Interaction of sedimenting spheres with multiple surface roughness scales

The interaction of a pair of spherical particles of different densities and/or sizes with microscopic surface roughness sedimenting due to gravity in a viscous fluid is analysed by theory and experiment. The surface topography is modelled as a combination of small uniformly distributed bumps of uniform height and larger bumps that are more sparsely distributed. The existence of these surface asperities allows the spheres to physically contact each other, so that both hydrodynamic and solid-contact forces are important. When the angle between the line of centres and vertical is small, the spheres may rotate as a rigid body because they are not able to roll up and over a large bump. As this angle increases, however, the heavy sphere rolls and slips past the lighter sphere, and the separation between the nominal surfaces of the spheres varies between the heights of the small and large asperities. When considering many encounters, there is a distribution of nominal separations at each angle due to the distribution of initial conditions and surface topography. The average nominal separation generally increases with increasing angle between the line of centres and vertical because the normal component of gravity, which drives the spheres close together after an encounter with a large bump lifts them apart, decreases as this angle increases.