The rate of absorption of Brownian particles by a sphere

Abstract

We consider the solution of the Fokker–Planck equation for the case where a uniform dilute system of Brownian particles filling the volume r≳R is absorbed at the boundary r=R for times t≳0. An approximate solution is obtained for this time-dependent problem by using the lowest order terms in a half-range moment expansion of the Brownian particle distribution function. The solution obtained is used to examine the validity of Fick’s law and to find the rate coefficient for the absorption process. This latter result is compared with the result found using the diffusion equation solution together with Fick’s law. We find that the rate coefficient can be substantially smaller than the result predicted by the diffusion equation; this conclusion is in general agreement with earlier results for a related steady-state problem.