  We study the hydrodynamic coupling between particles and solid, rough
boundaries characterized by random surface textures. Using the Lorentz
reciprocal theorem, we derive analytical expressions for the grand mobility
tensor of a spherical particle and find that roughness-induced velocities vary
nonmonotonically with the characteristic wavelength of the surface. In contrast
to sedimentation near a planar wall, our theory predicts continuous particle
translation transverse and perpendicular to the applied force. Most
prominently, this motion manifests itself in a variance of particle
displacements that grows quadratically in time along the direction of the
force. This increase is rationalized by surface roughness generating particle
sedimentation closer to or farther from the surface, which entails a
significant variability of settling velocities.
