Effect of contact forces on sedimenting spheres in stokes flow

Abstract

The macroscopic behavior of a suspension of sedimenting particles in a fluid is closely related to and depends on the microstructure and relative motion of particles in the suspension. Thus, the calculation of the trajectories of the particles is an essential step in the mathematical modeling of the macroscopic behavior of the suspension. Classical low Reynolds number hydrodynamics predicts that sedimenting solid spherical particles approach one another typically to within 10 −3 of a radius, indicating that the surface roughness of the particles can become significant and takes part in the interaction process. In this paper, assuming zero Reynolds number flow, the trajectories of two solid spheres sedimenting in either a quiescent fluid or a shear flow are calculated. The cases of ideally smooth and of rough spheres are compared in order to examine the effects of surface roughness on the trajectories.