A Spherical Particle Settling Towards a Corrugated Wall

Based on the assumption of low Reynolds number, the flow around a spherical particle settling towards a corrugated wall in a fluid at rest is described by Stokes equations. In the case of the small amplitude of wall roughness, the asymptotic expansion coupled with the Lorentz reciprocal theorem are used to derive analytical expressions of the hydrodynamic effects due to wall roughness. The evolution of these effects in terms of roughness parameters and also the sphere-wall distance are discussed.