Motion of a spherical particle along a rough wall in a shear flow

Hydrodynamic interactions between particles and rough surfaces are relevant in various applications involving suspension flow. A spherical particle moving in a shear flow in a fluid domain limited by a rough wall is considered here. Fluid inertia is negligible, that is the Reynolds number for the flow around the particle is low and the creeping flow equations apply. Particle inertia is also negligible. The rough wall has periodic corrugations, with small amplitude compared with the sphere radius. The torque, drag and lift forces on the sphere are calculated from an expansion of the solution of the creeping flow equations for small corrugations, coupled with the use of Lorentz reciprocal theorem and of earlier solutions in bispherical coordinates for creeping flows around a sphere near a plane wall. The translational and rotational velocities of a particle that is moving in a shear flow along a rough wall and submitted to a force and torque are then calculated. These results are exploited to calculate the trajectory of a freely moving particle.