control over separation based on molecular size.
Cost-effectiveness: Silica is one of the most abundant minerals on earth, hence its gel is a cost-effective choice for HPLC applications, making it widely adopted in laboratories.
The United States Pharmacopoeia (USP) has classified HPLC columns by L# types. The most popular column in this classification is an octadecyl carbon chain (C18)-bonded silica (USP classification L1). This is followed by C8-bonded silica (L7), pure silica (L3), cyano-bonded silica (CN) (L10) and phenyl-bonded silica (L11). Note that C18, C8 and phenyl are dedicated reversed-phase stationary phases, while CN columns can be used in a reversed-phase mode depending on analyte and mobile phase conditions. Not all C18 columns have identical retention properties. Surface functionalization of silica can be performed in a monomeric or a polymeric reaction with different short-chain organosilanes used in a second step to cover remaining silanol groups (end-capping). While the overall retention mechanism remains the same, subtle differences in the surface chemistries of different stationary phases will lead to changes in selectivity.
Modern columns have different polarity depending on the ligand bonded to the stationary phase. PFP is pentafluorphenyl. CN is cyano. NH2 is amino. ODS is octadecyl or C18. ODCN is a mixed mode column consisting of C18 and nitrile.
Recent developments in chromatographic supports and instrumentation for liquid chromatography (LC) facilitate rapid and highly efficient separations, using various stationary phases geometries. Various analytical strategies have been proposed, such as the use of silica-based monolithic supports, elevated mobile phase temperatures, and columns packed with sub-3 μm superficially porous particles (fused or solid core) or with sub-2 μm fully porous particles for use in ultra-high-pressure LC systems (UHPLC).
== Mobile phases ==
A comprehensive article on the modern trends and best practices of mobile phase selection in reversed-phase chromatography was published by Boyes and Dong. A mobile phase in reversed-phase chromatograpy consists of mixtures of water or aqueous buffers, to which organic solvents are added, to elute analytes from a reversed-phase column in a selective manner. The added organic solvents must be miscible with water, and the two most common organic solvents used are acetonitrile and methanol. Other solvents can also be used such as ethanol or 2-propanol (isopropyl alcohol) and tetrahydrofuran (THF). The organic solvent is called also a modifier, since it is added to the aqueous solution in the mobile phase in order to modify the polarity of the mobile phase. Water is the most polar solvent in the reversed phase mobile phase; therefore, lowering the polarity of the mobile phase by adding modifiers enhances its elution strength. The two most widely used organic modifiers are acetonitrile and methanol, although acetonitrile is the more popular choice. Isopropanol (2-propanol) can also be used, because of its strong eluting properties, but its use is limited by its high viscosity, which results in higher backpressures. Both acetonitrile and methanol are less viscous than isopropanol, although a mixture of 50:50 percent of methanol:water is also very viscous and causes high backpressures.
All three solvents are essentially UV transparent. This is a crucial property for common reversed phase chromatography since sample components are typically detected by UV detectors. Acetonitrile is more transparent than the others in low UV wavelengths range, therefore it is used almost exclusively when separating molecules with weak or no chromophores (UV-VIS absorbing groups), such as peptides. Most peptides only absorb at low wavelengths in the ultra-violet spectrum (typically less than 225 nm) and acetonitrile provides much lower background absorbance at low wavelengths than the other common solvents.
The pH of the mobile phase can have an important role on the retention of an analyte and can change the selectivity of certain analytes. For samples containing solutes with ionized functional groups, such as amines, carboxyls, phosphates, phosphonates, sulfates, and sulfonates, the ionization of these groups can be controlled using mobile phase buffers.
For example, carboxylic groups in solutes become increasingly negatively charged as the pH of the mobile phase rises above their pKa, hence the whole molecule becomes more polar and less retained on the a-polar stationary phase. In this case, raising the pH of the phase mobile above 4–5 = pH (which is the typical pKa range for carboxylic groups) increases their ionization, hence decreases their retention. Conversely, using a mobile phase at a pH lower than 4 will increase their retention, because it will decrease their ionization degree, rendering them less polar.
The same considerations apply to substances containing basic functional groups, such as amines, whose pKa ranges are around 8 and above, are retained more, as the pH of the mobile phase increases, approaching 8 and above, because they are less ionized, hence less polar. However, in the case of high pH mobile phases, most of the traditional silica gel based Reversed Phase columns are generally limited for use with mobile phases at pH 8 and above, therefore, control over the retention of amines in this range is limited.
The choice of buffer type is an important factor in RP-LC method development, as it can affect the retention, selectivity, and resolution of the analytes of interest. When selecting a buffer for RP-HPLC, there are a number of factors to consider, including:
The desired pH of the mobile phase: Buffers are most effective around their pKa value, so it is important to choose a buffer with a pKa that is close to the desired mobile phase pH needed.
The solubility of the buffer in the organic solvent: The buffer must be compatible with the organic solvent that is being used in the mobile phase, mostly with the common organic solvents mentioned above, acetonitrile, methanol, and isopropanol.
The UV cut-off of the buffer: In case of UV detection, the buffer should have a UV absorption that is below the detection wavelength of the analytes of interest. This will prevent the buffer from interfering with the detection of that analytes.
The compatibility of the buffer with the detector: If mass spectrometry (MS) is being used for detection, the buffer must be compatible with the mass spectrometry (MS) instrument. Some buffers, such as those containing phosphate salts, cannot be used with the MS detectors, as they are not volatile as needed, and they interfere with the MS detection by suppressing the analytes ionization, making them undetected by MS.
Some of the most common buffers used in RP-HPLC include:
Phosphate buffers: Phosphate buffer is versatile and can be used to achieve a wide range of pH values, thanks to 3 pKa values. They also have very low UV background for UV detection. However, they are not appropriate for MS detection.
Acetate buffers: Acetate buffers are also versatile and can be used to achieve range of pH values typically used in RP-LC. In terms of UV detection at sub 220 nm wavelength, it is not so favorable. The ammonium acetate buffer is compatible with MS.
Formate buffers: Formate buffers is similar to the acetate buffer in terms of range of pHs used and limited UV detection under 225 nm. Its ammonium acetate is also compatible with MS.
Ammonium buffers: Ammonium buffers are volatile and are often used in LC-MS methods. They also are limited for low UV detection.
Charged analytes can be separated on a reversed-phase column by the use of ion-pairing (also called ion-interaction). This technique is known as reversed-phase ion-pairing chromatography.
Elution can be performed isocratically (the water-solvent composition does not change during the separation process) or by using a solution gradient (the water-solvent composition changes during the separation process, usually by decreasing the polarity).
== See also ==
Aqueous normal-phase chromatography
== References ==
== External links ==
Tables summarizing different types of reverse phases, and information on the functionalization process | Wikipedia/Reversed-phase_chromatography |
Chromatography is a physical method of separation that distributes the components you want to separate between two phases, one stationary (stationary phase), the other (the mobile phase) moving in a definite direction. Cold ethanol precipitation, developed by Cohn in 1946, manipulates pH, ionic strength, ethanol concentration and temperature to precipitate different protein fractions from plasma. Chromatographic techniques utilise ion exchange, gel filtration and affinity resins to separate proteins. Since the 1980s it has emerged as an effective method of purifying blood components for therapeutic use.
== Human blood plasma ==
Blood plasma is the liquid component of blood, which contains dissolved proteins, nutrients, ions, and other soluble components. In whole blood, red blood cells, white blood cells, and platelets are suspended within the plasma. The goal of plasma purification and processing is to extract specific materials that are present in blood, and use them for restoration and repair. There are several components that make up blood plasma, one of which is the protein albumin. Albumin is a highly water-soluble protein with considerable structural stability. It serves as a transportation device for materials such as hormones, enzymes, fatty acids, metal ions, and medicinal products. It is also used for therapeutic purposes, being essential in restoration and maintenance of circulating blood volume in imperative situations such as severe trauma or surgery. With little room for error, extremely pure samples that are lacking impurities needs to be at hand in good amount. Human blood plasma is important for the body so the nutrients etc. can be stored.
== Development of chromatography ==
Traditionally, the Cohn process incorporating cold ethanol fractionation has been used for albumin purification. However, chromatographic methods for separation started being adopted in the early 1980s. Developments were ongoing in the time period between when Cohn fractionation started being used, in 1946, and when chromatography started being used, in 1983. In 1962, the Kistler & Nistchmann process was created which was a spinoff of the Cohn process. Chromatographic processes began to take shape in 1983. In the 1990s, the Zenalb and the CSL Albumex processes were created which incorporated chromatography with a few variations.
The general approach to using chromatography for plasma fractionation for albumin is: recovery of supernatant I, delipidation, anion exchange chromatography, cation exchange chromatography, and gel filtration chromatography.
The recovered purified material is formulated with combinations of sodium octanoate and sodium N-acetyl tryptophanate and then subjected to viral inactivation procedures, including pasteurisation at 60 °C.
This is a more efficient alternative than the Cohn process for four main reasons:
1) smooth automation and a relatively inexpensive plant was needed,
2) easier to sterilize equipment and maintain a good manufacturing environment,
3) chromatographic processes are less damaging to the albumin protein, and
4) a more successful albumin end result can be achieved.
Compared with the Cohn process, the albumin purity went up from about 95% to 98% using chromatography, and the yield increased from about 65% to 85%. Small percentage increases make a difference in regard to sensitive measurements like purity. There is one big drawback in using chromatography, which has to do with the economics of the process. Although the method was efficient from the processing aspect, acquiring the necessary equipment is a big task. Large machinery is necessary, and for a long time the lack of equipment availability was not conducive to its widespread use. The components are more readily available now but it is still a work in progress and will possibly be ready in the future to help the world.
== Bridging Methods ==
Integrating traditional and modern methods is a useful way to process albumin.
There are three main steps that combine Cohn fractionation with chromatography: 1) factors I, II, and III are removed via cold ethanol fractionation, 2) Sepharose fast flow ion exchange and sepharose fast flow chromatography procedures are run, and 3) gel filtration is run. The result is albumin with 9% lower aluminum levels with a processing time that is almost twice as fast.
Although it was hard to make chromatographic processing methods widely adopted, global expansion is a work in progress. Various blood components must be readily available at various medical treatment centers around the world. The Institute of Transfusion Medicine in Skopje, North Macedonia is a plasma fractionation center in the Balkans. Their modernized albumin purification process consists of five steps:
Starting material is plasma that has been pretreated by centrifugation,
A round of gel filtration is run,
ion exchange on DEAE Sepharose is run to bind the albumin to the column,
Albumin is eluted with a sodium acetate buffer, and
Final polishing with gel filtration.
The end result is a highly pure and safe batch of albumin that is 100% non-pyrogenic, sterile, and free of active HIV virus. The product purity is greater than 98% and the protein content is about 50 g/L.
== Non-chromatographic processing methods ==
Other plasma processing methods exist, but generally do not provide the resolution or purity of chromatographic methods.
Two-phase liquid extraction may be performed using polyethylene glycol (PEG)-phosphate Aqueous two-phase systems, with a PEG-rich top layer and a phosphate-rich bottom layer. Although this method is somewhat useful for protein recovery, it does not work as well for the recovery of other blood components.
Membrane fractionation has the advantage of minimal protein loss yet high removal of pathological plasma components. This method incorporates processes such as thermofiltration and applying pulsate flow. The latest two-stage membrane system utilizes a high flow recirculation circuit that is effective for removal of LDL cholesterol. It may prove useful for patients that have clogged arteries and other cardiovascular problems involving cholesterol.
Batch adsorption, e.g. onto ion exchange media, is only useful when dealing with smaller samples of plasma, typically 200 mL or less. Batch adsorption recovers the product in a larger volume of elution buffer than does column chromatography or frontal chromatography, and the resulting more dilute product requires concentration, typically on a membrane system, which can lead to loss of product by irreversible adsorption to the membrane.
== References == | Wikipedia/Chromatography_in_blood_processing |
The Freundlich equation or Freundlich adsorption isotherm, an adsorption isotherm, is an empirical relationship between the quantity of a gas adsorbed into a solid surface and the gas pressure. The same relationship is also applicable for the concentration of a solute adsorbed onto the surface of a solid and the concentration of the solute in the liquid phase. In 1909, Herbert Freundlich gave an expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with gas pressure. This equation is known as Freundlich adsorption isotherm or Freundlich adsorption equation. As this relationship is entirely empirical, in the case where adsorption behavior can be properly fit by isotherms with a theoretical basis, it is usually appropriate to use such isotherms instead (see for example the Langmuir and BET adsorption theories). The Freundlich equation is also derived (non-empirically) by attributing the change in the equilibrium constant of the binding process to the heterogeneity of the surface and the variation in the heat of adsorption.
== Freundlich adsorption isotherm ==
The Freundlich adsorption isotherm is mathematically expressed as
In Freundlich's notation (used for his experiments dealing with the adsorption of organic acids on coal in aqueous solutions),
x
/
m
{\displaystyle x/m}
signifies the ratio between the adsorbed mass or adsorbate
x
{\displaystyle x}
and the mass of the adsorbent
m
{\displaystyle m}
, which in Freundlich's studies was coal. In the figure above, the x-axis represents
c
e
q
{\displaystyle c_{\mathrm {\,eq} }}
, which denotes the equilibrium concentration of the adsorbate within the solvent.
Freundlich's numerical analysis of the three organic acids for the parameters
K
{\displaystyle K}
and
n
{\displaystyle n}
according to equation
1 were:
Freundlich's experimental data can also be used in a contemporary computer based fit. These values are added to appreciate the numerical work done in 1907.
△ K and △ n values are the error bars of the computer based fit. The K and n values itself are used to calculate the dotted lines in the figure.
Equation 1 can also be written as
log
x
m
=
log
K
+
1
n
log
c
e
q
{\displaystyle \log {\frac {x}{m}}=\log K+{\frac {1}{n}}\log c_{eq}}
Sometimes also this notation for experiments in the gas phase can be found:
log
x
m
=
log
K
+
1
n
log
p
{\displaystyle \log {\frac {x}{m}}=\log K+{\frac {1}{n}}\log p}
x = mass of adsorbate
m = mass of adsorbent
p = equilibrium pressure of the gaseous adsorbate in case of experiments made in the gas phase (gas/solid interaction with gaseous species/adsorbed species)
K and n are constants for a given adsorbate and adsorbent at a given temperature (from there, the term isotherm needed to avoid significant gas pressure fluctuations due to uncontrolled temperature variations in the case of adsorption experiments of a gas onto a solid phase).
K = distribution coefficient
n = correction factor
At high pressure 1/n = 0, hence extent of adsorption becomes independent of pressure.
The Freundlich equation is unique; consequently, if the data fit the equation, it is only likely, but not proved, that the surface is heterogeneous. The heterogeneity of the surface can be confirmed with calorimetry. Homogeneous surfaces (or heterogeneous surfaces that exhibit homogeneous adsorption (single site)) have a constant ΔH of adsorption. On the other hand, heterogeneous adsorption (multi-site) have a variable ΔH of adsorption depending on the percent of sites occupied. When the adsorbate pressure in the gas phase (or the concentration in solution) is low, high-energy sites will be occupied first. As the pressure in the gas phase (or the concentration in solution) increases, the low-energy sites will then be occupied resulting in a weaker ΔH of adsorption.
== Limitation of Freundlich adsorption isotherm ==
Experimentally it was determined that extent of gas adsorption varies directly with pressure, and then it directly varies with pressure raised to the power 1/n until saturation pressure Ps is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.
== See also ==
Langmuir adsorption model
== References ==
== Further reading ==
Jaroniec, M. (1975). "Adsorption on heterogeneous surfaces: The exponential equation for the overall adsorption isotherm". Surface Science. 50 (2): 553–564. Bibcode:1975SurSc..50..553J. doi:10.1016/0039-6028(75)90044-8.
Levan, M. Douglas; Vermeulen, Theodore (1981). "LeVan, M. Douglas, and Theodore Vermeulen. "Binary Langmuir and Freundlich isotherms for ideal adsorbed solutions." The Journal of Physical Chemistry 85.22 (1981): 3247–3250". The Journal of Physical Chemistry. 85 (22): 3247–3250. doi:10.1021/j150622a009.
"Freundlich Equation". Archived from the original on 3 March 2016.
== External links ==
"Freundlich equation solver".
"Freundlich Adsorption Isotherm". Archived from the original on 2 March 2012. | Wikipedia/Freundlich_equation |
Argentation chromatography is chromatography using a stationary phase that contains silver salts. Silver-containing stationary phases are well suited for separating organic compounds on the basis of the number and type of alkene groups. The technique is employed for gas chromatography and various types of liquid chromatography, including thin layer chromatography. Analytes containing alkene groups elute more slowly than the analogous compounds lacking alkenes. Separations are also sensitive to the type of alkene. The technique is especially useful in the analysis of fats and fatty acids, which are well known to exist in both saturated and unsaturated (alkene-containing) forms. For example, trans fats, undesirable contaminants in ultra-processed foods, are quantified by argentation chromatography.
== Theory ==
Silver ions form alkene complexes. The binding is reversible, but sufficient to impede the elution of the alkene-containing analytes.
== References == | Wikipedia/Argentation_chromatography |
Electrochromatography is a chemical separation technique in analytical chemistry, biochemistry and molecular biology used to resolve and separate mostly large biomolecules such as proteins. It is a combination of size exclusion chromatography (gel filtration chromatography) and gel electrophoresis. These separation mechanisms operate essentially in superposition along the length of a gel filtration column to which an axial electric field gradient has been added. The molecules are separated by size due to the gel filtration mechanism and by electrophoretic mobility due to the gel electrophoresis mechanism. Additionally there are secondary chromatographic solute retention mechanisms.
== Capillary electrochromatography ==
Capillary electrochromatography (CEC) is an electrochromatography technique in which the liquid mobile phase is driven through a capillary containing the chromatographic stationary phase by electroosmosis. It is a combination of high-performance liquid chromatography and capillary electrophoresis. The capillaries is packed with HPLC stationary phase and a high voltage is applied to achieve separation is achieved by electrophoretic migration of the analyte and differential partitioning in the stationary phase.
== See also ==
Chromatography
Protein electrophoresis
Electrofocusing
Two-dimensional gel electrophoresis
Temperature gradient gel electrophoresis
== References == | Wikipedia/Electrochromatography |
Aqueous normal-phase chromatography (ANP) is a chromatographic technique that involves the mobile phase compositions and polarities between reversed-phase chromatography (RP) and normal-phase chromatography (NP), while the stationary phases are polar.
