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 et al., 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. © 2003 American Institute of Physics. @DOI: 10.1063/1.1564824#