🫧 Foam Drainage — Plateau Borders & Laplace Pressure

Each polygon is a bubble in a 2D Voronoi foam generated from randomly placed seed points. Its fill colour encodes water content (darker and less saturated when dry, brighter cyan/blue when wet), the border thickness also grows with water content to suggest a thicker film, and small glowing dots at each vertex mark the Plateau borders where three films meet.

Every bubble gets a Laplace pressure P = γ/r from its surface tension γ and effective radius r — smaller bubbles have higher pressure. For every pair of neighbouring bubbles the flow is Q = κ·(P_i − P_j)·Δt, moving water from the higher-pressure (smaller) bubble to the lower-pressure (larger) one each frame, on top of a small constant gravity term that drains liquid toward the bottom of the canvas.

The model estimates a film-thickness proxy between each pair of neighbours from their combined water content divided by the distance between their centres. When that value drops below the Critical film h_crit slider, the shared film is treated as ruptured and the two bubbles are merged into one larger cell with combined area and water — visually this is foam coarsening, the same process by which real bubbles disappear and neighbours grow.

Surface tension γ scales every bubble's Laplace pressure, so higher γ produces stronger pressure gradients and faster flow. Drainage rate κ is a direct multiplier on the flow between neighbours, so it speeds up or slows down the whole simulation. Critical film h_crit sets the rupture threshold — raise it and films rupture (and bubbles merge) far more readily, producing a drier, more chaotic foam.

No — it is a simplified, qualitatively faithful model built for intuition rather than a full solution of the foam drainage equation or real 3D Plateau border geometry. The Voronoi cells approximate bubble shapes, radius and water content are proxies for true curvature and film thickness, and the pairwise flow/rupture rules capture the right trends (drainage from small to large bubbles, coarsening via rupture) without solving the underlying continuum equations exactly.