☕ 2D Coffee-Ring Effect: Evaporating Droplet, Capillary Outflow, Contact-Line Pinning and Marangoni Flow Lab

A pinned evaporating droplet: Hu-Larson diffusion-limited evaporation, the Deegan flux divergence, outflow computed from mass conservation, a Marangoni depth profile and Brownian tracer particles, with pinned, receding and stick-slip contact lines and seven in-page numerical checks.