Abstract of the paper ``Variational bounds on Darcy's constant''

Prager's variational method of obtaining upper bounds on the fluid permeability (Darcy's constant) for slow flow through porous media is reexamined. By exploiting the freedom one has in choosing the trial stress distributions, several new results are derived. One result is a phase interchange relation for permeability; when the fluid phase and particle phase are interchanged for a fixed geometry, we find an upper bound on a linear combination of the complementary permeabilities. Another result is a proof of the monotone properties of the bounds. The optimal two-point bounds from this class of variational principles are evaluated numerically and compared to exact results of low density expansions for assemblages of spheres.

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