Accurate bounds for the effective diffusion constant and for the permeability (Darcy's constant) of the porous media are obtained by a new variational formulation. These bounds are expressed in terms of the three two-point correlation functions, surface-surface, surface-void and void-void correlations. The results are applied to a randomly imbedded sphere model, and are found to agree well with the previous bound expressed by the three-point correlation functions.
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Masao Doi (1976) studied this question.
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