Numerical simulation of polydisperse sedimentation: equal-sized spheres

Abstract

This paper describes the results of numerical simulations for polydisperse sedimentation of equal-sized spheres, e.g. particles of different density. Using the Stokesian dynamics algorithm, mobility matrices are computed for random particle configurations and ensemble averages taken to calculate the mean mobility matrices. It is shown that the settling velocities of individual particles species may be expressed in terms of two scalar functions of total volume fraction. These are the selfmobility Mo, (∼ short-time self-diffusion coefficient) and the interaction mobility MI. This latter quality is related to the velocity of a force-free tracer particle in a suspension of identical particles subjected to a unit force. Numerical values for Mo and MI are calculated for a range of volume fractions from ϕ = 0.025 to 0.50. All results show excellent agreement with the dilute theory of Batchelor. Simple algebraic expressions are given which well correlate the numerical results.