Lid-driven Stokes slip flow in a rectangular cavity

Abstract

Slip flow in a rectangular cavity is studied. Using slip eigenfunctions, an exact series solution is found for a lid sliding longitudinally. For a transversely sliding lid, the stream function for Stokes flow is determined by a new set of slip eigenfunctions and supplemented by point match on the boundary. It is found that slip has considerable effect on the flow properties. Analyses of the region very close to the corner of the velocity discontinuity show the stress singularity of no-slip flow can be eliminated by slip for both longitudinal flow and transverse flow, except when the latter corner is a right angle.