== Principle ==
In normal-phase chromatography, the stationary phase is polar and the mobile phase is nonpolar. In reversed phase the opposite is true; the stationary phase is nonpolar and the mobile phase is polar. Typical stationary phases for normal-phase chromatography are silica or organic moieties with cyano and amino functional groups. For reversed phase, alkyl hydrocarbons are the preferred stationary phase; octadecyl (C18) is the most common stationary phase, but octyl (C8) and butyl (C4) are also used in some applications. The designations for the reversed phase materials refer to the length of the hydrocarbon chain.
In normal-phase chromatography, the least polar compounds elute first and the most polar compounds elute last. The mobile phase consists of a nonpolar solvent such as hexane or heptane mixed with a slightly more polar solvent such as isopropanol, ethyl acetate or chloroform. Retention decreases as the amount of polar solvent in the mobile phase increases. In reversed phase chromatography, the most polar compounds elute first with the more nonpolar compounds eluting later. The mobile phase is generally a mixture of water and miscible polarity-modifying organic solvent, such as methanol, acetonitrile or THF. Retention increases as the fraction of the polar solvent (water) in the mobile phase is higher. Normal phase chromatography retains molecules via an adsorptive mechanism, and is used for the analysis of solutes readily soluble in organic solvents. Separation is achieved based on the polarity differences among functional groups such as amines, acids, metal complexes, etc. as well as their steric properties, while in reversed-phase chromatography, a partition mechanism typically occurs for the separation by non-polar differences.
In the aqueous normal-phase chromatography the support is based on a silica with "hydride surface" which is distinguishable from the other silica support materials, used either in normal phase, reversed phase, or hydrophilic interaction chromatography. Most silica materials used for chromatography have a surface composed primarily of silanols (-Si-OH). In a "hydride surface" the terminal groups are primarily -Si-H. The hydride surface can also be functionalized with carboxylic acids and long-chain alkyl groups. Mobile phases for ANPC are based on organic solvents as bulk solvents (such as methanol or acetonitrile) with a small amount of water as a modifier of polarity; thus, the mobile phase is both "aqueous" (water is present) and "normal phase type" (less polar than the stationary phase). Thus, polar solutes (such as acids and amines) are more strongly retained, with the ability to affect the retention, which decreases as the amount of water in the mobile phase increases.
Typically the mobile phases are rich with organic solvents, with amount of the nonpolar solvent in the mobile phase at least 60% or greater to reach minimal required retention. A true ANP stationary phase will be able to function in both the reversed phase and normal phase modes with only the amount of water in the eluent varying. Thus a continuum of solvents can be used from 100% aqueous to pure organic. ANP retention has been demonstrated for a variety of polar compounds on the hydride based stationary phases. Recent investigations have demonstrated that silica hydride materials have a very thin water layer (about 0.5 monolayer) in comparison to HILIC phases that can have from 6–8 monolayers.[1] In addition the substantial negative charge on the surface of hydride phases is the result of hydroxide ion adsorption from the solvent rather than silanols.[2]
== Features ==
An interesting feature of these phases is that both polar and nonpolar compounds can be retained over some range of mobile phase composition (organic/aqueous). The retention mechanism of polar compounds has recently been shown to be the result of the formation of a hydroxide layer on the surface of the silica hydride.[3] Thus positively charged analytes are attracted to the negatively charged surface and other polar analytes are likely to be retained through displacement of hydroxide or other charged species on the surface. This property distinguishes it from a pure HILIC (hydrophilic interaction chromatography) columns where separation by polar differences is obtained through partitioning into a water-rich layer on the surface, or a pure RP stationary phase on which separation by nonpolar differences in solutes is obtained with very limited secondary mechanisms operating.
Another important feature of the hydride-based phases is that for many analyses it is usually not necessary to use a high pH mobile phase to analyze polar compounds such as bases. The aqueous component of the mobile phase usually contains from 0.1 to 0.5% formic or acetic acid, which is compatible with detector techniques that include mass spectral analysis.
== References ==
^ Pesek, J. J.; Matyska, M. T.; Prabhakaran, S. J. (2005). "Synthesis and characterization of chemically bonded stationary phases on hydride surfaces by hydrosilation of alkynes and dienes". Journal of Separation Science. 28 (18): 2437–43. doi:10.1002/jssc.200500249. PMID 16405172.
^ Pesek, J. J.; Matyska, M. T.; Gangakhedkar, S.; Siddiq, R. (2006). "Synthesis and HPLC evaluation of carboxylic acid phases on a hydride surface". Journal of Separation Science. 29 (6): 872–80. doi:10.1002/jssc.200500433. PMID 16830499.
^ Hemström, P.; Irgum, K. (2006). "Hydrophilic interaction chromatography". Journal of Separation Science. 29 (12): 1784–821. doi:10.1002/jssc.200600199. PMID 16970185.
^ C. Kulsing, Y. Nolvachai, P.J. Marriott, R.I. Boysen, M.T. Matyska, J.J. Pesek, M.T.W. Hearn, J. Phys. Chem B, 119 (2015) 3063-3069.
^ J. Soukup, P. Janas, P. Jandera, J. Chromatogr. A, 1286 (2013) 111-118 | Wikipedia/Aqueous_normal-phase_chromatography |
Ion chromatography (or ion-exchange chromatography) is a form of chromatography that separates ions and ionizable polar molecules based on their affinity to the ion exchanger. It works on almost any kind of charged molecule—including small inorganic anions, large proteins, small nucleotides, and amino acids. However, ion chromatography must be done in conditions that are one pH unit away from the isoelectric point of a protein.
The two types of ion chromatography are anion-exchange and cation-exchange. Cation-exchange chromatography is used when the molecule of interest is positively charged. The molecule is positively charged because the pH for chromatography is less than the pI (also known as pH(I)). In this type of chromatography, the stationary phase is negatively charged and positively charged molecules are loaded to be attracted to it. Anion-exchange chromatography is when the stationary phase is positively charged and negatively charged molecules (meaning that pH for chromatography is greater than the pI) are loaded to be attracted to it. It is often used in protein purification, water analysis, and quality control. The water-soluble and charged molecules such as proteins, amino acids, and peptides bind to moieties which are oppositely charged by forming ionic bonds to the insoluble stationary phase. The equilibrated stationary phase consists of an ionizable functional group where the targeted molecules of a mixture to be separated and quantified can bind while passing through the column—a cationic stationary phase is used to separate anions and an anionic stationary phase is used to separate cations. Cation exchange chromatography is used when the desired molecules to separate are cations and anion exchange chromatography is used to separate anions. The bound molecules then can be eluted and collected using an eluant which contains anions and cations by running a higher concentration of ions through the column or by changing the pH of the column.
One of the primary advantages for the use of ion chromatography is that only one interaction is involved the separation, as opposed to other separation techniques; therefore, ion chromatography may have higher matrix tolerance. Another advantage of ion exchange is the predictability of elution patterns (based on the presence of the ionizable group). For example, when cation exchange chromatography is used, certain cations will elute out first and others later. A local charge balance is always maintained. However, there are also disadvantages involved when performing ion-exchange chromatography, such as constant evolution of the technique which leads to the inconsistency from column to column. A major limitation to this purification technique is that it is limited to ionizable group.
== History ==
Ion chromatography has advanced through the accumulation of knowledge over a course of many years. Starting from 1947, Spedding and Powell used displacement ion-exchange chromatography for the separation of the rare earths. Additionally, they showed the ion-exchange separation of 14N and 15N isotopes in ammonia. At the start of the 1950s, Kraus and Nelson demonstrated the use of many analytical methods for metal ions dependent on their separation of their chloride, fluoride, nitrate or sulfate complexes by anion chromatography. Automatic in-line detection was progressively introduced from 1960 to 1980 as well as novel chromatographic methods for metal ion separations. A groundbreaking method by Small, Stevens and Bauman at Dow Chemical Co. unfolded the creation of the modern ion chromatography. Anions and cations could now be separated efficiently by a system of suppressed conductivity detection. In 1979, a method for anion chromatography with non-suppressed conductivity detection was introduced by Gjerde et al. Following it in 1980, was a similar method for cation chromatography.
As a result, a period of extreme competition began within the IC market, with supporters for both suppressed and non-suppressed conductivity detection. This competition led to fast growth of new forms and the fast evolution of IC. A challenge that needs to be overcome in the future development of IC is the preparation of highly efficient monolithic ion-exchange columns and overcoming this challenge would be of great importance to the development of IC.
The boom of Ion exchange chromatography primarily began between 1935 and 1950 during World War II and it was through the "Manhattan project" that applications and IC were significantly extended. Ion chromatography was originally introduced by two English researchers, agricultural Sir Thompson and chemist J T Way. The works of Thompson and Way involved the action of water-soluble fertilizer salts, ammonium sulfate and potassium chloride. These salts could not easily be extracted from the ground due to the rain. They performed ion methods to treat clays with the salts, resulting in the extraction of ammonia in addition to the release of calcium. It was in the fifties and sixties that theoretical models were developed for IC for further understanding and it was not until the seventies that continuous detectors were utilized, paving the path for the development from low-pressure to high-performance chromatography. Not until 1975 was "ion chromatography" established as a name in reference to the techniques, and was thereafter used as a name for marketing purposes. Today IC is important for investigating aqueous systems, such as drinking water. It is a popular method for analyzing anionic elements or complexes that help solve environmentally relevant problems. Likewise, it also has great uses in the semiconductor industry.
Because of the abundant separating columns, elution systems, and detectors available, chromatography has developed into the main method for ion analysis.
When this technique was initially developed, it was primarily used for water treatment. Since 1935, ion exchange chromatography rapidly manifested into one of the most heavily leveraged techniques, with its principles often being applied to majority of fields of chemistry, including distillation, adsorption, and filtration.
== Principle ==
Ion-exchange chromatography separates molecules based on their respective charged groups. Ion-exchange chromatography retains analyte molecules on the column based on coulombic (ionic) interactions. The ion exchange chromatography matrix consists of positively and negatively charged ions. Essentially, molecules undergo electrostatic interactions with opposite charges on the stationary phase matrix. The stationary phase consists of an immobile matrix that contains charged ionizable functional groups or ligands. The stationary phase surface displays ionic functional groups (R-X) that interact with analyte ions of opposite charge. To achieve electroneutrality, these immobilized charges couple with exchangeable counterions in the solution. Ionizable molecules that are to be purified, compete with these exchangeable counterions, for binding to the immobilized charges on the stationary phase. These ionizable molecules are retained or eluted based on their charge. Initially, molecules that do not bind or bind weakly to the stationary phase are first to be washed away. Altered conditions are needed for the elution of the molecules that bind to the stationary phase. The concentration of the exchangeable counterions, which competes with the molecules for binding, can be increased, or the pH can be changed to affect the ionic charge of the eluent or the solute. A change in pH affects the charge on the particular molecules and, therefore, alter their binding. When reducing the net charge of the solute's molecules, they start eluting out. This way, such adjustments can be used to release the proteins of interest. Additionally, concentration of counterions can be gradually varied to affect the retention of the ionized molecules, thus separate them. This type of elution is called gradient elution. On the other hand, step elution can be used, in which the concentration of counterions are varied in steps. This type of chromatography is further subdivided into cation exchange chromatography and anion-exchange chromatography. Positively charged molecules bind to cation exchange resins, while negatively charged molecules bind to anion exchange resins. The ionic compound consisting of the cationic species M+ and the anionic species B− can be retained by the stationary phase.
Cation exchange chromatography retains positively charged cations because the stationary phase displays a negatively charged functional group:
R-X
−
C
+
+
M
+
B
−
⇄
R-X
−
M
+
+
C
+
+
B
−
{\displaystyle {\text{R-X}}^{-}{\text{C}}^{+}\,+\,{\text{M}}^{+}\,{\text{B}}^{-}\rightleftarrows \,{\text{R-X}}^{-}{\text{M}}^{+}\,+\,{\text{C}}^{+}\,+\,{\text{B}}^{-}}
Anion exchange chromatography retains anions using positively charged functional group:
R-X
+
A
−
+
M
+
B
−
⇄
R-X
+
B
−
+
M
+
+
A
−
{\displaystyle {\text{R-X}}^{+}{\text{A}}^{-}\,+\,{\text{M}}^{+}\,{\text{B}}^{-}\rightleftarrows \,{\text{R-X}}^{+}{\text{B}}^{-}\,+\,{\text{M}}^{+}\,+\,{\text{A}}^{-}}
Note that the ion strength of either C+ or A− in the mobile phase can be adjusted to shift the equilibrium position, thus retention time.
The ion chromatogram shows a typical chromatogram obtained with an anion exchange column.
== Procedure ==
Before ion-exchange chromatography can be initiated, it must be equilibrated. The stationary phase must be equilibrated to certain requirements that depend on the experiment that you are working with. Once equilibrated, the charged ions in the stationary phase will be attached to its opposite charged exchangeable ions, such as Cl− or Na+. Next, a buffer should be chosen in which the desired protein can bind to. After equilibration, the column needs to be washed. The washing phase will help elute out all impurities that does not bind to the matrix while the protein of interest remains bounded. This sample buffer needs to have the same pH as the buffer used for equilibration to help bind the desired proteins. Uncharged proteins will be eluted out of the column at a similar speed of the buffer flowing through the column with no retention. Once the sample has been loaded onto to the column, and the column has been washed with the buffer to elute out all non-desired proteins, elution is carried out at specific conditions to elute the desired proteins that are bound to the matrix. Bound proteins are eluted out by utilizing a gradient of linearly increasing salt concentration. With increasing ionic strength of the buffer, the salt ions will compete with the desired proteins in order to bind to charged groups on the surface of the medium. This will cause desired proteins to be eluted out of the column. Proteins that have a low net charge will be eluted out first as the salt concentration increases causing the ionic strength to increase. Proteins with high net charge will need a higher ionic strength for them to be eluted out of the column.
It is possible to perform ion exchange chromatography in bulk, on thin layers of medium such as glass or plastic plates coated with a layer of the desired stationary phase, or in chromatography columns. Thin layer chromatography or column chromatography share similarities in that they both act within the same governing principles; there is constant and frequent exchange of molecules as the mobile phase travels along the stationary phase. It is not imperative to add the sample in minute volumes as the predetermined conditions for the exchange column have been chosen so that there will be strong interaction between the mobile and stationary phases. Furthermore, the mechanism of the elution process will cause a compartmentalization of the differing molecules based on their respective chemical characteristics. This phenomenon is due to an increase in salt concentrations at or near the top of the column, thereby displacing the molecules at that position, while molecules bound lower are released at a later point when the higher salt concentration reaches that area. These principles are the reasons that ion exchange chromatography is an excellent candidate for initial chromatography steps in a complex purification procedure as it can quickly yield small volumes of target molecules regardless of a greater starting volume.
Comparatively simple devices are often used to apply counterions of increasing gradient to a chromatography column. Counterions such as copper (II) are chosen most often for effectively separating peptides and amino acids through complex formation.
A simple device can be used to create a salt gradient. Elution buffer is consistently being drawn from the chamber into the mixing chamber, thereby altering its buffer concentration. Generally, the buffer placed into the chamber is usually of high initial concentration, whereas the buffer placed into the stirred chamber is usually of low concentration. As the high concentration buffer from the left chamber is mixed and drawn into the column, the buffer concentration of the stirred column gradually increase. Altering the shapes of the stirred chamber, as well as of the limit buffer, allows for the production of concave, linear, or convex gradients of counterion.
A multitude of different mediums are used for the stationary phase. Among the most common immobilized charged groups used are trimethylaminoethyl (TAM), triethylaminoethyl (TEAE), diethyl-2-hydroxypropylaminoethyl (QAE), aminoethyl (AE), diethylaminoethyl (DEAE), sulpho (S), sulphomethyl (SM), sulphopropyl (SP), carboxy (C), and carboxymethyl (CM).
Successful packing of the column is an important aspect of ion chromatography. Stability and efficiency of a final column depends on packing methods, solvent used, and factors that affect mechanical properties of the column. In contrast to early inefficient dry- packing methods, wet slurry packing, in which particles that are suspended in an appropriate solvent are delivered into a column under pressure, shows significant improvement. Three different approaches can be employed in performing wet slurry packing: the balanced density method (solvent's density is about that of porous silica particles), the high viscosity method (a solvent of high viscosity is used), and the low viscosity slurry method (performed with low viscosity solvents).
Polystyrene is used as a medium for ion- exchange. It is made from the polymerization of styrene with the use of divinylbenzene and benzoyl peroxide. Such exchangers form hydrophobic interactions with proteins which can be irreversible. Due to this property, polystyrene ion exchangers are not suitable for protein separation. They are used on the other hand for the separation of small molecules in amino acid separation and removal of salt from water. Polystyrene ion exchangers with large pores can be used for the separation of protein but must be coated with a hydrophilic substance.
Cellulose based medium can be used for the separation of large molecules as they contain large pores. Protein binding in this medium is high and has low hydrophobic character. DEAE is an anion exchange matrix that is produced from a positive side group of diethylaminoethyl bound to cellulose or Sephadex.
Agarose gel based medium contain large pores as well but their substitution ability is lower in comparison to dextrans. The ability of the medium to swell in liquid is based on the cross-linking of these substances, the pH and the ion concentrations of the buffers used.
Incorporation of high temperature and pressure allows a significant increase in the efficiency of ion chromatography, along with a decrease in time. Temperature has an influence of selectivity due to its effects on retention properties. The retention factor (k = (tRg − tMg)/(tMg − text)) increases with temperature for small ions, and the opposite trend is observed for larger ions.
Despite ion selectivity in different mediums, further research is being done to perform ion exchange chromatography through the range of 40–175 °C.
An appropriate solvent can be chosen based on observations of how column particles behave in a solvent. Using an optical microscope, one can easily distinguish a desirable dispersed state of slurry from aggregated particles.
== Weak and strong ion exchangers ==
A "strong" ion exchanger will not lose the charge on its matrix once the column is equilibrated and so a wide range of pH buffers can be used. "Weak" ion exchangers have a range of pH values in which they will maintain their charge. If the pH of the buffer used for a weak ion exchange column goes out of the capacity range of the matrix, the column will lose its charge distribution and the molecule of interest may be lost. Despite the smaller pH range of weak ion exchangers, they are often used over strong ion exchangers due to their having greater specificity. In some experiments, the retention times of weak ion exchangers are just long enough to obtain desired data at a high specificity.
