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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.
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Jacob Rubinstein (1986) studied this question.
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