Numerical simulation of the settling of polydisperse suspensions of spheres

The extension of Kynchʹs kinematical theory of ideal suspensions to polydisperse suspensions of spheres leads to a nonlinear system of conservation laws for the volumetric concentration of each species. In this work, we consider particle species different in sizes and densities, including the buoyant case. We show that modern shock-capturing numerical schemes for the solution of systems of conservation laws can be employed as an efficient tool for the simulation of the settling and separation of polydisperse suspensions. This is demonstrated by comparison with published experimental and theoretical results and by simulating some hypothetical configurations. Particular attention is focused on the emergence of rarefaction waves.