Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres

Abstract

The influence of microscopic surface roughness on the statistical motion of a heavy sphere falling through a dilute suspension of neutrally buoyant spheres is analyzed for conditions of low Reynolds number and large Péclet number. The presence of roughness on their surfaces allows interacting spheres to come into contact. A stick/rotate model (based on rigid-body motion) and a roll/slip model (based on solid contact friction) are proposed for the motion normal to the line-of-centers of the heavy sphere and a neutrally buoyant sphere when in contact. A trajectory analysis is used to describe pairwise interactions and their contributions to the mean velocity, velocity variance, and hydrodynamic diffusivity of the heavy sphere as it undergoes a fluctuating motion due to interactions with the background spheres. The horizontal component of the hydrodynamic diffusivity becomes nonzero as a direct result of surface roughness and contact, since ideally smooth spheres undergo symmetric pairwise trajectories which result in zero net horizontal displacement. The effects of surface roughness on the vertical components of the diffusivity, mean velocity, and velocity variance are relatively small when the heavy and background spheres are of nearly equal size, but the effects of surface roughness are large for disparate size ratios. The limited experimental data available show better agreement with the roll/slip model than with the stick/rotate model.