Resins (often termed 'beads') of ion exchange columns may include functional groups such as weak/strong acids and weak/strong bases. There are also special columns that have resins with amphoteric functional groups that can exchange both cations and anions. Some examples of functional groups of strong ion exchange resins are quaternary ammonium cation (Q), which is an anion exchanger, and sulfonic acid (S, -SO2OH), which is a cation exchanger. These types of exchangers can maintain their charge density over a pH range of 0–14. Examples of functional groups of Weak ion exchange resins include diethylaminoethyl (DEAE, -C2H4N(C2H5)2), which is an anion exchanger, and carboxymethyl (CM, -CH2-COOH), which is a cation exchanger. These two types of exchangers can maintain the charge density of their columns over a pH range of 5–9.
In ion chromatography, the interaction of the solute ions and the stationary phase based on their charges determines which ions will bind and to what degree. When the stationary phase features positive groups which attracts anions, it is called an anion exchanger; when there are negative groups on the stationary phase, cations are attracted and it is a cation exchanger. The attraction between ions and stationary phase also depends on the resin, organic particles used as ion exchangers.
Each resin features relative selectivity which varies based on the solute ions present who will compete to bind to the resin group on the stationary phase. The selectivity coefficient, the equivalent to the equilibrium constant, is determined via a ratio of the concentrations between the resin and each ion, however, the general trend is that ion exchangers prefer binding to the ion with a higher charge, smaller hydrated radius, and higher polarizability, or the ability for the electron cloud of an ion to be disrupted by other charges. Despite this selectivity, excess amounts of an ion with a lower selectivity introduced to the column would cause the lesser ion to bind more to the stationary phase as the selectivity coefficient allows fluctuations in the binding reaction that takes place during ion exchange chromatography.
Following table shows the commonly used ion exchangers
== Typical technique ==
A sample is introduced, either manually or with an autosampler, into a sample loop of known volume. A buffered aqueous solution known as the mobile phase carries the sample from the loop onto a column that contains some form of stationary phase material. This is typically a resin or gel matrix consisting of agarose or cellulose beads with covalently bonded charged functional groups. Equilibration of the stationary phase is needed in order to obtain the desired charge of the column. If the column is not properly equilibrated the desired molecule may not bind strongly to the column. The target analytes (anions or cations) are retained on the stationary phase but can be eluted by increasing the concentration of a similarly charged species that displaces the analyte ions from the stationary phase. For example, in cation exchange chromatography, the positively charged analyte can be displaced by adding positively charged sodium ions. The analytes of interest must then be detected by some means, typically by conductivity or UV/visible light absorbance.
Control an IC system usually requires a chromatography data system (CDS). In addition to IC systems, some of these CDSs can also control gas chromatography (GC) and HPLC.
== Membrane exchange chromatography ==
A type of ion exchange chromatography, membrane exchange is a relatively new method of purification designed to overcome limitations of using columns packed with beads. Membrane Chromatographic devices are cheap to mass-produce and disposable unlike other chromatography devices that require maintenance and time to revalidate. There are three types of membrane absorbers that are typically used when separating substances. The three types are flat sheet, hollow fibre, and radial flow. The most common absorber and best suited for membrane chromatography is multiple flat sheets because it has more absorbent volume. It can be used to overcome mass transfer limitations and pressure drop, making it especially advantageous for isolating and purifying viruses, plasmid DNA, and other large macromolecules. The column is packed with microporous membranes with internal pores which contain adsorptive moieties that can bind the target protein. Adsorptive membranes are available in a variety of geometries and chemistry which allows them to be used for purification and also fractionation, concentration, and clarification in an efficiency that is 10 fold that of using beads. Membranes can be prepared through isolation of the membrane itself, where membranes are cut into squares and immobilized. A more recent method involved the use of live cells that are attached to a support membrane and are used for identification and clarification of signaling molecules.
== Separating proteins ==
Ion exchange chromatography can be used to separate proteins because they contain charged functional groups. The ions of interest (in this case charged proteins) are exchanged for another ions (usually H+) on a charged solid support. The solutes are most commonly in a liquid phase, which tends to be water. Take for example proteins in water, which would be a liquid phase that is passed through a column. The column is commonly known as the solid phase since it is filled with porous synthetic particles that are of a particular charge. These porous particles are also referred to as beads, may be aminated (containing amino groups) or have metal ions in order to have a charge. The column can be prepared using porous polymers, for macromolecules of a mass of over 100 000 Da, the optimum size of the porous particle is about 1 μm2. This is because slow diffusion of the solutes within the pores does not restrict the separation quality. The beads containing positively charged groups, which attract the negatively charged proteins, are commonly referred to as anion exchange resins. The amino acids that have negatively charged side chains at pH 7 (pH of water) are glutamate and aspartate. The beads that are negatively charged are called cation exchange resins, as positively charged proteins will be attracted. The amino acids that have positively charged side chains at pH 7 are lysine, histidine and arginine.
The isoelectric point is the pH at which a compound - in this case a protein - has no net charge. A protein's isoelectric point or PI can be determined using the pKa of the side chains, if the amino (positive chain) is able to cancel out the carboxyl (negative) chain, the protein would be at its PI. Using buffers instead of water for proteins that do not have a charge at pH 7 is a good idea as it enables the manipulation of pH to alter ionic interactions between the proteins and the beads. Weakly acidic or basic side chains are able to have a charge if the pH is high or low enough respectively. Separation can be achieved based on the natural isoelectric point of the protein. Alternatively a peptide tag can be genetically added to the protein to give the protein an isoelectric point away from most natural proteins (e.g., 6 arginines for binding to a cation-exchange resin or 6 glutamates for binding to an anion-exchange resin such as DEAE-Sepharose).
Elution by increasing ionic strength of the mobile phase is more subtle. It works because ions from the mobile phase interact with the immobilized ions on the stationary phase, thus "shielding" the stationary phase from the protein, and letting the protein elute.
Elution from ion-exchange columns can be sensitive to changes of a single charge- chromatofocusing. Ion-exchange chromatography is also useful in the isolation of specific multimeric protein assemblies, allowing purification of specific complexes according to both the number and the position of charged peptide tags.
=== Gibbs–Donnan effect ===
In ion exchange chromatography, the Gibbs–Donnan effect is observed when the pH of the applied buffer and the ion exchanger differ, even up to one pH unit. For example, in anion-exchange columns, the ion exchangers repeal protons so the pH of the buffer near the column differs is higher than the rest of the solvent. As a result, an experimenter has to be careful that the protein(s) of interest is stable and properly charged in the "actual" pH.
This effect comes as a result of two similarly charged particles, one from the resin and one from the solution, failing to distribute properly between the two sides; there is a selective uptake of one ion over another. For example, in a sulphonated polystyrene resin, a cation exchange resin, the chlorine ion of a hydrochloric acid buffer should equilibrate into the resin. However, since the concentration of the sulphonic acid in the resin is high, the hydrogen of HCl has no tendency to enter the column. This, combined with the need of electroneutrality, leads to a minimum amount of hydrogen and chlorine entering the resin.
== Uses ==
=== Clinical utility ===
A use of ion chromatography can be seen in argentation chromatography. Usually, silver and compounds containing acetylenic and ethylenic bonds have very weak interactions. This phenomenon has been widely tested on olefin compounds. The ion complexes the olefins make with silver ions are weak and made based on the overlapping of pi, sigma, and d orbitals and available electrons therefore cause no real changes in the double bond. This behavior was manipulated to separate lipids, mainly fatty acids from mixtures in to fractions with differing number of double bonds using silver ions. The ion resins were impregnated with silver ions, which were then exposed to various acids (silicic acid) to elute fatty acids of different characteristics.
Detection limits as low as 1 μM can be obtained for alkali metal ions.
It may be used for measurement of HbA1c, porphyrin and with water purification. Ion Exchange Resins(IER) have been widely used especially in medicines due to its high capacity and the uncomplicated system of the separation process. One of the synthetic uses is to use Ion Exchange Resins for kidney dialysis. This method is used to separate the blood elements by using the cellulose membraned artificial kidney.
Another clinical application of ion chromatography is in the rapid anion exchange chromatography technique used to separate creatine kinase (CK) isoenzymes from human serum and tissue sourced in autopsy material (mostly CK rich tissues were used such as cardiac muscle and brain). These isoenzymes include MM, MB, and BB, which all carry out the same function given different amino acid sequences. The functions of these isoenzymes are to convert creatine, using ATP, into phosphocreatine expelling ADP. Mini columns were filled with DEAE-Sephadex A-50 and further eluted with tris- buffer sodium chloride at various concentrations (each concentration was chosen advantageously to manipulate elution). Human tissue extract was inserted in columns for separation. All fractions were analyzed to see total CK activity and it was found that each source of CK isoenzymes had characteristic isoenzymes found within. Firstly, CK- MM was eluted, then CK-MB, followed by CK-BB. Therefore, the isoenzymes found in each sample could be used to identify the source, as they were tissue specific.
Using the information from results, correlation could be made about the diagnosis of patients and the kind of CK isoenzymes found in most abundant activity. From the finding, about 35 out of 71 patients studied suffered from heart attack (myocardial infarction) also contained an abundant amount of the CK-MM and CK-MB isoenzymes. Findings further show that many other diagnosis including renal failure, cerebrovascular disease, and pulmonary disease were only found to have the CK-MM isoenzyme and no other isoenzyme. The results from this study indicate correlations between various diseases and the CK isoenzymes found which confirms previous test results using various techniques. Studies about CK-MB found in heart attack victims have expanded since this study and application of ion chromatography.
=== Industrial applications ===
Since 1975 ion chromatography has been widely used in many branches of industry. The main beneficial advantages are reliability, very good accuracy and precision, high selectivity, high speed, high separation efficiency, and low cost of consumables. The most significant development related to ion chromatography are new sample preparation methods; improving the speed and selectivity of analytes separation; lowering of limits of detection and limits of quantification; extending the scope of applications; development of new standard methods; miniaturization and extending the scope of the analysis of a new group of substances. Allows for quantitative testing of electrolyte and proprietary additives of electroplating baths. It is an advancement of qualitative hull cell testing or less accurate UV testing. Ions, catalysts, brighteners and accelerators can be measured. Ion exchange chromatography has gradually become a widely known, universal technique for the detection of both anionic and cationic species. Applications for such purposes have been developed, or are under development, for a variety of fields of interest, and in particular, the pharmaceutical industry. The usage of ion exchange chromatography in pharmaceuticals has increased in recent years, and in 2006, a chapter on ion exchange chromatography was officially added to the United States Pharmacopia-National Formulary (USP-NF). Furthermore, in 2009 release of the USP-NF, the United States Pharmacopia made several analyses of ion chromatography available using two techniques: conductivity detection, as well as pulse amperometric detection. Majority of these applications are primarily used for measuring and analyzing residual limits in pharmaceuticals, including detecting the limits of oxalate, iodide, sulfate, sulfamate, phosphate, as well as various electrolytes including potassium, and sodium. In total, the 2009 edition of the USP-NF officially released twenty eight methods of detection for the analysis of active compounds, or components of active compounds, using either conductivity detection or pulse amperometric detection.
=== Drug development ===
There has been a growing interest in the application of IC in the analysis of pharmaceutical drugs. IC is used in different aspects of product development and quality control testing. For example, IC is used to improve stabilities and solubility properties of pharmaceutical active drugs molecules as well as used to detect systems that have higher tolerance for organic solvents. IC has been used for the determination of analytes as a part of a dissolution test. For instance, calcium dissolution tests have shown that other ions present in the medium can be well resolved among themselves and also from the calcium ion. Therefore, IC has been employed in drugs in the form of tablets and capsules in order to determine the amount of drug dissolve with time. IC is also widely used for detection and quantification of excipients or inactive ingredients used in pharmaceutical formulations. Detection of sugar and sugar alcohol in such formulations through IC has been done due to these polar groups getting resolved in ion column. IC methodology also established in analysis of impurities in drug substances and products. Impurities or any components that are not part of the drug chemical entity are evaluated and they give insights about the maximum and minimum amounts of drug that should be administered in a patient per day.
== See also ==
Anion-exchange chromatography
Chromatofocusing
High performance liquid chromatography
Isoelectric point
== References ==
== Bibliography ==
Small, Hamish (1989). Ion chromatography. New York: Plenum Press. ISBN 978-0-306-43290-3.
Tatjana Weiss; Weiss, Joachim (2005). Handbook of Ion Chromatography. Weinheim: Wiley-VCH. ISBN 978-3-527-28701-7.
Gjerde, Douglas T.; Fritz, James S. (2000). Ion Chromatography. Weinheim: Wiley-VCH. ISBN 978-3-527-29914-0.
Jackson, Peter; Haddad, Paul R. (1990). Ion chromatography: principles and applications. Amsterdam: Elsevier. ISBN 978-0-444-88232-5.
Mercer, Donald W (1974). "Separation of tissue and serum creatine kinase isoenzymes by ion-exchange column chromatography". Clinical Chemistry. 20 (1): 36–40. doi:10.1093/clinchem/20.1.36. PMID 4809470.
Morris, L. J. (1966). "Separations of lipids by silver ion chromatography". Journal of Lipid Research. 7 (6): 717–732. doi:10.1016/S0022-2275(20)38948-3. PMID 5339485.
Ghosh, Raja (2002). "Protein separation using membrane chromatography: opportunities and challenges". Journal of Chromatography A. 952 (1): 13–27. doi:10.1016/s0021-9673(02)00057-2. PMID 12064524.
== External links ==
Media related to Ion chromatography at Wikimedia Commons | Wikipedia/Ion_exchange_chromatography |
Micellar electrokinetic chromatography (MEKC) is a chromatography technique used in analytical chemistry. It is a modification of capillary electrophoresis (CE), extending its functionality to neutral analytes, where the samples are separated by differential partitioning between micelles (pseudo-stationary phase) and a surrounding aqueous buffer solution (mobile phase).
The basic set-up and detection methods used for MEKC are the same as those used in CE. The difference is that the solution contains a surfactant at a concentration that is greater than the critical micelle concentration (CMC). Above this concentration, surfactant monomers are in equilibrium with micelles.
In most applications, MEKC is performed in open capillaries under alkaline conditions to generate a strong electroosmotic flow. Sodium dodecyl sulfate (SDS) is the most commonly used surfactant in MEKC applications. The anionic character of the sulfate groups of SDS causes the surfactant and micelles to have electrophoretic mobility that is counter to the direction of the strong electroosmotic flow. As a result, the surfactant monomers and micelles migrate quite slowly, though their net movement is still toward the cathode. During a MEKC separation, analytes distribute themselves between the hydrophobic interior of the micelle and hydrophilic buffer solution as shown in figure 1.
Analytes that are insoluble in the interior of micelles should migrate at the electroosmotic flow velocity,
u
o
{\displaystyle u_{o}}
, and be detected at the retention time of the buffer,
t
M
{\displaystyle t_{M}}
. Analytes that solubilize completely within the micelles (analytes that are highly hydrophobic) should migrate at the micelle velocity,
u
c
{\displaystyle u_{c}}
, and elute at the final elution time,
t
c
{\displaystyle t_{c}}
.
== Theory ==
The micelle velocity is defined by:
u
c
=
u
p
+
u
o
{\displaystyle u_{c}=u_{p}+u_{o}}
where
u
p
{\displaystyle u_{p}}
is the electrophoretic velocity of a micelle.
The retention time of a given sample should depend on the capacity factor,
k
1
{\displaystyle k^{1}}
:
k
1
=
n
c
n
w
{\displaystyle k^{1}={\frac {n_{c}}{n_{w}}}}
where
n
c
{\displaystyle n_{c}}
is the total number of moles of solute in the micelle and
n
w
{\displaystyle n_{w}}
is the total moles in the aqueous phase. The retention time of a solute should then be within the range:
t
M
≤
t
r
≤
t
c
{\displaystyle t_{M}\leq t_{r}\leq t_{c}}
Charged analytes have a more complex interaction in the capillary because they exhibit electrophoretic mobility, engage in electrostatic interactions with the micelle, and participate in hydrophobic partitioning.
The fraction of the sample in the aqueous phase,
R
{\displaystyle R}
, is given by:
R
=
u
s
−
u
c
u
o
−
u
c
{\displaystyle R={\frac {u_{s}-u_{c}}{u_{o}-u_{c}}}}
where
u
s
{\displaystyle u_{s}}
is the migration velocity of the solute. The value
R
{\displaystyle R}
can also be expressed in terms of the capacity factor:
R
=
1
1
+
k
1
{\displaystyle R={\frac {1}{1+k^{1}}}}
Using the relationship between velocity, tube length from the injection end to the detector cell (
L
{\displaystyle L}
), and retention time,
u
o
=
L
/
t
M
{\displaystyle u_{o}=L/t_{M}}
,
u
c
=
L
/
t
c
{\displaystyle u_{c}=L/t_{c}}
and
u
s
=
L
/
t
r
{\displaystyle u_{s}=L/t_{r}}
, a relationship between the capacity factor and retention times can be formulated:
k
1
=
t
r
−
t
M
t
M
(
1
−
(
t
r
/
t
c
)
)
{\displaystyle k^{1}={\frac {t_{r}-t_{M}}{t_{M}(1-(t_{r}/t_{c}))}}}
The extra term enclosed in parentheses accounts for the partial mobility of the hydrophobic phase in MEKC. This equation resembles an expression derived for
k
1
{\displaystyle k^{1}}
in conventional packed bed chromatography:
k
=
t
r
−
t
M
t
M
{\displaystyle k={\frac {t_{r}-t_{M}}{t_{M}}}}
A rearrangement of the previous equation can be used to write an expression for the retention factor:
t
r
=
(
1
+
k
1
1
+
(
t
M
/
t
c
)
k
1
)
t
M
{\displaystyle t_{r}=\left({\frac {1+k^{1}}{1+(t_{M}/t_{c})k^{1}}}\right)t_{M}}
From this equation it can be seen that all analytes that partition strongly into the micellar phase (where
k
1
{\displaystyle k^{1}}
is essentially ∞) migrate at the same time,
t
c
{\displaystyle t_{c}}
. In conventional chromatography, separation of similar compounds can be improved by gradient elution. In MEKC, however, techniques must be used to extend the elution range to separate strongly retained analytes.
