Slip flow past a tangential flat plate at low Reynolds numbers

Abstract

In this paper the slip flow of viscous fluid at low Reynolds numbers past a flat plate aligned with the flow is studied theoretically on the basis of Oseen-Stokes equations of motion. An integral equation for the distribution of fundamental singularities representing the plate is derived and solved approximately in the vicinity of the edge and main portion of the plate. A formula for the local skin friction is obtained and discussed numerically. It is also shown that the slippage of the flow gives rise to reduction of the drag force on the plate by an amount O(K|ln K|), where K is the Knudsen number. The velocity change near the edge of the plate is of particular interest and is found to be logarithmically singular there.