On the Boundary Condition at the Surface of a Porous Medium

A theoretical justification is given for an empirical boundary condition proposed by Beavers and Joseph 1. The method consists of first using a statistical approach to extend Darcy's law to non homogeneous porous medium. The limiting case of a step function distribution of permeability and porosity is then examined by boundary layer techniques, and shown to give the required boundary condition. In an Appendix, the statistical approach is checked by using it to derive Einstein's law for the viscosity of dilute suspensions.