Coupled Burgers equations: A model of polydispersive sedimentation

Abstract

This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The velocity of sedimentation (or creaming) depends upon the volume fraction of the constituting particles and leads to Burgers-like equations for concentration profiles. It is shown that even the bi-dispersive system of two coupled Burgers equations has rich dynamics. The study of polydispersive case reveals a continuous ``renormalization'' of the polydispersity. We compare the Burgers system evolution with the experimental results on mono- and polydispersive sedimentation. The influence of thermal fluctuations is briefly discussed.Comment: 35 pages, PHYZZX.TEX, six figures upon request (please enclose your postal address