Abstract
The flow through a layer of porous medium sandwiched between two plates with striations or surface roughness of small amplitudes is considered. The upper plate moves in a direction perpendicular to the corrugations while the lower one is stationary. The considered problem is a cross-Couette flow, and the Brinkman-extended Darcy's equation is used to model fluid flow in the porous medium. An analytic perturbation procedure, with respect to the nondimensional amplitude epsilon, is developed leading to expressions for the steady and unsteady force components acting on the stationary plate, up to O(epsilon(2)), as functions of the statistics of the corrugations and permeability of the porous medium. The limiting cases of Stokes and Darcy flows of these expressions are discussed. Asymptotic results for the long and short wavelengths of the corrugations are developed to the force components. Plots of the steady and unsteady force components are presented and discussed for various values of the wavelengths of the corrugations and the permeability parameter. It is found that the unsteady force component vanishes when the moving plate is flat.