Mean velocities in polydisperse suspensions

Abstract

Extending the results of Beenakker and Mazur to polydisperse suspensions of spheres, we calculate each species' mean velocity for two different boundary conditions. Relative to the suspension, these means are the same for both cases. Theoretical values for a single sphere settling in a dispersion of smaller spheres are compared with those of Batchelor and Wen and with experimental results from previously unpublished work by Verhoeven and Tory. In contrast to the predicted decrease in sedimentation speed, the single large sphere settled faster, on the average, as the concentration of small spheres increased to 0.04. The fundamental grouping of particles is not a close pair, but a transient cluster of several spheres. The experimental results support the conclusion that Batchelor's analysis, which is based on close pairs, is fundamentally flawed.