On the steady-state flow of an incompressible fluid through a randomly perforated porous medium

An incompressible fluid is assumed to satisfy the time-independent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain in R-n that is perforated for each epsilon > 0 by epsilon-dilations of a subset of R-n arising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as epsilon --> 0 by means of stochastic two-scale convergence in the mean and the homogenized limit is shown to satisfy a two-pressure Stokes system containing both deterministic and stochastic derivatives and a Darcy-type law which generalizes the Darcy law obtained for fluid now in periodically perforated porous media. (C) 1998 Academic Press.