Optimal bounds on the trapping constant and permeability of porous media.
We derive exact expressions for so-called "void" bounds on the trapping constant gamma and fluid permeability k for coated-sphere and coated-cylinder models of porous media. We find that in some cases the bounds are optimal. In these instances, exact expressions are obtained for the relevant length scale that arises in the void bounds, which depends on a two-point correlation function that characterizes the porous medium. This is the first time that model microstructures have been found that exactly realize bounds on either the trapping constant or fluid permeability.
Torquato
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Department of Chemistry and Materials Institute, Princeton University, Princeton, New Jersey 08544, USA. torquato@princeton.edu
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