Creeping flow in two-dimensional channels

Creeping flow in two-dimensional periodic channels of arbitrary geometry is considered. The problem is formulated using the boundary-integral method for Stokes flow, presently adapted for periodic flows with special geometrical characteristics. Numerical calculations for steady flow in channels constricted by a plane and a sinusoidal wall are performed. Detailed streamline patterns are presented and criteria for flow reversal are established. It is shown that for narrow channels the mechanism driving the flow has a strong effect on the structure of the flow. The results are discussed with reference to lubrication, coating and molecular-convective processes.