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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