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We derive exact expressions for so-called ``void'' bounds on the trappingconstant $\gamma$ and fluid permeability $k$ for coated-spheres andcoated-cylinders models of porous media. We find that in some cases the boundsare optimal, i.e., the void bounds coincide with the corresponding exactsolutions of $\gamma$ and $k$ for these coated-inclusions models. In theseinstances, exact expressions are obtained for the relevant length scale thatarises in the void bounds, which depends on a two-point correlation functionthat characterizes the porous medium. In contrast to bounds on the effectiveconductivity and elastic moduli of composite media, this is the first time thatmodel microstructures have been found that exactly realize bounds on either thetrapping constant or fluid permeability

Optimal Bounds on the Trapping Constant and Permeability of Porous Media