Slip boundary condition on an idealized porous wall

Abstract

Slip boundary condition on a porous wall is investigated by considering a viscous flow near an idealized porous wall based on the Stokes’ approximation. The idealized porous wall is composed of a large number of parallel and equidistant thin semi-infinite plates. The flow is assumed to be a simple shear flow far from the plates and stagnant deep inside the channels of the plates. The slip velocity on the idealized porous wall is calculated by solving a Wiener–Hopf equation. From the streamline patterns shown, it is found that Moffatt’s infinite sequence of viscous eddies developed between the two adjacent plates. Pressure and shear stress distributions on the plates are shown and local flow near the edge of the plate is discussed. Laminar shear flow at the farfield unidirectional along the edges of the plates is also considered.