Particle density stratification in transient sedimentation

Theoretical predictions for the scaling of particle velocity fluctuations with container size in homogeneous Stokes suspensions are not consistent with experimental observations. Several explanations have been advanced, including the formation of stratification in bounded systems, such as those used in experiments. Numerical simulations of transient Stokes sedimentation in bounded cells are presented here for several cell sizes. The simulated cells have top and bottom wall boundaries and periodic boundaries in the horizontal. Throughout the course of the simulations the number and distribution of particles in the cell evolve, with impacts on the bulk mean particle velocity, velocity fluctuations, and particle density gradient. Initially the sedimentation follows the classical description, with a sharp front and uniform particle concentration below, but this is not sustained. A layer of higher particle concentration develops below the front. This is unstable and there is a large-scale overturning of the fluid. As a consequence, there is a redistribution of the particles, leaving behind a mass loading of the particles, which is stably stratified (subject to small density fluctuations between horizontal levels). The mean velocity and fluctuations of the particles initially grow and then decay once stable stratification has developed.