Elution ranges can be extended by several techniques including the use of organic modifiers, cyclodextrins, and mixed micelle systems. Short-chain alcohols or acetonitrile can be used as organic modifiers that decrease
t
M
{\displaystyle t_{M}}
and
k
1
{\displaystyle k^{1}}
to improve the resolution of analytes that co-elute with the micellar phase. These agents, however, may alter the level of the EOF. Cyclodextrins are cyclic polysaccharides that form inclusion complexes that can cause competitive hydrophobic partitioning of the analyte. Since analyte-cyclodextrin complexes are neutral, they will migrate toward the cathode at a higher velocity than that of the negatively charged micelles. Mixed micelle systems, such as the one formed by combining SDS with the non-ionic surfactant Brij-35, can also be used to alter the selectivity of MEKC.
== Applications ==
The simplicity and efficiency of MEKC have made it an attractive technique for a variety of applications. Further improvements can be made to the selectivity of MEKC by adding chiral selectors or chiral surfactants to the system. Unfortunately, this technique is not suitable for protein analysis because proteins are generally too large to partition into a surfactant micelle and tend to bind to surfactant monomers to form SDS-protein complexes.
Recent applications of MEKC include the analysis of uncharged pesticides, essential and branched-chain amino acids in nutraceutical products, hydrocarbon and alcohol contents of the marjoram herb.
MEKC has also been targeted for its potential to be used in combinatorial chemical analysis. The advent of combinatorial chemistry has enabled medicinal chemists to synthesize and identify large numbers of potential drugs in relatively short periods of time. Small sample and solvent requirements and the high resolving power of MEKC have enabled this technique to be used to quickly analyze a large number of compounds with good resolution.
Traditional methods of analysis, like high-performance liquid chromatography (HPLC), can be used to identify the purity of a combinatorial library, but assays need to be rapid with good resolution for all components to provide useful information for the chemist. The introduction of surfactant to traditional capillary electrophoresis instrumentation has dramatically expanded the scope of analytes that can be separated by capillary electrophoresis.
MEKC can also be used in routine quality control of antibiotics in pharmaceuticals or feedstuffs.
== References ==
== Sources ==
Kealey, D.;Haines P.J.; instant notes, Analytical Chemistry page 182-188 | Wikipedia/Micellar_electrokinetic_chromatography |
A protein skimmer or foam fractionator is a device used to remove organic compounds such as food and waste particles from water. It is most commonly used in commercial applications like municipal water treatment facilities, public aquariums, and aquaculture facilities. Smaller protein skimmers are also used for filtration of home saltwater aquariums and even freshwater aquariums and ponds.
== Function ==
Protein skimming removes certain organic compounds, including proteins and amino acids found in food particles and fish waste, by using the polarity of the protein itself. Due to their intrinsic charge, water-borne proteins are either repelled or attracted by the air–water interface and these molecules can be described as hydrophobic (such as fats or oils) or hydrophilic (such as salt, sugar, ammonia, most amino acids, and most inorganic compounds). However, some larger organic molecules can have both hydrophobic and hydrophilic portions. These molecules are called amphipathic or amphiphilic. Commercial protein skimmers work by generating a large air–water interface, specifically by injecting large numbers of bubbles into the water column. In general, the smaller the bubbles the more effective the protein skimming is because the surface area of small bubbles occupying the same volume is much greater than the same volume of larger bubbles. Large numbers of small bubbles present an enormous air–water interface for hydrophobic organic molecules and amphipathic organic molecules to collect on the bubble surface (the air–water interface). Water movement hastens diffusion of organic molecules, which effectively brings more organic molecules to the air–water interface and lets the organic molecules accumulate on the surface of the air bubbles. This process continues until the interface is saturated, unless the bubble is removed from the water or it bursts, in which case the accumulated molecules release back into the water column. However, it is important to note that further exposure of a saturated air bubble to organic molecules may continue to result in changes as compounds that bind more strongly may replace those molecules with a weaker binding that have already accumulated on the interface. Although some aquarists believe that increasing the contact time (or dwell time as it is sometimes called) is always good, it is incorrect to claim that it is always better to increase the contact time between bubbles and the aquarium water. As the bubbles increase near the top of the protein skimmer water column, they become denser and the water begins to drain and create the foam that will carry the organic molecules to the skimmate collection cup or to a separate skimmate waste collector and the organic molecules, and any inorganic molecules that may have become bound to the organic molecules, will be exported from the water system.
In addition to the proteins removed by skimming, there are a number of other organic and inorganic molecules that are typically removed. These include a variety of fats, fatty acids, carbohydrates, metals such as copper, and trace elements such as iodine. Particulates, phytoplankton, bacteria, and detritus are also removed; this is desired by some aquarists, and is often enhanced by placement of the skimmer before other forms of filtration, lessening the burden on the filtration system as a whole. There is at least one published study that provides a detailed list of the export products removed by the skimmer. Aquarists who keep filter-feeding invertebrates, however, sometimes prefer to keep these particulates in the water to serve as natural food.
Protein skimmers are used to harvest algae and phytoplankton gently enough to maintain viability for culturing or commercial sale as live cultures.
Alternative forms of water filtration have recently come into use, including the algae scrubber, which leaves food particles in the water for corals and small fish to consume, but removes the noxious compounds including ammonia, nitrite, nitrate, and phosphate that protein skimmers do not remove.
== Design ==
All skimmers have key features in common: water flows through a chamber and is brought into contact with a column of fine bubbles. The bubbles collect proteins and other substances and carry them to the top of the device where the foam, but not the water, collects in a cup. Here the foam condenses to a liquid, which can be easily removed from the system. The material that collects in the cup can range from pale greenish-yellow, watery liquid to a thick black tar.
Consider this summary of optimal protein skimmer design by Randy Holmes-Farley:
For a skimmer to function maximally, the following things must take place:
1. A large amount of air–water interface must be generated.
2. Organic molecules must be allowed to collect at the air–water interface.
3. The bubbles forming this air–water interface must come together to form a foam.
4. The water in the foam must partially drain without the bubbles popping prematurely.
5. The drained foam must be separated from the bulk water and discarded.
Also under considerable recent attention has been the general shape of a skimmer as well. In particular, much attention has been given to the introduction of cone shaped skimmer units. Originally designed by Klaus Jensen in 2004, the concept was founded on the principle that a conical body allows the foam to accumulate more steadily through a gently sloping transition. It was claimed that this reduces the overall turbulence, resulting in more efficient skimming. However, this design reduces the overall volume inside the skimmer, reducing dwell time. Cylindrical-shaped protein skimmers are the most popular design and allow for the largest volume of air and water.
Overall, protein skimmers can be classed in two ways depending on whether they operate by co-current flow or counter-current flow. In a co-current flow system, air is introduced at the bottom of the chamber and is in contact with the water as it rises upwards towards the collection chamber. In a counter-current system, air is forced into the system under pressure and moves against the flow of the water for a while before it rises up towards the collection cup. Because the air bubbles may be in contact with the water for a longer period in a counter-current flow system, protein skimmers of this type are considered by some to be more effective at removing organic wastes.
=== Co-current flow systems ===
==== Air stone ====
The original method of protein skimming, running pressurized air through a diffuser to produce large quantities of microbubbles, remains a viable, effective, and economic choice, although newer technologies may require lower maintenance. The air stone is most often an oblong, partially hollowed block of wood, most often of the genus Tilia. The most popular wooden air-stones for skimmers are made from limewood (Tilia europaea or European limewood) although basswood (Tilia americana or American linden), works as well, may be cheaper and is often more readily available. The wooden blocks are drilled, tapped, fitted with an air fitting, and connected by air tubing to one or more air pumps delivering at least 1 cfm. The wooden air stone is placed at the bottom of a tall column of water. The tank water is pumped into the column, allowed to pass by the rising bubbles, and back into the tank. To get enough contact time with the bubble, these units can be many feet in height.
Air stone protein skimmers may be constructed as a DIY project from pvc pipes and fittings at low cost [1] [2] and with varying degrees of complexity [3].
Air stone protein skimmers require powerful air pumps which are often power hungry, loud, and hot, leading to an increase in the aquarium water temperatures. While this method has been around for many years, due to more efficient technologies emerging, many regard it as inefficient current uses in larger systems or systems with large bio-loads.
==== Venturi ====
The premise behind these skimmers is that a high-pressure pump, combined with a venturi, can be used to introduce the bubbles into the water stream. The tank water is pumped through the venturi, in which fine bubbles are introduced via pressure differential, then enters the skimmer body. This method was popular due to its compact size and high efficiency for the time but venturi designs are now outdated and surpassed by more efficient needle-wheel designs.
=== Counter-current flow systems ===
==== Aspirating: pin-wheel/adrian-wheel, needle-wheel, mesh-wheel ====
This basic concept is more correctly known as an aspirating skimmer, since some skimmer designs using an aspirator do not use a pin-wheel/Adrian-wheel or needle-wheel. Pin-wheel/Adrian-wheel describes the look of an impeller that consists of a disk with pins mounted perpendicular (90°) to the disc and parallel to the rotor. Needle-wheel describes the look of an impeller that consists of a series of pins projecting out perpendicular to the rotor from a central axis. Mesh-wheel describes the look of an impeller that consists of a mesh material attached to a plate or central axis on the rotor. The purpose of these modified impellers is to chop or shred the air that is introduced via an air aspirator apparatus or external air pump into very fine bubbles. The mesh-wheel design provides excellent results in the short term because of its ability to create fine bubbles with its thin cutting surfaces, but its propensity for clogging makes it an unreliable design.
The air aspirator differs from the venturi by the positioning of the water pump. With a venturi, the water is pushed through the unit, creating a vacuum to draw in air. With an air aspirator, the water is pulled through the unit, creating a vacuum to draw in air. These terms, however, are often incorrectly interchanged.
This style of protein skimmer has become very popular with public aquariums and is believed to be the most popular type of skimmer used with residential reef aquariums today. It has been particularly successful in smaller aquariums due to its usually compact size, ease of set up and use, and quiet operation. Since the pump is pushing a mixture of air and water, the power required to turn the rotor can be decreased and may result in a lower power requirement for that pump vs. the same pump with a different impeller when it is only pumping water.
==== Downdraft ====
The downdraft skimmer is both a proprietary skimmer design and a style of protein skimmer that injects water under high pressure into tubes that have a foam or bubble generating mechanism and carry the air–water mixture down into the skimmer and into a separate chamber. The proprietary design is protected in the United States with patents and commercial skimmer products in the US are limited to that single company. Their design uses one or more tubes with plastic media such as bio balls inside to mix water under high pressure and air in the body of the skimmer resulting in foam that collects protein waste in a collection cup. This was one of the earlier high performance protein skimmer designs and large models were produced that saw success in large and public aquariums.
==== Beckett skimmer ====
The Beckett skimmer has some similarities to the downdraft skimmer but introduced a foam nozzle to produce the flow of air bubbles. The name Beckett comes from the patented foam nozzle developed and sold by the Beckett Corporation (United States), although similar foam nozzle designs are sold by other companies outside the United States (e.g. Sicce (Italy)). Instead of using the plastic media that is found in downdraft skimmer designs, the Beckett skimmer uses design concepts from previous generations of skimmers, specifically the downdraft skimmer and the venturi skimmer (the Beckett 1408 Foam Nozzle is a modified 4 port venturi) to produce a hybrid that is capable of using powerful pressure rated water pumps and quickly processing large amounts of aquarium water in a short period of time. Commercial Beckett skimmers come in single Beckett, dual Beckett, and quad Beckett designs. Well engineered Beckett skimmers are quiet and reliable. Due to the advances in pump technologies and introduction of DC pumps, the concerns of powerful pumps taking up additional space, introducing additional noise, and using more electricity have all been alleviated. Unlike the Downdraft and Spray Induction skimmers, Beckett skimmer designs are produced by a number of companies in the United States and elsewhere and are not known to be restricted by patents.
==== Spray induction ====
This method is related to the downdraft, but uses a pump to power a spray nozzle, fixed a few inches above the water level. The spray action entraps and shreds the air in the base of the unit, similar to holding your thumb over a garden hose, which then rises to the collection chamber. In the United States, one company has patented the spray induction technology and the commercial product offerings are limited to that single company.
=== Recirculating skimmer designs ===
A recent trend is to change the method by which the skimmer is fed 'dirty' water from the aquarium as a means to recirculate water within the skimmer multiple times before it is returned to the sump or the aquarium. Aspirating pump skimmers are the most popular type of skimmer to use recirculating designs although other types of skimmers, such as Beckett skimmers, are also available in recirculating versions. While there is a popular belief among some aquarist that this recirculation increases the dwell or contact time of the generated air bubbles within the skimmer there is no authoritative evidence that this is true. Each time water is recirculated within the skimmer any air bubbles in that water sample are destroyed and new bubbles are generated by the recirculating pump venturi apparatus so the air-water contact time begins again for these newly created bubbles. In non-recirculating skimmer designs, a skimmer has one inlet supplied by a pump that pulls water in from the aquarium and injects it with air into the skimmer and releasing the foam or air–water mix into the reaction chamber. With a recirculating design, the one inlet is usually driven by a separate feed pump, or in some cases may be gravity fed, to receive the dirty water to process, while the pump providing the foam or air–water mix into the reaction chamber is set up separately in a closed loop on the side of the skimmer. The recirculating pump pulls water out of the skimmer and injects air to generate the foam or air–water mix before returning it to the skimmer reaction chamber—thus 'recirculating' it. The feed pump in a recirculating design typically injects a smaller amount of dirty water than co/counter-current designs. The separate feed pump allows easy control of the rate of water exchange through the skimmer and for many aquarists this is one of the important attractions of recirculating skimmer designs. Because the pump configuration of these skimmers is similar to that of aspirating pump skimmers, the power consumption advantages are also similar.
== References ==
== Further reading ==
Delbeek, J. Charles; Julian Sprung (1994). Reef Aquarium, The, Volume 1. Coconut Grove, Florida: Ricordea Publishing.
Frank Marini. "Skimming Basics 101: Understanding Your Skimmer". Reefkeeping ... an online magazine for the marine aquarist. Retrieved 14 June 2006.
Frank Marini. ""Bite the Bullet" The Evolution of the Precision Marine Bullet 2 Skimmer". Reefkeeping ... an online magazine for the marine aquarist. Retrieved 4 October 2006.
Randy Holmes-Farley. "What is Skimming?". Reefkeeping ... an online magazine for the marine aquarist. Retrieved 4 October 2006.
Delbeek, J. Charles; Julian Sprung (2005). The Reef Aquarium Volume Three: Science, Art, and Technology. Coconut Grove, Florida: Ricordea Publishing.
Ronald L. Shimek, Ph.D. "Down the Drain, Exports From Reef Aquaria". Reefkeeping ... an online magazine for the marine aquarist. Retrieved 27 October 2007. | Wikipedia/Protein_skimmer |
Periodic counter-current chromatography (PCC) is a method for running affinity chromatography in a quasi-continuous manner. Today, the process is mainly employed for the purification of antibodies in the biopharmaceutical industry as well as in research and development. When purifying antibodies, protein A is used as affinity matrix. However, periodic counter-current processes can be applied to any affinity type chromatography.
== Basic principle ==
In conventional affinity chromatography, a single chromatography column is loaded with feed material up to the point before target material (product) cannot be retained by the affinity material anymore.
The resin with the adsorbed product on it is then washed to remove impurities. Finally, the pure product is eluted with a different buffer. Notably, if too much feed material is loaded onto the column, the product can break through and product is consequently lost. Therefore, it is very important to only partially load the column to maximize the yield.
Periodic counter-current chromatography puts this problem aside by utilizing more than one column. PCC processes can be run with any number of columns, starting from two. The following paragraph will explain a two-column version of PCC, but other protocols with more columns rely on the same principles (see below).
A diagram depicting the individual process steps is shown on the right. In Step 1, the so-called sequential loading phase, columns 1 and 2 are interconnected. Column 1 is fully loaded with sample (red) while its breakthrough is captured on column 2. In Step 2, column 1 is washed, eluted, cleaned and re-equilibrated while loading separately continues on column 2. In Step 3, after regeneration of column 1, the columns are again inter-connected and column 2 is fully loaded while its breakthrough is captured on column 1. Finally, in Step 4 column 2 is washed, eluted, cleaned and re-equilibrated while loading continues independently on column 1. This cyclic process is repeated in a continuous way.
Several variations of periodic counter-current chromatography with more than two columns exist. In these cases, additional columns are either placed within the feed stream during loading, having the same effect as using longer columns. Alternatively, additional columns can be kept in an unoccupied stand-by mode during loading. This mode offers additional assurance that the main process is not influenced by washing and cleaning protocols, albeit in practice this is rarely required. On the other hand, the underutilized columns reduce the theoretical maximum productivity for such processes. Generally, the advantages and disadvantages of different multi-column protocols are the subject of debate. However, without a doubt, compared to single column batch processes, periodic counter-current processes provide significantly increased productivity.
== Dynamic process control ==
On the time scale of continuous chromatography runs, it is fairly common to observe changes in important process parameters, such as column health, buffer quality, feed titer (concentration) or feed composition. Such changes result in an altered maximum column capacity, relative to the amount of loaded feed material. In order to achieve a steady quality and yield for each process cycle, the timing of the individual process steps therefore has to be adjusted. Manual changes are in principle conceivable, but rather impractical. More commonly, dynamic process control algorithms monitor the process parameters and apply changes as needed automatically.
There are two different operating modes for dynamic process controllers in use today (see Figure on the right).
The first one, called DeltaUV, monitors the difference between two signals from detectors situated before and after the first column. During initial loading, there is a large difference between the two signals, but it is diminishing as the impurities make their way through the column. Once the column is fully saturated with impurities and only additional product is being held back, the difference between the signals reaches a constant value. As long as the product is completely being captured on the column, the difference between the signals will remain constant. As soon as some of the product breaks through the column (compare above), the difference diminishes. Thus, the timing and amount of product breakthrough can be determined.
