The Stokes-flow friction on a wedge surface by the sliding of a plate

Abstract

A theoretical analysis is conducted on the frictional stress in the Stokes flow in a channel. A triangular wedge is attached on the bottom plate, and the flow is induced by the top sliding plate. The governing harmonic equation is solved in the transformed zeta-plane, which is obtained by applying conformal mappings. By use of the transformation technique, a closed-form expression is secured for the local frictional stress tau on the wedge surface. In. general, tau increases as the wedge height h increases for a fixed wedge apex angle 2theta. When h is held constant, tau decreases (increases) near the wedge apex (base), as theta increases. Iso-velocity lines are computed for two limiting cases of the wedge shape. These limiting-case solutions are consistent with the previous physical descriptions. (C) 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.