Colloidal Coagulation Kinetics 2D — Population Balance

Colloidal particles stay dispersed only as long as an electrostatic energy barrier keeps them apart. Rather than animating a 3D box of colliding spheres, this 2D-native version integrates the actual discrete Smoluchowski population-balance equation: every cluster size from 1 monomer up carries its own population count, and the full size-class histogram evolves frame by frame under the real size-dependent Brownian coagulation kernel, scaled down by the Fuchs/DLVO stability ratio. A second panel tracks the running total particle count against the closed-form mean-field decay curve the theory predicts from the current instant, so you can watch the simulation trace — or depart from — the textbook hyperbolic Smoluchowski decay in real time. Raise the electrolyte concentration past the simulated critical coagulation concentration and watch the whole population collapse from a slow, barrier-limited crawl into fast, diffusion-limited aggregation.