The second possibility, called AutomAb, requires only the signal of a single detector situated behind the first column. During initial loading, the signal increases, as more and more impurities make their way through the column. When the column is saturated with impurities and as long as the product is completely being captured on the column, the signal then remains constant. As soon as some of the product breaks through the column (compare above), the signal increases again. Thus, the timing and amount of product breakthrough can again be determined.
Both iterations work equally well in theory. In practice, the requirement for two synced signals and the exposure of one detector to unpurified feed material, makes the DetaUV approach less reliable than AutomAb.
== Commercial situation ==
As of 2017, Cytiva holds patents around three-column periodic counter-current chromatography: this technology is used in their Äkta PCC instrument. Likewise, ChromaCon holds patents for an optimized two-column version (CaptureSMB). CaptureSMB is used in ChromaCon's Contichrom CUBE and under license in YMC's Ecoprime Twin systems. Additional manufacturers of systems capable of periodic counter-current chromatography include Novasep and Pall.
== References == | Wikipedia/Periodic_counter-current_chromatography |
Paper chromatography is an analytical method used to separate colored chemicals or substances. It can also be used for colorless chemicals that can be located by a stain or other visualisation method after separation. It is now primarily used as a teaching tool, having been replaced in the laboratory by other chromatography methods such as thin-layer chromatography (TLC).
This analytic method has three components, a mobile phase, stationary phase and a support medium (the paper). The mobile phase is generally a non-polar organic solvent in which the sample is dissolved. The stationary phase consists of (polar) water molecules that were incorporated into the paper when it was manufactured. The mobile phase travels up the stationary phase by capillary action, carrying the sample with it. The difference between TLC and paper chromatography is that the stationary phase in TLC is a layer of adsorbent (usually silica gel, or aluminium oxide), and the stationary phase in paper chromatography is less absorbent paper.
A paper chromatography variant, two-dimensional chromatography, involves using two solvents and rotating the paper 90° in between. This is useful for separating complex mixtures of compounds having similar polarity, for example, amino acids.
== Rƒ value, solutes, and solvents ==
The retention factor (Rƒ) may be defined as the ratio of the distance travelled by the solute to the distance travelled by the solvent. It is used in chromatography to quantify the amount of retardation of a sample in a stationary phase relative to a mobile phase. Rƒ values are usually expressed as a fraction of two decimal places.
If Rƒ value of a solution is zero, the solute remains in the stationary phase and thus it is immobile.
If Rƒ value = 1 then the solute has no affinity for the stationary phase and travels with the solvent front.
For example, if a compound travels 9.9 cm and the solvent front travels 12.7 cm, the Rƒ value = (9.9/12.7) = 0.779 or 0.78. Rƒ value depends on temperature and the solvent used in experiment, so several solvents offer several Rƒ values for the same mixture of compound. A solvent in chromatography is the liquid the paper is placed in, and the solute is the ink which is being separated.
== Pigments and polarity ==
Paper chromatography is one method for testing the purity of compounds and identifying substances. Paper chromatography is a useful technique because it is relatively quick and requires only small quantities of material. Separations in paper chromatography involve the principle of partition. In paper chromatography, substances are distributed between a stationary phase and a mobile phase. The stationary phase is the water trapped between the cellulose fibers of the paper. The mobile phase is a developing solution that travels up the stationary phase, carrying the samples with it. Components of the sample will separate readily according to how strongly they adsorb onto the stationary phase versus how readily they dissolve in the mobile phase.
When a colored chemical sample is placed on a filter paper, the colors separate from the sample by placing one end of the paper in a solvent. The solvent diffuses up the paper, dissolving the various molecules in the sample according to the polarities of the molecules and the solvent. If the sample contains more than one color, that means it must have more than one kind of molecule. Because of the different chemical structures of each kind of molecule, the chances are very high that each molecule will have at least a slightly different polarity, giving each molecule a different solubility in the solvent. The unequal solubility causes the various color molecules to leave solution at different places as the solvent continues to move up the paper. The more soluble a molecule is, the higher it will migrate up the paper. If a chemical is very non-polar it will not dissolve at all in a very polar solvent. This is the same for a very polar chemical and a very non-polar solvent.
When using water (a very polar substance) as a solvent, the more polar the color, the higher it will rise on the papers.
== Types ==
=== Descending ===
Development of the chromatogram is done by allowing the solvent to travel down the paper. Here, the mobile phase is placed in a solvent holder at the top. The spot is kept at the top and solvent flows down the paper from above.
=== Ascending ===
Here the solvent travels up the chromatographic paper. Both descending and ascending paper chromatography are used for the separation of organic and inorganic substances.
The sample and solvent move upward.
=== The ascending and descending method ===
This is the hybrid of both of the above techniques. The upper part of ascending chromatography can be folded over a rod in order to allow the paper to become descending after crossing the rod.
=== Circular chromatography ===
A circular filter paper is taken and the sample is deposited at the center of the paper. After drying the spot, the filter paper is tied horizontally on a Petri dish containing solvent, so that the wick of the paper is dipped in the solvent. The solvent rises through the wick and the components are separated into concentric rings.
=== Two-dimensional ===
In this technique a square or rectangular paper is used. Here the sample is applied to one of the corners and development is performed at a right angle to the direction of the first run.
== History of paper chromatography ==
The discovery of paper chromatography in 1943 by Martin and Synge provided, for the first time, the means of surveying constituents of plants and for their separation and identification. Erwin Chargaff credits in Weintraub's history of the man the 1944 article by Consden, Gordon and Martin. There was an explosion of activity in this field after 1945.
== References ==
== Bibliography ==
Block, Richard J.; Durrum, Emmett L.; Zweig, Gunter (1955). A Manual of Paper Chromatography and Paper Electrophoresis. Elsevier. p. 4. ISBN 978-1-4832-7680-9 – via Google Books. {{cite book}}: ISBN / Date incompatibility (help) | Wikipedia/Chromatography_paper |
Thin-layer chromatography (TLC) is a chromatography technique that separates components in non-volatile mixtures.
It is performed on a TLC plate made up of a non-reactive solid coated with a thin layer of adsorbent material. This is called the stationary phase. The sample is deposited on the plate, which is eluted with a solvent or solvent mixture known as the mobile phase (or eluent). This solvent then moves up the plate via capillary action. As with all chromatography, some compounds are more attracted to the mobile phase, while others are more attracted to the stationary phase. Therefore, different compounds move up the TLC plate at different speeds and become separated. To visualize colourless compounds, the plate is viewed under UV light or is stained. Testing different stationary and mobile phases is often necessary to obtain well-defined and separated spots.
TLC is quick, simple, and gives high sensitivity for a relatively low cost. It can monitor reaction progress, identify compounds in a mixture, determine purity, or purify small amounts of compound.
== Procedure ==
The process for TLC is similar to paper chromatography but provides faster runs, better separations, and the choice between different stationary phases. Plates can be labelled before or after the chromatography process with a pencil or other implement that will not interfere with the process.
There are four main stages to running a thin-layer chromatography plate:
Plate preparation: Using a capillary tube, a small amount of a concentrated solution of the sample is deposited near the bottom edge of a TLC plate. The solvent is allowed to completely evaporate before the next step. A vacuum chamber may be necessary for non-volatile solvents. To make sure there is sufficient compound to obtain a visible result, the spotting procedure can be repeated. Depending on the application, multiple different samples may be placed in a row the same distance from the bottom edge; each sample will move up the plate in its own "lane."
Development chamber preparation: The development solvent or solvent mixture is placed into a transparent container (separation/development chamber) to a depth of less than 1 centimetre. A strip of filter paper (aka "wick") is also placed along the container wall. This filter paper should touch the solvent and almost reach the top of the container. The container is covered with a lid and the solvent vapors are allowed to saturate the atmosphere of the container. Failure to do so results in poor separation and non-reproducible results.
Development: The TLC plate is placed in the container such that the sample spot(s) are not submerged into the mobile phase. The container is covered to prevent solvent evaporation. The solvent migrates up the plate by capillary action, meets the sample mixture, and carries it up the plate (elutes the sample). The plate is removed from the container before the solvent reaches the top of the plate; otherwise, the results will be misleading. The solvent front, the highest mark the solvent has travelled along the plate, is marked.
Visualization: The solvent evaporates from the plate. Visualization methods include UV light, staining, and many more.
== Separation process and principle ==
The separation of compounds is due to the differences in their attraction to the stationary phase and because of differences in solubility in the solvent. As a result, the compounds and the mobile phase compete for binding sites on the stationary phase. Different compounds in the sample mixture travel at different rates due to the differences in their partition coefficients. Different solvents, or different solvent mixtures, gives different separation. The retardation factor (Rf), or retention factor, quantifies the results. It is the distance traveled by a given substance divided by the distance traveled by the mobile phase.
In normal-phase TLC, the stationary phase is polar. Silica gel is very common in normal-phase TLC. More polar compounds in a sample mixture interact more strongly with the polar stationary phase. As a result, more-polar compounds move less (resulting in smaller Rf) while less-polar compounds move higher up the plate (higher Rf). A more-polar mobile phase also binds more strongly to the plate, competing more with the compound for binding sites; a more-polar mobile phase also dissolves polar compounds more. As such, all compounds on the TLC plate move higher up the plate in polar solvent mixtures. "Strong" solvents move compounds higher up the plate, whereas "weak" solvents move them less.
If the stationary phase is non-polar, like C18-functionalized silica plates, it is called reverse-phase TLC. In this case, non-polar compounds move less and polar compounds move more. The solvent mixture will also be much more polar than in normal-phase TLC.
=== Solvent choice ===
An eluotropic series, which orders solvents by how much they move compounds, can help in selecting a mobile phase. Solvents are also divided into solvent selectivity groups. Using solvents with different elution strengths or different selectivity groups can often give very different results. While single-solvent mobile phases can sometimes give good separation, some cases may require solvent mixtures.
In normal-phase TLC, the most common solvent mixtures include ethyl acetate/hexanes (EtOAc/Hex) for less-polar compounds and methanol/dichloromethane (MeOH/DCM) for more polar compounds. Different solvent mixtures and solvent ratios can help give better separation. In reverse-phase TLC, solvent mixtures are typically water with a less-polar solvent: Typical choices are water with tetrahydrofuran (THF), acetonitrile (ACN), or methanol.
== Analysis ==
As the chemicals being separated may be colourless, several methods exist to visualise the spots:
Placing the plate under blacklight (366 nm light) makes fluorescent compounds glow
TLC plates containing a small amount of fluorescent compound (usually manganese-activated zinc silicate) in the adsorbent layer allow for visualisation of some compounds under UV-C light (254 nm). The adsorbent layer will fluoresce light-green, while spots containing compounds that absorb UV-C light will not.
Placing the plate in a container filled with iodine vapours temporarily stains the spots. They typically become a yellow or brown colour.
The TLC plate can either be dipped in or sprayed with a stain and sometimes heated depending on the stain used. Many stains exist for a large range of chemical moieties but some examples include:
Potassium permanganate (no heating, for oxidisable groups)
Ninhydrin (heating, amines and amino-acids)
Acidic vanillin (heating, general reagent)
Phosphomolybdic acid (no heating, general reagent)
In the case of lipids, the chromatogram may be transferred to a polyvinylidene fluoride membrane and then subjected to further analysis, for example, mass spectrometry. This technique is known as far-eastern blot.
== Plate production ==
TLC plates are usually commercially available, with standard particle size ranges to improve reproducibility. They are prepared by mixing the adsorbent, such as silica gel, with a small amount of inert binder like calcium sulfate (gypsum) and water. This mixture is spread as a thick slurry on an unreactive carrier sheet, usually glass, thick aluminum foil, or plastic. The resultant plate is dried and activated by heating in an oven for thirty minutes at 110 °C. The thickness of the absorbent layer is typically around 0.1–0.25 mm for analytical purposes and around 0.5–2.0 mm for preparative TLC. Other adsorbent coatings include aluminium oxide (alumina), or cellulose.
== Applications ==
=== Reaction monitoring and characterization ===
TLC is a useful tool for reaction monitoring. For this, the plate normally contains a spot of starting material, a spot from the reaction mixture, and a co-spot (or cross-spot) containing both. The analysis will show if the starting material disappeared and if any new products appeared. This provides a quick and easy way to estimate how far a reaction has proceeded. In one study, TLC has been applied in the screening of organic reactions. The researchers react an alcohol and a catalyst directly in the co-spot of a TLC plate before developing it. This provides quick and easy small-scale testing of different reagents.
Compound characterization with TLC is also possible and is similar to reaction monitoring. However, rather than spotting with starting material and reaction mixture, it is with an unknown and a known compound. They may be the same compound if both spots have the same Rf and look the same under the chosen visualization method. However, co-elution complicates both reaction monitoring and characterization. This is because different compounds will move to the same spot on the plate. In such cases, different solvent mixtures may provide better separation.
=== Purity and purification ===
TLC helps show the purity of a sample. A pure sample should only contain one spot by TLC. TLC is also useful for small-scale purification. Because the separated compounds will be on different areas of the plate, a scientist can scrape off the stationary phase particles containing the desired compound and dissolve them into an appropriate solvent. Once all the compound dissolves in the solvent, they filter out the silica particles, then evaporate the solvent to isolate the product. Big preparative TLC plates with thick silica gel coatings can separate more than 100 mg of material.
For larger-scale purification and isolation, TLC is useful to quickly test solvent mixtures before running flash column chromatography on a large batch of impure material. A compound elutes from a column when the amount of solvent collected is equal to 1/Rf. The eluent from flash column chromatography gets collected across several containers (for example, test tubes) called fractions. TLC helps show which fractions contain impurities and which contain pure compound.
Furthermore, two-dimensional TLC can help check if a compound is stable on a particular stationary phase. This test requires two runs on a square-shaped TLC plate. The plate is rotated by 90º before the second run. If the target compound appears on the diagonal of the square, it is stable on the chosen stationary phase. Otherwise, it is decomposing on the plate. If this is the case, an alternative stationary phase may prevent this decomposition.
TLC is also an analytical method for the direct separation of enantiomers and the control of enantiomeric purity, e.g. active pharmaceutical ingredients (APIs) that are chiral.
Separation of green plant matter in spinach (note that images from steps 1-6 are zoomed into the bottom of the plate)
== See also ==
Column chromatography
HPTLC
Radial chromatography
Chiral thin-layer chromatography
== References ==
== Bibliography == | Wikipedia/Thin-layer_chromatography |
Chromatography is a 2004 post trip-hop album by Second Person.
This is the band's debut album and all songs were written by Julia Johnson and Mark Maclaine, except "Word for Word" which also credits Ed Webber and Tristan Kajanus, "Demons Die" which also credits Álvaro López and "Divine" which was written by Julia Johnson. The album was recorded, produced and mixed by Mark Maclaine (aka The Silence) at The Silence Corporation Studios, London. The songs "I Spy" and "My Baby Only Cares For Me" were originally written for the 2003 ski/snowboard film: Snow's in the House 2 and they can be found as earlier incarnations on the film's soundtrack.
== Track listing ==
"Too Cold To Snow" – 4:42
"Demons In The Scenery" – 3:48
"No Window" – 4:21
"I Spy" – 4:12
"Wreckage" – 3:16
"Demons Die" – 3:30
"Word For Word" – 3:43
"Nerve" – 4:07
"My Baby Only Cares For Me" – 3:30
"Senseless Sentences" – 4:20
"Divine" – 4:09
"Lucky Breaks" – 4:08
"Grace" – 5:02
"Harry: Walkies" - 0:09
== References ==
BBC Radio 2 Interview (The Weekender with Matthew Wright - 3 November 2005)
Future Music Magazine interview (November 2005) | Wikipedia/Chromatography_(album) |
Ion chromatography (or ion-exchange chromatography) is a form of chromatography that separates ions and ionizable polar molecules based on their affinity to the ion exchanger. It works on almost any kind of charged molecule—including small inorganic anions, large proteins, small nucleotides, and amino acids. However, ion chromatography must be done in conditions that are one pH unit away from the isoelectric point of a protein.
The two types of ion chromatography are anion-exchange and cation-exchange. Cation-exchange chromatography is used when the molecule of interest is positively charged. The molecule is positively charged because the pH for chromatography is less than the pI (also known as pH(I)). In this type of chromatography, the stationary phase is negatively charged and positively charged molecules are loaded to be attracted to it. Anion-exchange chromatography is when the stationary phase is positively charged and negatively charged molecules (meaning that pH for chromatography is greater than the pI) are loaded to be attracted to it. It is often used in protein purification, water analysis, and quality control. The water-soluble and charged molecules such as proteins, amino acids, and peptides bind to moieties which are oppositely charged by forming ionic bonds to the insoluble stationary phase. The equilibrated stationary phase consists of an ionizable functional group where the targeted molecules of a mixture to be separated and quantified can bind while passing through the column—a cationic stationary phase is used to separate anions and an anionic stationary phase is used to separate cations. Cation exchange chromatography is used when the desired molecules to separate are cations and anion exchange chromatography is used to separate anions. The bound molecules then can be eluted and collected using an eluant which contains anions and cations by running a higher concentration of ions through the column or by changing the pH of the column.
One of the primary advantages for the use of ion chromatography is that only one interaction is involved the separation, as opposed to other separation techniques; therefore, ion chromatography may have higher matrix tolerance. Another advantage of ion exchange is the predictability of elution patterns (based on the presence of the ionizable group). For example, when cation exchange chromatography is used, certain cations will elute out first and others later. A local charge balance is always maintained. However, there are also disadvantages involved when performing ion-exchange chromatography, such as constant evolution of the technique which leads to the inconsistency from column to column. A major limitation to this purification technique is that it is limited to ionizable group.
== History ==
Ion chromatography has advanced through the accumulation of knowledge over a course of many years. Starting from 1947, Spedding and Powell used displacement ion-exchange chromatography for the separation of the rare earths. Additionally, they showed the ion-exchange separation of 14N and 15N isotopes in ammonia. At the start of the 1950s, Kraus and Nelson demonstrated the use of many analytical methods for metal ions dependent on their separation of their chloride, fluoride, nitrate or sulfate complexes by anion chromatography. Automatic in-line detection was progressively introduced from 1960 to 1980 as well as novel chromatographic methods for metal ion separations. A groundbreaking method by Small, Stevens and Bauman at Dow Chemical Co. unfolded the creation of the modern ion chromatography. Anions and cations could now be separated efficiently by a system of suppressed conductivity detection. In 1979, a method for anion chromatography with non-suppressed conductivity detection was introduced by Gjerde et al. Following it in 1980, was a similar method for cation chromatography.
