On the interface boundary condition of Beavers, Joseph, and Saffman

We consider the laminar viscous channel ow over a porous surface. It is sup posed, as in the experiment by Beavers and Joseph, that a uniform pressure gradient is maintained in the longitudinal direction in both the channel an d the porous medium. After studying the corresponding boundary layers, we o btain rigorously Saffman's modification of the interface condition observed by Beavers and Joseph. It is valid when the pore size of the porous medium tends to zero. Furthermore, the coefficient in the law is determined throu gh an auxiliary boundary-layer type problem.