Stokes flow in arbitrary two-dimensional domains: Shear flow over ridges and cavities

A method is described for solving the integral equations governing Stokes flow in arbitrary two-dimensional domains. It is demonstrated that the boundary-integral method provides an accurate, efficient and easy-to-implement strategy for the solution of Stokes-flow problems. Calculations are presented for simple shear flow in a variety of geometries including cylindrical and rectangular, ridges and cavities. A full description of the flow field is presented including streamline patterns, velocity profiles and shear-stress distributions along the solid surfaces. The results are discussed with special relevance to convective transport processes in low-Reynolds-number flows.