Sliding Tractions on a Deformable Porous Layer

Abstract

The problem of sliding surface tractions on a porous biphasic layer with viscous interstitial fluid is solved, which can serve as the basis for solving problems of elastohydrodynamic lubrication of deformable porous layers bonded to a rigid substrate. A general small strain solution is derived for a layer of arbitrary thickness, using Fourier transform methods. The applied tractions, consisting of two normal components and two shear components, have arbitrary distributions and are assumed to slide at a constant speed along the layer surface. It is found that the solution to this problem is dependent on five nondimensional parameters; one of these, Rh , is the ratio of the sliding speed to the characteristic speed of fluid flow within the porous layer; another, τf , controls the transition between Darcy-like and Navier-Stokes flow. Results are presented for various values of these parameters, particularly in relation to the flux of fluid relative to the solid phase along the tangential and normal directions to the layer surface. Discussion of these results and their potential effect on the analysis of elastohydrodynamic lubrication of deformable porous bearings is provided.