Notes on Brownian Coagulation
2006, v.12, №2, 407-412
This lecture discusses the derivation of Smoluchowski's coagulation equation as the large-particle-number limit for a system of Brownian particles, in three dimensions, which coagulate on collision. Smoluchowski [Drei vortrageuber diffusion, brownsche bewegung und koagulation von kolloidteilchen. Phys. Zeitschr., 1916, v.17, 557-559] proposed the kernel $K$, given below, for the rate of coagulation of Brownian particles in 1916. We show in [Brownian coagulation, in preparation] that the kernel and coagulation equation can be arrived at rigorously starting from the natural probabilistic model of finitely many Brownian motions which coagulate on collision. The following account inevitably omits many details and is intended only to describe the problem and give a flavour of the arguments.
Keywords: coagulation,Smoluchowski's equation,Brownian motion