docs/examples.md

# Numerical examples

The 17 cases bundled with LAMPSUI come from Moreno et al., *Comput. Phys.
Commun.* 2026. Plus a `test_100` smoke test that's example 01 with
`prodRun=100`, `preRun=0` for fast iteration.

| Folder | What it studies | Validation type |
|--------|-----------------|-----------------|
| `01_Young-laplace` | Surface tension via the pressure jump across a droplet (Δp = σ/r in 2D) | Static |
| `02_stretched_droplet` | Retraction of a stretched droplet — surface tension drives return to spherical | Static |
| `03_Static_contact_angle` | Contact angle between droplet and solid wall | Static |
| `04_Triple_contact_angle` | Three-phase contact between three different droplets | Static |
| `05_Poiseuille_one_phase` | Pressure-driven flow in a channel, single phase | Dynamic |
| `06_Reverse_Poiseuille_one_phase` | Reverse Poiseuille (force-driven, no fixed walls) | Dynamic |
| `07_flow_around_cylinder` | 2D flow past an obstacle — drag/lift | Dynamic |
| `08_Poiseuille_two_phases` | Two-phase Poiseuille flow | Dynamic |
| `09_Taylor_Def_vs_Capillary` | Droplet deformation as a function of capillary number | Dynamic |
| `10_Droplet_break-up` | When a droplet shears apart in extensional flow | Dynamic |
| `11_Thixotropic_channel` | Single-phase thixotropic shear flow in a channel | Thixotropic |
| `12_LLPS` | Liquid–liquid phase separation from a random initial state | Exploratory |
| `13_Poiseuille_two_phases_thixotropic` | Two-phase Poiseuille with one phase thixotropic | Exploratory |
| `14_Emulsion_thixotropic_fluid` | Emulsion: thixotropic continuous phase, Newtonian droplets | Exploratory |
| `15_Emulsion_thixotropic_droplets` | Emulsion: Newtonian continuous phase, thixotropic droplets | Exploratory |
| `16_Constricted_channel` | Droplet dynamics in a periodically constricted channel | Exploratory |
| `17_Droplet_merging` | Droplet merging using micro-devices | Exploratory |
| `test_100` | Smoke test: `prodRun=100`, `preRun=0` cloned from `01_Young-laplace` | Use for first-time UI checks |

## Picking an example

| If the user wants… | Use |
|---|---|
| The fastest possible run to verify the install | `test_100` |
| A surface-tension validation | `01_Young-laplace` |
| A pressure-driven flow benchmark | `05_Poiseuille_one_phase` |
| A multiphase emulsion | `14_Emulsion_thixotropic_fluid` or `15_Emulsion_thixotropic_droplets` |
| A thixotropy-only study (no second phase) | `11_Thixotropic_channel` |
| Random initial dispersion | `12_LLPS` |
| Droplet break-up under shear | `09_Taylor_Def_vs_Capillary` or `10_Droplet_break-up` |

## Cost estimates

Single-rank, on a workstation (16-core, 22500 atoms, `dh=0.2`):

- `prodRun=100`: ~10 s
- `prodRun=5 000`: ~5 min
- `prodRun=250 000` (full case 01): ~5 h

On HF Free Spaces (2 vCPU): roughly 8× slower — so `prodRun ≤ 5 000` is
practical for live demos.