Estimation of hydrodynamic diffusivity in monodisperse sedimentation process by regularization method

Abstract

Successful design of sedimentation process in practice or in the laboratory requires knowledge of the sedimentation velocity of the particles over the relevant range of volume fractions and the role of interparticle forces in determining the structure of the volume fraction distribution. To analyze this settling process precisely, we have to express diffusion coefficient among others, as a function of volume fraction. In monodisperse sedimentation process, the volume fraction profile of the particles is governed by the self-sharpening effect of hindered settling, hydrodynamic diffusion by velocity fluctuation and distribution of the particle size. The process can be modeled by the equation of mass conservation in terms of volume fraction of the particles. This equation includes both self-sharpening effect which narrows interface and velocity fluctuation effect which broadens interface. Asymptotic solution of the model was derived under the assumption of fully developed volume fraction profile at large time. The volume fraction data in the interfacial region were measured using NMR-CT technique. Assuming that the hindered velocity was known, the hydrodynamic diffusivity was estimated by regularization and spline approximation method, and the effect of the regularization on the estimation was demonstrated. The estimated diffusivity has the maximum values appearing around c = 0.05 ~ 0.07 that is consistent with previous works (Davis and Hassen, 1988, Ham and Homsy, 1988). But the diffusivity values were larger by a factor of 5 since the self-sharpening effect is considered in this study.