Effective equations for flow in random porous media with a large number of scales

Abstract

We rederive Brinkman's equations for the flow of slow viscous fluid past a random distribution of identical obstacles using the Foldy's approximation. It is shown explicitly that such a derivation is valid for extremely dilute systems. We argue that Brinkman's equation can be used even in systems with lower porosity by proposing a model of porous media that has a very large number of scales.