Effect of membrane thickness on the slip and drift velocity in parallel shear flow

Shear flow past a planar membrane or screen, idealized as an infinite plate perforated by parallel periodic slots, is discussed with emphasis on the effect of the plate thickness on the slip velocity, defined as the displacement of the linear velocity profile on the side of the plate where a shear flow is imposed, and on the drift velocity prevailing on the other side of the membrane. Numerical results based on boundary-element methods for longitudinal and transverse flow show that, while the plate thickness has only a moderate effect on the slip velocity, it has a profound effect on the drift velocity. The structure of the flow near the membrane pores is illustrated in terms of the wall shear stress distribution, the velocity distribution for longitudinal flow, and the streamline pattern for transverse flow. The latter reveals the possible occurrence of counter-rotating eddies inducing a back flow.