Diffusivities and front propagation in sedimentation

Continuum models for particles sedimenting in a fluid often assume that the diffusivity is a local function of the particulate volume fraction. Since the hydrodynamically induced diffusivity is a result of the velocity fluctuations of particles, the recent identification [e.g., Tee , Phys. Rev. Lett. 89, 054501 (2002)] of particle density stratification as a controlling parameter for the velocity fluctuations also extends to the diffusivities. In particular, the stratification control strongly affects the diffusivity in the vicinity of the falling sediment front between particle-laden fluid below and clarified fluid above. The resulting scaling for stratification-controlled diffusivities in creeping flow sedimentation is presented and compares favorably with measurements from dilute-limit particle simulations. Steadily falling concentration profiles for dilute sedimentation with these diffusivities are then presented, and an extension of the model to higher volume fractions is discussed. (C) 2003 American Institute of Physics.