NONLINEAR CORRECTIONS TO DARCYS-LAW AT LOW REYNOLDS-NUMBERS

Under fairly general assumptions, this paper shows that for periodic p orous media, whose period is of the same order as that of the inclusio n, the nonlinear correction to Darcy's law is quadratic in terms of th e Reynolds number, i.e. cubic with respect to the seepage velocity. Th is claim is substantiated by reinspection of well-known experimental r esults, a mathematical proof (restricted to periodic porous media), an d numerical calculations.