A model for the boundary condition of a porous material. Part 1

TLDR: In this article, an artificial mathematical model of a porous medium is proposed for which the flow can be calculated both inside and outside the surface, and the experimental results agree with the calculations.

Abstract: In problems where a viscous fluid flows past a porous solid it has frequently been assumed that the tangential component of surface velocity is zero. When the porous solid has an open structure with large pores the external surface stress may produce a tangential flow below the surface. Recently, Beavers & Joseph (1967) have assumed that the surface velocity UB depends on the mean tangential stress in the fluid outside the porous solid through the relation \[ \left[\mu\frac{d\overline{u}}{dy}\right]_{y=0} = \frac{\mu\alpha}{k^{\frac{1}{2}}}(U_B-Q), \] where Q is the volume flow rate per unit cross-section within the porous material due to the pressure gradient, k is the Darcy constant and α is a constant which depends only on the nature of the porosity. An artificial mathematical model of a porous medium is proposed for which the flow can be calculated both inside and outside the surface. This conceptual model was materialized and the experimental results agree with the calculations. The calculated values of α so found are not quite independent of the external means of producing the external tangential stress.