Time-scale separations and the validity of the Smoluchowski, Fokker-Planck and Langevin equations as applied to concentrated particle suspensions

Abstract

In order to derive the Smoluchowski, Fokker-Planck and Langevin equations, that so often form the starting point for theoretical work on the properties of suspensions of brownian particles, it is necessary to assume time-scale separations between the decay times of correlation functions of the particles' positions, those of their momenta and those of the fluid forces acting on them. We re-examine whether these assumptions can be justified for a normal, experimental set-up, and we conclude that for concentrated suspensions, where the volume fraction of brownian particles is not negligible, there are good reasons for thinking that in fact the assumptions are not necessarily valid. We finally briefly indicate how one might set about deriving more complex but hopefully better justified equations to treat such systems.