The Four Stages (Build in Order)

Stage 1 — Baseline (Build First): Tier 0 (erosion ∝ drop-mass flux) + Noyes-Whitney dissolution with single global k. Validate against pilot mass-vs-time. Benchark: ±2% of wet-weighing repeatability.

Stage 2 — Tier 1 + Geometry: Add √U velocity weighting, cos(θ), self-shadowing, k ∝ √(local flow). Benchark: sprayed face faster, shadowed preserved, film-region volume → quadratic decay.

Stage 3 — Heterogeneity: Per-region c_s/k for marbled colors (2-3 classes). Calibrate from visible recession rates. High-value, cheap.

Stage 4 — Tier 2 Gel (Only If Justified): Two-state gel only after film-only and spray-off experiments. Build only if Tier 1 leaves structured residuals.

What NOT to Build

Navier-Stokes/VOF drop-impact solver: Millions of core-hours, zero benefit
Full shallow-water film solver: High effort, second-order effect. Use wetness map.
Gel viscoelastic rheology: Fascinating, impossible to calibrate with your data
Thermal-field solving: Bar small, thermalizes fast. Temperature → c_s(T), a scalar.
Natural-convection CFD: Negligible on sprayed face.

Priority Measurements

240 fps video: Confirm drop velocity and size (sets We, Re, √U slope)
Flux field mapping: Your single largest error source (dye test or thermal)
Runoff temperature: Estimate c_s(T)
Film-only control: Isolates dissolution from impacts

The golden rule: The measured flux field is the most critical input. Everything scales off it. If your flux map is wrong, no fancy physics saves your simulation. Get the flux right, and Tier 1 + Noyes-Whitney captures most of the signal.

Soap Physics

Physics of Soap Erosion

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