Hydrodynamic interactions of spherical particles in a fluid confined by a rough no-slip wall.

In this paper we develop a theoretical framework to study the hydrodynamic interactions in the presence of a nonflat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self-mobility and the two-body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self-mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surface roughness in the two-body hydrodynamic interactions is also analyzed numerically.