As a result, a period of extreme competition began within the IC market, with supporters for both suppressed and non-suppressed conductivity detection. This competition led to fast growth of new forms and the fast evolution of IC. A challenge that needs to be overcome in the future development of IC is the preparation of highly efficient monolithic ion-exchange columns and overcoming this challenge would be of great importance to the development of IC.
The boom of Ion exchange chromatography primarily began between 1935 and 1950 during World War II and it was through the "Manhattan project" that applications and IC were significantly extended. Ion chromatography was originally introduced by two English researchers, agricultural Sir Thompson and chemist J T Way. The works of Thompson and Way involved the action of water-soluble fertilizer salts, ammonium sulfate and potassium chloride. These salts could not easily be extracted from the ground due to the rain. They performed ion methods to treat clays with the salts, resulting in the extraction of ammonia in addition to the release of calcium. It was in the fifties and sixties that theoretical models were developed for IC for further understanding and it was not until the seventies that continuous detectors were utilized, paving the path for the development from low-pressure to high-performance chromatography. Not until 1975 was "ion chromatography" established as a name in reference to the techniques, and was thereafter used as a name for marketing purposes. Today IC is important for investigating aqueous systems, such as drinking water. It is a popular method for analyzing anionic elements or complexes that help solve environmentally relevant problems. Likewise, it also has great uses in the semiconductor industry.
Because of the abundant separating columns, elution systems, and detectors available, chromatography has developed into the main method for ion analysis.
When this technique was initially developed, it was primarily used for water treatment. Since 1935, ion exchange chromatography rapidly manifested into one of the most heavily leveraged techniques, with its principles often being applied to majority of fields of chemistry, including distillation, adsorption, and filtration.
== Principle ==
Ion-exchange chromatography separates molecules based on their respective charged groups. Ion-exchange chromatography retains analyte molecules on the column based on coulombic (ionic) interactions. The ion exchange chromatography matrix consists of positively and negatively charged ions. Essentially, molecules undergo electrostatic interactions with opposite charges on the stationary phase matrix. The stationary phase consists of an immobile matrix that contains charged ionizable functional groups or ligands. The stationary phase surface displays ionic functional groups (R-X) that interact with analyte ions of opposite charge. To achieve electroneutrality, these immobilized charges couple with exchangeable counterions in the solution. Ionizable molecules that are to be purified, compete with these exchangeable counterions, for binding to the immobilized charges on the stationary phase. These ionizable molecules are retained or eluted based on their charge. Initially, molecules that do not bind or bind weakly to the stationary phase are first to be washed away. Altered conditions are needed for the elution of the molecules that bind to the stationary phase. The concentration of the exchangeable counterions, which competes with the molecules for binding, can be increased, or the pH can be changed to affect the ionic charge of the eluent or the solute. A change in pH affects the charge on the particular molecules and, therefore, alter their binding. When reducing the net charge of the solute's molecules, they start eluting out. This way, such adjustments can be used to release the proteins of interest. Additionally, concentration of counterions can be gradually varied to affect the retention of the ionized molecules, thus separate them. This type of elution is called gradient elution. On the other hand, step elution can be used, in which the concentration of counterions are varied in steps. This type of chromatography is further subdivided into cation exchange chromatography and anion-exchange chromatography. Positively charged molecules bind to cation exchange resins, while negatively charged molecules bind to anion exchange resins. The ionic compound consisting of the cationic species M+ and the anionic species B− can be retained by the stationary phase.
Cation exchange chromatography retains positively charged cations because the stationary phase displays a negatively charged functional group:
R-X
−
C
+
+
M
+
B
−
⇄
R-X
−
M
+
+
C
+
+
B
−
{\displaystyle {\text{R-X}}^{-}{\text{C}}^{+}\,+\,{\text{M}}^{+}\,{\text{B}}^{-}\rightleftarrows \,{\text{R-X}}^{-}{\text{M}}^{+}\,+\,{\text{C}}^{+}\,+\,{\text{B}}^{-}}
Anion exchange chromatography retains anions using positively charged functional group:
R-X
+
A
−
+
M
+
B
−
⇄
R-X
+
B
−
+
M
+
+
A
−
{\displaystyle {\text{R-X}}^{+}{\text{A}}^{-}\,+\,{\text{M}}^{+}\,{\text{B}}^{-}\rightleftarrows \,{\text{R-X}}^{+}{\text{B}}^{-}\,+\,{\text{M}}^{+}\,+\,{\text{A}}^{-}}
Note that the ion strength of either C+ or A− in the mobile phase can be adjusted to shift the equilibrium position, thus retention time.
The ion chromatogram shows a typical chromatogram obtained with an anion exchange column.
== Procedure ==
Before ion-exchange chromatography can be initiated, it must be equilibrated. The stationary phase must be equilibrated to certain requirements that depend on the experiment that you are working with. Once equilibrated, the charged ions in the stationary phase will be attached to its opposite charged exchangeable ions, such as Cl− or Na+. Next, a buffer should be chosen in which the desired protein can bind to. After equilibration, the column needs to be washed. The washing phase will help elute out all impurities that does not bind to the matrix while the protein of interest remains bounded. This sample buffer needs to have the same pH as the buffer used for equilibration to help bind the desired proteins. Uncharged proteins will be eluted out of the column at a similar speed of the buffer flowing through the column with no retention. Once the sample has been loaded onto to the column, and the column has been washed with the buffer to elute out all non-desired proteins, elution is carried out at specific conditions to elute the desired proteins that are bound to the matrix. Bound proteins are eluted out by utilizing a gradient of linearly increasing salt concentration. With increasing ionic strength of the buffer, the salt ions will compete with the desired proteins in order to bind to charged groups on the surface of the medium. This will cause desired proteins to be eluted out of the column. Proteins that have a low net charge will be eluted out first as the salt concentration increases causing the ionic strength to increase. Proteins with high net charge will need a higher ionic strength for them to be eluted out of the column.
It is possible to perform ion exchange chromatography in bulk, on thin layers of medium such as glass or plastic plates coated with a layer of the desired stationary phase, or in chromatography columns. Thin layer chromatography or column chromatography share similarities in that they both act within the same governing principles; there is constant and frequent exchange of molecules as the mobile phase travels along the stationary phase. It is not imperative to add the sample in minute volumes as the predetermined conditions for the exchange column have been chosen so that there will be strong interaction between the mobile and stationary phases. Furthermore, the mechanism of the elution process will cause a compartmentalization of the differing molecules based on their respective chemical characteristics. This phenomenon is due to an increase in salt concentrations at or near the top of the column, thereby displacing the molecules at that position, while molecules bound lower are released at a later point when the higher salt concentration reaches that area. These principles are the reasons that ion exchange chromatography is an excellent candidate for initial chromatography steps in a complex purification procedure as it can quickly yield small volumes of target molecules regardless of a greater starting volume.
Comparatively simple devices are often used to apply counterions of increasing gradient to a chromatography column. Counterions such as copper (II) are chosen most often for effectively separating peptides and amino acids through complex formation.
A simple device can be used to create a salt gradient. Elution buffer is consistently being drawn from the chamber into the mixing chamber, thereby altering its buffer concentration. Generally, the buffer placed into the chamber is usually of high initial concentration, whereas the buffer placed into the stirred chamber is usually of low concentration. As the high concentration buffer from the left chamber is mixed and drawn into the column, the buffer concentration of the stirred column gradually increase. Altering the shapes of the stirred chamber, as well as of the limit buffer, allows for the production of concave, linear, or convex gradients of counterion.
A multitude of different mediums are used for the stationary phase. Among the most common immobilized charged groups used are trimethylaminoethyl (TAM), triethylaminoethyl (TEAE), diethyl-2-hydroxypropylaminoethyl (QAE), aminoethyl (AE), diethylaminoethyl (DEAE), sulpho (S), sulphomethyl (SM), sulphopropyl (SP), carboxy (C), and carboxymethyl (CM).
Successful packing of the column is an important aspect of ion chromatography. Stability and efficiency of a final column depends on packing methods, solvent used, and factors that affect mechanical properties of the column. In contrast to early inefficient dry- packing methods, wet slurry packing, in which particles that are suspended in an appropriate solvent are delivered into a column under pressure, shows significant improvement. Three different approaches can be employed in performing wet slurry packing: the balanced density method (solvent's density is about that of porous silica particles), the high viscosity method (a solvent of high viscosity is used), and the low viscosity slurry method (performed with low viscosity solvents).
Polystyrene is used as a medium for ion- exchange. It is made from the polymerization of styrene with the use of divinylbenzene and benzoyl peroxide. Such exchangers form hydrophobic interactions with proteins which can be irreversible. Due to this property, polystyrene ion exchangers are not suitable for protein separation. They are used on the other hand for the separation of small molecules in amino acid separation and removal of salt from water. Polystyrene ion exchangers with large pores can be used for the separation of protein but must be coated with a hydrophilic substance.
Cellulose based medium can be used for the separation of large molecules as they contain large pores. Protein binding in this medium is high and has low hydrophobic character. DEAE is an anion exchange matrix that is produced from a positive side group of diethylaminoethyl bound to cellulose or Sephadex.
Agarose gel based medium contain large pores as well but their substitution ability is lower in comparison to dextrans. The ability of the medium to swell in liquid is based on the cross-linking of these substances, the pH and the ion concentrations of the buffers used.
Incorporation of high temperature and pressure allows a significant increase in the efficiency of ion chromatography, along with a decrease in time. Temperature has an influence of selectivity due to its effects on retention properties. The retention factor (k = (tRg − tMg)/(tMg − text)) increases with temperature for small ions, and the opposite trend is observed for larger ions.
Despite ion selectivity in different mediums, further research is being done to perform ion exchange chromatography through the range of 40–175 °C.
An appropriate solvent can be chosen based on observations of how column particles behave in a solvent. Using an optical microscope, one can easily distinguish a desirable dispersed state of slurry from aggregated particles.
== Weak and strong ion exchangers ==
A "strong" ion exchanger will not lose the charge on its matrix once the column is equilibrated and so a wide range of pH buffers can be used. "Weak" ion exchangers have a range of pH values in which they will maintain their charge. If the pH of the buffer used for a weak ion exchange column goes out of the capacity range of the matrix, the column will lose its charge distribution and the molecule of interest may be lost. Despite the smaller pH range of weak ion exchangers, they are often used over strong ion exchangers due to their having greater specificity. In some experiments, the retention times of weak ion exchangers are just long enough to obtain desired data at a high specificity.
Resins (often termed 'beads') of ion exchange columns may include functional groups such as weak/strong acids and weak/strong bases. There are also special columns that have resins with amphoteric functional groups that can exchange both cations and anions. Some examples of functional groups of strong ion exchange resins are quaternary ammonium cation (Q), which is an anion exchanger, and sulfonic acid (S, -SO2OH), which is a cation exchanger. These types of exchangers can maintain their charge density over a pH range of 0–14. Examples of functional groups of Weak ion exchange resins include diethylaminoethyl (DEAE, -C2H4N(C2H5)2), which is an anion exchanger, and carboxymethyl (CM, -CH2-COOH), which is a cation exchanger. These two types of exchangers can maintain the charge density of their columns over a pH range of 5–9.
In ion chromatography, the interaction of the solute ions and the stationary phase based on their charges determines which ions will bind and to what degree. When the stationary phase features positive groups which attracts anions, it is called an anion exchanger; when there are negative groups on the stationary phase, cations are attracted and it is a cation exchanger. The attraction between ions and stationary phase also depends on the resin, organic particles used as ion exchangers.
Each resin features relative selectivity which varies based on the solute ions present who will compete to bind to the resin group on the stationary phase. The selectivity coefficient, the equivalent to the equilibrium constant, is determined via a ratio of the concentrations between the resin and each ion, however, the general trend is that ion exchangers prefer binding to the ion with a higher charge, smaller hydrated radius, and higher polarizability, or the ability for the electron cloud of an ion to be disrupted by other charges. Despite this selectivity, excess amounts of an ion with a lower selectivity introduced to the column would cause the lesser ion to bind more to the stationary phase as the selectivity coefficient allows fluctuations in the binding reaction that takes place during ion exchange chromatography.
Following table shows the commonly used ion exchangers
== Typical technique ==
A sample is introduced, either manually or with an autosampler, into a sample loop of known volume. A buffered aqueous solution known as the mobile phase carries the sample from the loop onto a column that contains some form of stationary phase material. This is typically a resin or gel matrix consisting of agarose or cellulose beads with covalently bonded charged functional groups. Equilibration of the stationary phase is needed in order to obtain the desired charge of the column. If the column is not properly equilibrated the desired molecule may not bind strongly to the column. The target analytes (anions or cations) are retained on the stationary phase but can be eluted by increasing the concentration of a similarly charged species that displaces the analyte ions from the stationary phase. For example, in cation exchange chromatography, the positively charged analyte can be displaced by adding positively charged sodium ions. The analytes of interest must then be detected by some means, typically by conductivity or UV/visible light absorbance.
Control an IC system usually requires a chromatography data system (CDS). In addition to IC systems, some of these CDSs can also control gas chromatography (GC) and HPLC.
== Membrane exchange chromatography ==
A type of ion exchange chromatography, membrane exchange is a relatively new method of purification designed to overcome limitations of using columns packed with beads. Membrane Chromatographic devices are cheap to mass-produce and disposable unlike other chromatography devices that require maintenance and time to revalidate. There are three types of membrane absorbers that are typically used when separating substances. The three types are flat sheet, hollow fibre, and radial flow. The most common absorber and best suited for membrane chromatography is multiple flat sheets because it has more absorbent volume. It can be used to overcome mass transfer limitations and pressure drop, making it especially advantageous for isolating and purifying viruses, plasmid DNA, and other large macromolecules. The column is packed with microporous membranes with internal pores which contain adsorptive moieties that can bind the target protein. Adsorptive membranes are available in a variety of geometries and chemistry which allows them to be used for purification and also fractionation, concentration, and clarification in an efficiency that is 10 fold that of using beads. Membranes can be prepared through isolation of the membrane itself, where membranes are cut into squares and immobilized. A more recent method involved the use of live cells that are attached to a support membrane and are used for identification and clarification of signaling molecules.
== Separating proteins ==
Ion exchange chromatography can be used to separate proteins because they contain charged functional groups. The ions of interest (in this case charged proteins) are exchanged for another ions (usually H+) on a charged solid support. The solutes are most commonly in a liquid phase, which tends to be water. Take for example proteins in water, which would be a liquid phase that is passed through a column. The column is commonly known as the solid phase since it is filled with porous synthetic particles that are of a particular charge. These porous particles are also referred to as beads, may be aminated (containing amino groups) or have metal ions in order to have a charge. The column can be prepared using porous polymers, for macromolecules of a mass of over 100 000 Da, the optimum size of the porous particle is about 1 μm2. This is because slow diffusion of the solutes within the pores does not restrict the separation quality. The beads containing positively charged groups, which attract the negatively charged proteins, are commonly referred to as anion exchange resins. The amino acids that have negatively charged side chains at pH 7 (pH of water) are glutamate and aspartate. The beads that are negatively charged are called cation exchange resins, as positively charged proteins will be attracted. The amino acids that have positively charged side chains at pH 7 are lysine, histidine and arginine.
The isoelectric point is the pH at which a compound - in this case a protein - has no net charge. A protein's isoelectric point or PI can be determined using the pKa of the side chains, if the amino (positive chain) is able to cancel out the carboxyl (negative) chain, the protein would be at its PI. Using buffers instead of water for proteins that do not have a charge at pH 7 is a good idea as it enables the manipulation of pH to alter ionic interactions between the proteins and the beads. Weakly acidic or basic side chains are able to have a charge if the pH is high or low enough respectively. Separation can be achieved based on the natural isoelectric point of the protein. Alternatively a peptide tag can be genetically added to the protein to give the protein an isoelectric point away from most natural proteins (e.g., 6 arginines for binding to a cation-exchange resin or 6 glutamates for binding to an anion-exchange resin such as DEAE-Sepharose).
Elution by increasing ionic strength of the mobile phase is more subtle. It works because ions from the mobile phase interact with the immobilized ions on the stationary phase, thus "shielding" the stationary phase from the protein, and letting the protein elute.
Elution from ion-exchange columns can be sensitive to changes of a single charge- chromatofocusing. Ion-exchange chromatography is also useful in the isolation of specific multimeric protein assemblies, allowing purification of specific complexes according to both the number and the position of charged peptide tags.
=== Gibbs–Donnan effect ===
In ion exchange chromatography, the Gibbs–Donnan effect is observed when the pH of the applied buffer and the ion exchanger differ, even up to one pH unit. For example, in anion-exchange columns, the ion exchangers repeal protons so the pH of the buffer near the column differs is higher than the rest of the solvent. As a result, an experimenter has to be careful that the protein(s) of interest is stable and properly charged in the "actual" pH.
This effect comes as a result of two similarly charged particles, one from the resin and one from the solution, failing to distribute properly between the two sides; there is a selective uptake of one ion over another. For example, in a sulphonated polystyrene resin, a cation exchange resin, the chlorine ion of a hydrochloric acid buffer should equilibrate into the resin. However, since the concentration of the sulphonic acid in the resin is high, the hydrogen of HCl has no tendency to enter the column. This, combined with the need of electroneutrality, leads to a minimum amount of hydrogen and chlorine entering the resin.
== Uses ==
=== Clinical utility ===
A use of ion chromatography can be seen in argentation chromatography. Usually, silver and compounds containing acetylenic and ethylenic bonds have very weak interactions. This phenomenon has been widely tested on olefin compounds. The ion complexes the olefins make with silver ions are weak and made based on the overlapping of pi, sigma, and d orbitals and available electrons therefore cause no real changes in the double bond. This behavior was manipulated to separate lipids, mainly fatty acids from mixtures in to fractions with differing number of double bonds using silver ions. The ion resins were impregnated with silver ions, which were then exposed to various acids (silicic acid) to elute fatty acids of different characteristics.
Detection limits as low as 1 μM can be obtained for alkali metal ions.
It may be used for measurement of HbA1c, porphyrin and with water purification. Ion Exchange Resins(IER) have been widely used especially in medicines due to its high capacity and the uncomplicated system of the separation process. One of the synthetic uses is to use Ion Exchange Resins for kidney dialysis. This method is used to separate the blood elements by using the cellulose membraned artificial kidney.
