A New Variational Approach to the Diffusion and the Flow Problem in Porous Media

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.