Coupled Burgers equations: A model of polydispersive sedimentation

This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss noninteracting (apart from hydrodynamic interaction) 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 bidispersive system of two coupled Burgers equations has rich dynamics. The study of a polydispersive case reveals a continuous ``renormalization'' of the polydispersity. We compare the Burgers system evolution with the experimental results on monodispersive and polydispersive sedimentation.