Another clinical application of ion chromatography is in the rapid anion exchange chromatography technique used to separate creatine kinase (CK) isoenzymes from human serum and tissue sourced in autopsy material (mostly CK rich tissues were used such as cardiac muscle and brain). These isoenzymes include MM, MB, and BB, which all carry out the same function given different amino acid sequences. The functions of these isoenzymes are to convert creatine, using ATP, into phosphocreatine expelling ADP. Mini columns were filled with DEAE-Sephadex A-50 and further eluted with tris- buffer sodium chloride at various concentrations (each concentration was chosen advantageously to manipulate elution). Human tissue extract was inserted in columns for separation. All fractions were analyzed to see total CK activity and it was found that each source of CK isoenzymes had characteristic isoenzymes found within. Firstly, CK- MM was eluted, then CK-MB, followed by CK-BB. Therefore, the isoenzymes found in each sample could be used to identify the source, as they were tissue specific.
Using the information from results, correlation could be made about the diagnosis of patients and the kind of CK isoenzymes found in most abundant activity. From the finding, about 35 out of 71 patients studied suffered from heart attack (myocardial infarction) also contained an abundant amount of the CK-MM and CK-MB isoenzymes. Findings further show that many other diagnosis including renal failure, cerebrovascular disease, and pulmonary disease were only found to have the CK-MM isoenzyme and no other isoenzyme. The results from this study indicate correlations between various diseases and the CK isoenzymes found which confirms previous test results using various techniques. Studies about CK-MB found in heart attack victims have expanded since this study and application of ion chromatography.
=== Industrial applications ===
Since 1975 ion chromatography has been widely used in many branches of industry. The main beneficial advantages are reliability, very good accuracy and precision, high selectivity, high speed, high separation efficiency, and low cost of consumables. The most significant development related to ion chromatography are new sample preparation methods; improving the speed and selectivity of analytes separation; lowering of limits of detection and limits of quantification; extending the scope of applications; development of new standard methods; miniaturization and extending the scope of the analysis of a new group of substances. Allows for quantitative testing of electrolyte and proprietary additives of electroplating baths. It is an advancement of qualitative hull cell testing or less accurate UV testing. Ions, catalysts, brighteners and accelerators can be measured. Ion exchange chromatography has gradually become a widely known, universal technique for the detection of both anionic and cationic species. Applications for such purposes have been developed, or are under development, for a variety of fields of interest, and in particular, the pharmaceutical industry. The usage of ion exchange chromatography in pharmaceuticals has increased in recent years, and in 2006, a chapter on ion exchange chromatography was officially added to the United States Pharmacopia-National Formulary (USP-NF). Furthermore, in 2009 release of the USP-NF, the United States Pharmacopia made several analyses of ion chromatography available using two techniques: conductivity detection, as well as pulse amperometric detection. Majority of these applications are primarily used for measuring and analyzing residual limits in pharmaceuticals, including detecting the limits of oxalate, iodide, sulfate, sulfamate, phosphate, as well as various electrolytes including potassium, and sodium. In total, the 2009 edition of the USP-NF officially released twenty eight methods of detection for the analysis of active compounds, or components of active compounds, using either conductivity detection or pulse amperometric detection.
=== Drug development ===
There has been a growing interest in the application of IC in the analysis of pharmaceutical drugs. IC is used in different aspects of product development and quality control testing. For example, IC is used to improve stabilities and solubility properties of pharmaceutical active drugs molecules as well as used to detect systems that have higher tolerance for organic solvents. IC has been used for the determination of analytes as a part of a dissolution test. For instance, calcium dissolution tests have shown that other ions present in the medium can be well resolved among themselves and also from the calcium ion. Therefore, IC has been employed in drugs in the form of tablets and capsules in order to determine the amount of drug dissolve with time. IC is also widely used for detection and quantification of excipients or inactive ingredients used in pharmaceutical formulations. Detection of sugar and sugar alcohol in such formulations through IC has been done due to these polar groups getting resolved in ion column. IC methodology also established in analysis of impurities in drug substances and products. Impurities or any components that are not part of the drug chemical entity are evaluated and they give insights about the maximum and minimum amounts of drug that should be administered in a patient per day.
== See also ==
Anion-exchange chromatography
Chromatofocusing
High performance liquid chromatography
Isoelectric point
== References ==
== Bibliography ==
Small, Hamish (1989). Ion chromatography. New York: Plenum Press. ISBN 978-0-306-43290-3.
Tatjana Weiss; Weiss, Joachim (2005). Handbook of Ion Chromatography. Weinheim: Wiley-VCH. ISBN 978-3-527-28701-7.
Gjerde, Douglas T.; Fritz, James S. (2000). Ion Chromatography. Weinheim: Wiley-VCH. ISBN 978-3-527-29914-0.
Jackson, Peter; Haddad, Paul R. (1990). Ion chromatography: principles and applications. Amsterdam: Elsevier. ISBN 978-0-444-88232-5.
Mercer, Donald W (1974). "Separation of tissue and serum creatine kinase isoenzymes by ion-exchange column chromatography". Clinical Chemistry. 20 (1): 36–40. doi:10.1093/clinchem/20.1.36. PMID 4809470.
Morris, L. J. (1966). "Separations of lipids by silver ion chromatography". Journal of Lipid Research. 7 (6): 717–732. doi:10.1016/S0022-2275(20)38948-3. PMID 5339485.
Ghosh, Raja (2002). "Protein separation using membrane chromatography: opportunities and challenges". Journal of Chromatography A. 952 (1): 13–27. doi:10.1016/s0021-9673(02)00057-2. PMID 12064524.
== External links ==
Media related to Ion chromatography at Wikimedia Commons | Wikipedia/Ion_chromatography |
Column chromatography in chemistry is a chromatography method used to isolate a single chemical compound from a mixture. Chromatography is able to separate substances based on differential absorption of compounds to the adsorbent; compounds move through the column at different rates, allowing them to be separated into fractions. The technique is widely applicable, as many different adsorbents (normal phase, reversed phase, or otherwise) can be used with a wide range of solvents. The technique can be used on scales from micrograms up to kilograms. The main advantage of column chromatography is the relatively low cost and disposability of the stationary phase used in the process. The latter prevents cross-contamination and stationary phase degradation due to recycling. Column chromatography can be done using gravity to move the solvent, or using compressed gas to push the solvent through the column.
A thin-layer chromatography can show how a mixture of compounds will behave when purified by column chromatography. The separation is first optimised using thin-layer chromatography before performing column chromatography.
== Column preparation ==
A column is prepared by packing a solid adsorbent into a cylindrical glass or plastic tube. The size will depend on the amount of compound being isolated. The base of the tube contains a filter, either a cotton or glass wool plug, or glass frit to hold the solid phase in place. A solvent reservoir may be attached at the top of the column.
Two methods are generally used to prepare a column: the dry method and the wet method. For the dry method, the column is first filled with dry stationary phase powder, followed by the addition of mobile phase, which is flushed through the column until it is completely wet, and from this point is never allowed to run dry. For the wet method, a slurry is prepared of the eluent with the stationary phase powder and then carefully poured into the column. The top of the silica should be flat, and the top of the silica can be protected by a layer of sand. Eluent is slowly passed through the column to advance the organic material.
The individual components are retained by the stationary phase differently and separate from each other while they are running at different speeds through the column with the eluent. At the end of the column they elute one at a time. During the entire chromatography process the eluent is collected in a series of fractions. Fractions can be collected automatically by means of fraction collectors. The productivity of chromatography can be increased by running several columns at a time. In this case multi stream collectors are used. The composition of the eluent flow can be monitored and each fraction is analyzed for dissolved compounds, e.g. by analytical chromatography, UV absorption spectra, or fluorescence. Colored compounds (or fluorescent compounds with the aid of a UV lamp) can be seen through the glass wall as moving bands.
== Stationary phase ==
The stationary phase or adsorbent in column chromatography is a solid. The most common stationary phase for column chromatography is silica gel, the next most common being alumina. Cellulose powder has often been used in the past. A wide range of stationary phases are available in order to perform ion exchange chromatography, reversed-phase chromatography (RP), affinity chromatography or expanded bed adsorption (EBA). The stationary phases are usually finely ground powders or gels and/or are microporous for an increased surface, though in EBA a fluidized bed is used. There is an important ratio between the stationary phase weight and the dry weight of the analyte mixture that can be applied onto the column. For silica column chromatography, this ratio lies within 20:1 to 100:1, depending on how close to each other the analyte components are being eluted.
== Mobile phase (eluent) ==
The mobile phase or eluent is a solvent or a mixture of solvents used to move the compounds through the column. It is chosen so that the retention factor value of the compound of interest is roughly around 0.2 - 0.3 in order to minimize the time and the amount of eluent to run the chromatography. The eluent has also been chosen so that the different compounds can be separated effectively. The eluent is optimized in small scale pretests, often using thin layer chromatography (TLC) with the same stationary phase, using solvents of different polarity until a suitable solvent system is found. Common mobile phase solvents, in order of increasing polarity, include hexane, dichloromethane, ethyl acetate, acetone, and methanol. A common solvent system is a mixture of hexane and ethyl acetate, with proportions adjusted until the target compound has a retention factor of 0.2 - 0.3. Contrary to common misconception, methanol alone can be used as an eluent for highly polar compounds, and does not dissolve silica gel.
There is an optimum flow rate for each particular separation. A faster flow rate of the eluent minimizes the time required to run a column and thereby minimizes diffusion, resulting in a better separation. However, the maximum flow rate is limited because a finite time is required for the analyte to equilibrate between the stationary phase and mobile phase, see Van Deemter's equation. A simple laboratory column runs by gravity flow. The flow rate of such a column can be increased by extending the fresh eluent filled column above the top of the stationary phase or decreased by the tap controls. Faster flow rates can be achieved by using a pump or by using compressed gas (e.g. air, nitrogen, or argon) to push the solvent through the column (flash column chromatography).
The particle size of the stationary phase is generally finer in flash column chromatography than in gravity column chromatography. For example, one of the most widely used silica gel grades in the former technique is mesh 230 – 400 (40 – 63 μm), while the latter technique typically requires mesh 70 – 230 (63 – 200 μm) silica gel.
A spreadsheet that assists in the successful development of flash columns has been developed. The spreadsheet estimates the retention volume and band volume of analytes, the fraction numbers expected to contain each analyte, and the resolution between adjacent peaks. This information allows users to select optimal parameters for preparative-scale separations before the flash column itself is attempted.
== Automated systems ==
Column chromatography is an extremely time-consuming stage in any lab and can quickly become the bottleneck for any process lab. Many manufacturers like Biotage, Buchi, Interchim and Teledyne Isco have developed automated flash chromatography systems (typically referred to as LPLC, low pressure liquid chromatography, around 350–525 kPa or 50.8–76.1 psi) that minimize human involvement in the purification process. Automated systems will include components normally found on more expensive high performance liquid chromatography (HPLC) systems such as a gradient pump, sample injection ports, a UV detector and a fraction collector to collect the eluent. Typically these automated systems can separate samples from a few milligrams up to an industrial many kilogram scale and offer a much cheaper and quicker solution to doing multiple injections on prep-HPLC systems.
The resolution (or the ability to separate a mixture) on an LPLC system will always be lower compared to HPLC, as the packing material in an HPLC column can be much smaller, typically only 5 micrometre thus increasing stationary phase surface area, increasing surface interactions and giving better separation. However, the use of this small packing media causes the high back pressure and is why it is termed high pressure liquid chromatography. The LPLC columns are typically packed with silica of around 50 micrometres, thus reducing back pressure and resolution, but it also removes the need for expensive high pressure pumps. Manufacturers are now starting to move into higher pressure flash chromatography systems and have termed these as medium pressure liquid chromatography (MPLC) systems which operate above 1 MPa (150 psi).
== Column chromatogram resolution calculation ==
Typically, column chromatography is set up with peristaltic pumps, flowing buffers and the solution sample through the top of the column. The solutions and buffers pass through the column where a fraction collector at the end of the column setup collects the eluted samples. Prior to the fraction collection, the samples that are eluted from the column pass through a detector such as a spectrophotometer or mass spectrometer so that the concentration of the separated samples in the sample solution mixture can be determined.
For example, if you were to separate two different proteins with different binding capacities to the column from a solution sample, a good type of detector would be a spectrophotometer using a wavelength of 280 nm. The higher the concentration of protein that passes through the eluted solution through the column, the higher the absorbance of that wavelength.
Because the column chromatography has a constant flow of eluted solution passing through the detector at varying concentrations, the detector must plot the concentration of the eluted sample over a course of time. This plot of sample concentration versus time is called a chromatogram.
The ultimate goal of chromatography is to separate different components from a solution mixture. The resolution expresses the extent of separation between the components from the mixture. The higher the resolution of the chromatogram, the better the extent of separation of the samples the column gives. This data is a good way of determining the column's separation properties of that particular sample. The resolution can be calculated from the chromatogram.
The separate curves in the diagram represent different sample elution concentration profiles over time based on their affinity to the column resin. To calculate resolution, the retention time and curve width are required.
Retention time is the time from the start of signal detection by the detector to the peak height of the elution concentration profile of each different sample.
Curve width is the width of the concentration profile curve of the different samples in the chromatogram in units of time.
A simplified method of calculating chromatogram resolution is to use the plate model. The plate model assumes that the column can be divided into a certain number of sections, or plates and the mass balance can be calculated for each individual plate. This approach approximates a typical chromatogram curve as a Gaussian distribution curve. By doing this, the curve width is estimated as 4 times the standard deviation of the curve, 4σ. The retention time is the time from the start of signal detection to the time of the peak height of the Gaussian curve.
From the variables in the figure above, the resolution, plate number, and plate height of the column plate model can be calculated using the equations:
Resolution (Rs):
Rs = 2(tRB – tRA)/(wB + wA),
where:
tRB = retention time of solute B
tRA = retention time of solute A
wB = Gaussian curve width of solute B
wA = Gaussian curve width of solute A
Plate Number (N):
N = (tR)2/(w/4)2
Plate Height (H):
H = L/N
where L is the length of the column.
== Column adsorption equilibrium ==
For an adsorption column, the column resin (the stationary phase) is composed of microbeads. Even smaller particles such as proteins, carbohydrates, metal ions, or other chemical compounds are conjugated onto the microbeads. Each binding particle that is attached to the microbead can be assumed to bind in a 1:1 ratio with the solute sample sent through the column that needs to be purified or separated.
Binding between the target molecule to be separated and the binding molecule on the column beads can be modeled using a simple equilibrium reaction Keq = [CS]/([C][S]) where Keq is the equilibrium constant, [C] and [S] are the concentrations of the target molecule and the binding molecule on the column resin, respectively. [CS] is the concentration of the complex of the target molecule bound to the column resin.
Using this as a basis, three different isotherms can be used to describe the binding dynamics of a column chromatography: linear, Langmuir, and Freundlich.
The linear isotherm occurs when the solute concentration needed to be purified is very small relative to the binding molecule. Thus, the equilibrium can be defined as:
[CS] = Keq[C].
For industrial scale uses, the total binding molecules on the column resin beads must be factored in because unoccupied sites must be taken into account. The Langmuir isotherm and Freundlich isotherm are useful in describing this equilibrium. The Langmuir isotherm is given by:
[CS] = (KeqStot[C])/(1 + Keq[C]), where Stot is the total binding molecules on the beads.
The Freundlich isotherm is given by:
[CS] = Keq[C]1/n
The Freundlich isotherm is used when the column can bind to many different samples in the solution that needs to be purified. Because the many different samples have different binding constants to the beads, there are many different Keqs. Therefore, the Langmuir isotherm is not a good model for binding in this case.
== See also ==
Fast protein liquid chromatography (FPLC) – separation of proteins using column chromatography
High-performance liquid chromatography (HPLC) – column chromatography using high pressure
== References ==
== External links ==
Flash Column Chromatography Guide (pdf)
Radial Flow Chromatography | Wikipedia/Column_chromatography |
Solvations describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the solute, including solubility, reactivity, and color, as well as influencing the properties of the solvent such as its viscosity and density. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. The surrounded solute particles then move away from the solid solute and out into the solution. Ions are surrounded by a concentric shell of solvent. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes and involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a solute by water is called hydration.
Solubility of solid compounds depends on a competition between lattice energy and solvation, including entropy effects related to changes in the solvent structure.
== Distinction from solubility ==
By an IUPAC definition, solvation is an interaction of a solute with the solvent, which leads to stabilization of the solute species in the solution. In the solvated state, an ion or molecule in a solution is surrounded or complexed by solvent molecules. Solvated species can often be described by coordination number, and the complex stability constants. The concept of the solvation interaction can also be applied to an insoluble material, for example, solvation of functional groups on a surface of ion-exchange resin.
Solvation is, in concept, distinct from solubility. Solvation or dissolution is a kinetic process and is quantified by its rate. Solubility quantifies the dynamic equilibrium state achieved when the rate of dissolution equals the rate of precipitation. The consideration of the units makes the distinction clearer. The typical unit for dissolution rate is mol/s. The units for solubility express a concentration: mass per volume (mg/mL), molarity (mol/L), etc.
== Solvents and intermolecular interactions ==
Solvation involves different types of intermolecular interactions:
Hydrogen bonding
Ion–dipole interactions
The van der Waals forces, which consist of dipole–dipole, dipole–induced dipole, and induced dipole–induced dipole interactions.
Which of these forces are at play depends on the molecular structure and properties of the solvent and solute. The similarity or complementary character of these properties between solvent and solute determines how well a solute can be solvated by a particular solvent.
Solvent polarity is the most important factor in determining how well it solvates a particular solute. Polar solvents have molecular dipoles, meaning that part of the solvent molecule has more electron density than another part of the molecule. The part with more electron density will experience a partial negative charge while the part with less electron density will experience a partial positive charge. Polar solvent molecules can solvate polar solutes and ions because they can orient the appropriate partially charged portion of the molecule towards the solute through electrostatic attraction. This stabilizes the system and creates a solvation shell (or hydration shell in the case of water) around each particle of solute. The solvent molecules in the immediate vicinity of a solute particle often have a much different ordering than the rest of the solvent, and this area of differently ordered solvent molecules is called the cybotactic region. Water is the most common and well-studied polar solvent, but others exist, such as ethanol, methanol, acetone, acetonitrile, and dimethyl sulfoxide. Polar solvents are often found to have a high dielectric constant, although other solvent scales are also used to classify solvent polarity. Polar solvents can be used to dissolve inorganic or ionic compounds such as salts. The conductivity of a solution depends on the solvation of its ions. Nonpolar solvents cannot solvate ions, and ions will be found as ion pairs.
