Evolution of fluctuations in a suspension sedimenting in a container bounded by horizontal walls

Abstract

Evolution of linear large-scale disturbances in sedimenting suspension bounded by two horizontal walls is studied. Analytical solution is obtained for particle concentration and fluid velocity fields based on the continuum model of particle transport and linear-perturbation theory. The concentration inhomogeneities and velocity fluctuations are shown to decay with time. The decay is due to decrease of particles’ number because of their deposition on the bottom wall and the variation of sedimentation-front shape. Calculated velocity fluctuations and correlation functions agree qualitatively with experimental values. Fluctuations grow linearly with the height in a cubic container, but saturate or even decrease as the container width grows at fixed height. The mechanisms of inhomogeneity attenuation are discussed which are not described by linear theory but should be taken into account for large containers.