About the Beavers and Joseph Boundary Condition

A large number of papers are adopting the Beavers and Joseph (BJ) condition (Beavers and Joseph, J Fluid Mech 30(1): 197-207, 1967) for describing the boundary condition between a saturated porous medium and a free fluid, in place of the adherence condition. The aim of the paper is to bring some insight into the domain of validity of the BJ condition. After a short review of some papers on the subject, we point out that the experimental conditions of BJ do not show a good separation of scales. That makes the BJ condition not transposable to different macroscopic situations. When the separation of scales is good, an intrinsic boundary condition is obtained by using the homogenization technique of multiple scale asymptotic expansions. As in the BJ condition and other theoretical works, e.g., Jager and Mikelic (Transp Porous media, 2009, to appear) we obtain the adherence condition of the free fluid at the first order approximation. However, the corrector to the adherence condition is O(epsilon(2)) whereas it is O(epsilon) in the BJ condition, where e is the separation of scales parameter.