Hydrogen bonding among solvent and solute molecules depends on the ability of each to accept H-bonds, donate H-bonds, or both. Solvents that can donate H-bonds are referred to as protic, while solvents that do not contain a polarized bond to a hydrogen atom and cannot donate a hydrogen bond are called aprotic. H-bond donor ability is classified on a scale (α). Protic solvents can solvate solutes that can accept hydrogen bonds. Similarly, solvents that can accept a hydrogen bond can solvate H-bond-donating solutes. The hydrogen bond acceptor ability of a solvent is classified on a scale (β). Solvents such as water can both donate and accept hydrogen bonds, making them excellent at solvating solutes that can donate or accept (or both) H-bonds.
Some chemical compounds experience solvatochromism, which is a change in color due to solvent polarity. This phenomenon illustrates how different solvents interact differently with the same solute. Other solvent effects include conformational or isomeric preferences and changes in the acidity of a solute.
== Solvation energy and thermodynamic considerations ==
The solvation process will be thermodynamically favored only if the overall Gibbs energy of the solution is decreased, compared to the Gibbs energy of the separated solvent and solid (or gas or liquid). This means that the change in enthalpy minus the change in entropy (multiplied by the absolute temperature) is a negative value, or that the Gibbs energy of the system decreases. A negative Gibbs energy indicates a spontaneous process but does not provide information about the rate of dissolution.
Solvation involves multiple steps with different energy consequences. First, a cavity must form in the solvent to make space for a solute. This is both entropically and enthalpically unfavorable, as solvent ordering increases and solvent-solvent interactions decrease. Stronger interactions among solvent molecules leads to a greater enthalpic penalty for cavity formation. Next, a particle of solute must separate from the bulk. This is enthalpically unfavorable since solute-solute interactions decrease, but when the solute particle enters the cavity, the resulting solvent-solute interactions are enthalpically favorable. Finally, as solute mixes into solvent, there is an entropy gain.
The enthalpy of solution is the solution enthalpy minus the enthalpy of the separate systems, whereas the entropy of solution is the corresponding difference in entropy. The solvation energy (change in Gibbs free energy) is the change in enthalpy minus the product of temperature (in Kelvin) times the change in entropy. Gases have a negative entropy of solution, due to the decrease in gaseous volume as gas dissolves. Since their enthalpy of solution does not decrease too much with temperature, and their entropy of solution is negative and does not vary appreciably with temperature, most gases are less soluble at higher temperatures.
Enthalpy of solvation can help explain why solvation occurs with some ionic lattices but not with others. The difference in energy between that which is necessary to release an ion from its lattice and the energy given off when it combines with a solvent molecule is called the enthalpy change of solution. A negative value for the enthalpy change of solution corresponds to an ion that is likely to dissolve, whereas a high positive value means that solvation will not occur. It is possible that an ion will dissolve even if it has a positive enthalpy value. The extra energy required comes from the increase in entropy that results when the ion dissolves. The introduction of entropy makes it harder to determine by calculation alone whether a substance will dissolve or not. A quantitative measure for solvation power of solvents is given by donor numbers.
Although early thinking was that a higher ratio of a cation's ion charge to ionic radius, or the charge density, resulted in more solvation, this does not stand up to scrutiny for ions like iron(III) or lanthanides and actinides, which are readily hydrolyzed to form insoluble (hydrous) oxides. As these are solids, it is apparent that they are not solvated.
Strong solvent–solute interactions make the process of solvation more favorable. One way to compare how favorable the dissolution of a solute is in different solvents is to consider the free energy of transfer. The free energy of transfer quantifies the free energy difference between dilute solutions of a solute in two different solvents. This value essentially allows for comparison of solvation energies without including solute-solute interactions.
In general, thermodynamic analysis of solutions is done by modeling them as reactions. For example, if you add sodium chloride to water, the salt will dissociate into the ions sodium(+aq) and chloride(-aq). The equilibrium constant for this dissociation can be predicted by the change in Gibbs energy of this reaction.
The Born equation is used to estimate Gibbs free energy of solvation of a gaseous ion.
Recent simulation studies have shown that the variation in solvation energy between the ions and the surrounding water molecules underlies the mechanism of the Hofmeister series.
== Macromolecules and assemblies ==
Solvation (specifically, hydration) is important for many biological structures and processes. For instance, solvation of ions and/or of charged macromolecules, like DNA and proteins, in aqueous solutions influences the formation of heterogeneous assemblies, which may be responsible for biological function. As another example, protein folding occurs spontaneously, in part because of a favorable change in the interactions between the protein and the surrounding water molecules. Folded proteins are stabilized by 5-10 kcal/mol relative to the unfolded state due to a combination of solvation and the stronger intramolecular interactions in the folded protein structure, including hydrogen bonding. Minimizing the number of hydrophobic side chains exposed to water by burying them in the center of a folded protein is a driving force related to solvation.
Solvation also affects host–guest complexation. Many host molecules have a hydrophobic pore that readily encapsulates a hydrophobic guest. These interactions can be used in applications such as drug delivery, such that a hydrophobic drug molecule can be delivered in a biological system without needing to covalently modify the drug in order to solubilize it. Binding constants for host–guest complexes depend on the polarity of the solvent.
Hydration affects electronic and vibrational properties of biomolecules.
== Importance of solvation in computer simulations ==
Due to the importance of the effects of solvation on the structure of macromolecules, early computer simulations which attempted to model their behaviors without including the effects of solvent (in vacuo) could yield poor results when compared with experimental data obtained in solution. Small molecules may also adopt more compact conformations when simulated in vacuo; this is due to favorable van der Waals interactions and intramolecular electrostatic interactions which would be dampened in the presence of a solvent.
As computer power increased, it became possible to try and incorporate the effects of solvation within a simulation and the simplest way to do this is to surround the molecule being simulated with a "skin" of solvent molecules, akin to simulating the molecule within a drop of solvent if the skin is sufficiently deep.
== See also ==
== References ==
== Further reading ==
Dogonadze, Revaz; et al., eds. (1985–88). The Chemical Physics of Solvation (3 vol. ed.). Amsterdam: Elsevier. ISBN 0-444-42551-9 (part A), ISBN 0-444-42674-4 (part B), ISBN 0-444-42984-0 (Chemistry).
Jiang D.; Urakawa A.; Yulikov M.; Mallat T.; Jeschke G.; Baiker A. (2009). "Size selectivity of a copper metal-organic framework and origin of catalytic activity in epoxide alcoholysis". Chemistry: A European Journal. 15 (45): 12255–62. doi:10.1002/chem.200901510. PMID 19806616. One example of a solvated MOF, where partial dissolution is described.
Serafin, J.M. (October 2003). "Transfer Free Energy and the Hydrophobic Effect". J. Chem. Educ. 80 (10): 1194–1196. Bibcode:2003JChEd..80.1194S. doi:10.1021/ed080p1194.
== External links == | Wikipedia/Dissolution_(chemistry) |
Clinical pathology is a medical specialty that is concerned with the diagnosis of disease based on the laboratory analysis of bodily fluids, such as blood, urine, and tissue homogenates or extracts using the tools of chemistry, microbiology, hematology, molecular pathology, and Immunohaematology. This specialty requires a medical residency.
Clinical pathology is a term used in the US, UK, Ireland, many Commonwealth countries, Portugal, Brazil, Italy, Japan, and Peru; countries using the equivalent in the home language of "laboratory medicine" include Austria, Germany, Romania, Poland and other Eastern European countries; other terms are "clinical analysis" (Spain) and "clinical/medical biology (France, Belgium, Netherlands, North and West Africa).
== Licensing and subspecialities ==
The American Board of Pathology certifies clinical pathologists, and recognizes the following secondary specialties of clinical pathology:
Chemical pathology, also called clinical chemistry
Hematopathology
Blood banking - Transfusion medicine
Clinical microbiology
Cytogenetics
Molecular genetics pathology.
In some countries other sub specialities fall under certified Clinical Biologists responsibility:
Reproductive biology including Assisted reproductive technology, Sperm bank and Semen analysis
Immunopathology
== Organization ==
Clinical pathologists are often medical doctors. In some countries in South America, Europe, Africa or Asia, this specialty can be practiced by non-physicians, such as Ph.D. or Pharm.D. after a variable number of years of residency.
=== In the United States ===
Clinical pathologists work in close collaboration with clinical scientists (clinical biochemists, clinical microbiologists, etc.), medical technologists, hospital administrators, and referring physicians to ensure the accuracy and optimal utilization of laboratory testing.
Clinical pathology is one of the two major divisions of pathology, the other being anatomical pathology. Often, pathologists practice both anatomical and clinical pathology, a combination sometimes known as general pathology. Similar specialties exist in veterinary pathology.
Clinical pathology is itself divided into subspecialties, the main ones being clinical chemistry, clinical hematology/blood banking, hematopathology and clinical microbiology and emerging subspecialties such as molecular diagnostics and proteomics. Many areas of clinical pathology overlap with anatomic pathology. Both can serve as medical directors of CLIA certified laboratories. Under the CLIA law, only the US Department of Health and Human Services approved Board Certified Ph.D., DSc, or MD and DO can perform the duties of a Medical or Clinical Laboratory Director. This overlap includes immunoassays, flow cytometry, microbiology and cytogenetics and any assay done on tissue. Overlap between anatomic and clinical pathology is expanding to molecular diagnostics and proteomics as we move towards making the best use of new technologies for personalized medicine.
Clinical pathologists may assist physicians in interpreting complex tests such as platelet aggregometry, hemoglobin or serum protein electrophoresis, or coagulation profiles. If interfering substances are suspected, they may recommend alternate test methods. For example, hemolysis, icterus, lipemia, or heterophile antibodies may confound results obtained by traditional methods such as ion-selective electrodes, enzymatic assays or immunoassays. Alternate methods such as blood gas analysers, point-of-care testing or mass spectrometry may help resolve the clinical question.
=== In Europe ===
Recently, EFLM has chosen the name of "Specialists in Laboratory Medicine" to define all European Clinical pathologists, regardless of their training (M.D., Ph.D. or Pharm.D.).
In France, Clinical Pathology is called Medical Biology ("Biologie médicale") and is practiced by both M.D.s and Pharm.D.s. The residency lasts four years. Specialists in this discipline are called "Biologiste médical" which literally translates as Clinical Biologist rather than "Clinical pathologist".
== Tools ==
Tangible tools include microscopes, analyzers, strips, and centrifuges.
=== Macroscopic examination ===
Visual examination of the specimen may provide information to the pathologist or the physician. For example, fluid drained from an abscess may appear cloudy, or cerebrospinal fluid obtained by lumbar puncture may exhibit xanthochromia, suggesting a bleed has occurred. Laboratory technologists may provide qualitative descriptions accordingly.
=== Microscopical examination ===
Microscopic analysis is an important activity of the pathologist and the laboratory technologist. They have many different stains at their disposal (GRAM, MGG, Grocott, Ziehl–Neelsen, etc.). Immunofluorescence, cytochemistry, the immunocytochemistry, and FISH are also used in order make a correct diagnosis.
Pathologists may review samples such as pleural, peritoneal, synovial, or pericardial fluids to characterize them as "normal", tumoral, inflammatory, or even infectious. Microscopic examination can also determine the causal infectious agent – often a bacterium, mould, yeast, parasite, or (rarely) virus.
=== Laboratory Analysers ===
Automated analysers, by the association of robotics and spectrophotometry, have allowed these last decades better reproducibility of the results, in particular in medical biochemistry and hematology.
Efficiency and productivity can be enhanced by automating the pre-analytical processing, including barcode reading, sorting, centrifuging, and aliquoting specimens.
The analysers must undergo daily controls prior to performing patient testing. Analysers must also undergo daily, weekly and monthly maintenance. Quality management involves reviewing quality control trends to detect emerging problems in instrument calibration, correlating results between instruments that perform similar testing, and running standardized samples to prove linearity and precision.
Some laboratory processes involve automated analysis combined with manual review by technologists. For example, when hematology analysers flag samples as abnormal, automated white blood cell differential counts may be superseded by manual differential counts using stained slides read at the microscope or scanned by digital imaging software. Laboratory technologists may flag abnormal samples for pathologist review. The pathologist may recommend additional testing, such as flow cytometry to identify lymphoma or leukemia cells, or cytology to characterize solid tumor cells.
=== Cultures ===
Samples undergoing examination for pathogens, primarily in medical microbiology, may be incubated with culture media. Those allow, for example, the description of one or several infectious agents responsible of the clinical signs.
=== Values known as "normal" or reference values ===
A reference range in medicine is the range or the interval of values that is deemed normal for a physiological measurement in healthy persons (for example, the amount of creatinine in the blood, or the partial pressure of oxygen). It is a basis for comparison for a physician or other health professional to interpret a set of test results for a particular patient. Some important reference ranges in medicine are reference ranges for blood tests and reference ranges for urine tests.
== See also ==
== Notes and references ==
== External links ==
American Association for Clinical Chemistry
American Society for Clinical Pathology
American Board of Pathology
College of American Pathologists
European Federation of Clinical Chemistry and Laboratory Medicine
Academy of Clinical Laboratory Physicians and Scientists | Wikipedia/Clinical_pathology |
Paper chromatography is an analytical method used to separate colored chemicals or substances. It can also be used for colorless chemicals that can be located by a stain or other visualisation method after separation. It is now primarily used as a teaching tool, having been replaced in the laboratory by other chromatography methods such as thin-layer chromatography (TLC).
This analytic method has three components, a mobile phase, stationary phase and a support medium (the paper). The mobile phase is generally a non-polar organic solvent in which the sample is dissolved. The stationary phase consists of (polar) water molecules that were incorporated into the paper when it was manufactured. The mobile phase travels up the stationary phase by capillary action, carrying the sample with it. The difference between TLC and paper chromatography is that the stationary phase in TLC is a layer of adsorbent (usually silica gel, or aluminium oxide), and the stationary phase in paper chromatography is less absorbent paper.
A paper chromatography variant, two-dimensional chromatography, involves using two solvents and rotating the paper 90° in between. This is useful for separating complex mixtures of compounds having similar polarity, for example, amino acids.
== Rƒ value, solutes, and solvents ==
The retention factor (Rƒ) may be defined as the ratio of the distance travelled by the solute to the distance travelled by the solvent. It is used in chromatography to quantify the amount of retardation of a sample in a stationary phase relative to a mobile phase. Rƒ values are usually expressed as a fraction of two decimal places.
If Rƒ value of a solution is zero, the solute remains in the stationary phase and thus it is immobile.
If Rƒ value = 1 then the solute has no affinity for the stationary phase and travels with the solvent front.
For example, if a compound travels 9.9 cm and the solvent front travels 12.7 cm, the Rƒ value = (9.9/12.7) = 0.779 or 0.78. Rƒ value depends on temperature and the solvent used in experiment, so several solvents offer several Rƒ values for the same mixture of compound. A solvent in chromatography is the liquid the paper is placed in, and the solute is the ink which is being separated.
== Pigments and polarity ==
Paper chromatography is one method for testing the purity of compounds and identifying substances. Paper chromatography is a useful technique because it is relatively quick and requires only small quantities of material. Separations in paper chromatography involve the principle of partition. In paper chromatography, substances are distributed between a stationary phase and a mobile phase. The stationary phase is the water trapped between the cellulose fibers of the paper. The mobile phase is a developing solution that travels up the stationary phase, carrying the samples with it. Components of the sample will separate readily according to how strongly they adsorb onto the stationary phase versus how readily they dissolve in the mobile phase.
When a colored chemical sample is placed on a filter paper, the colors separate from the sample by placing one end of the paper in a solvent. The solvent diffuses up the paper, dissolving the various molecules in the sample according to the polarities of the molecules and the solvent. If the sample contains more than one color, that means it must have more than one kind of molecule. Because of the different chemical structures of each kind of molecule, the chances are very high that each molecule will have at least a slightly different polarity, giving each molecule a different solubility in the solvent. The unequal solubility causes the various color molecules to leave solution at different places as the solvent continues to move up the paper. The more soluble a molecule is, the higher it will migrate up the paper. If a chemical is very non-polar it will not dissolve at all in a very polar solvent. This is the same for a very polar chemical and a very non-polar solvent.
When using water (a very polar substance) as a solvent, the more polar the color, the higher it will rise on the papers.
== Types ==
=== Descending ===
Development of the chromatogram is done by allowing the solvent to travel down the paper. Here, the mobile phase is placed in a solvent holder at the top. The spot is kept at the top and solvent flows down the paper from above.
=== Ascending ===
Here the solvent travels up the chromatographic paper. Both descending and ascending paper chromatography are used for the separation of organic and inorganic substances.
The sample and solvent move upward.
=== The ascending and descending method ===
This is the hybrid of both of the above techniques. The upper part of ascending chromatography can be folded over a rod in order to allow the paper to become descending after crossing the rod.
=== Circular chromatography ===
A circular filter paper is taken and the sample is deposited at the center of the paper. After drying the spot, the filter paper is tied horizontally on a Petri dish containing solvent, so that the wick of the paper is dipped in the solvent. The solvent rises through the wick and the components are separated into concentric rings.
=== Two-dimensional ===
In this technique a square or rectangular paper is used. Here the sample is applied to one of the corners and development is performed at a right angle to the direction of the first run.
== History of paper chromatography ==
The discovery of paper chromatography in 1943 by Martin and Synge provided, for the first time, the means of surveying constituents of plants and for their separation and identification. Erwin Chargaff credits in Weintraub's history of the man the 1944 article by Consden, Gordon and Martin. There was an explosion of activity in this field after 1945.
== References ==
== Bibliography ==
Block, Richard J.; Durrum, Emmett L.; Zweig, Gunter (1955). A Manual of Paper Chromatography and Paper Electrophoresis. Elsevier. p. 4. ISBN 978-1-4832-7680-9 – via Google Books. {{cite book}}: ISBN / Date incompatibility (help) | Wikipedia/Paper_chromatography |
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