Optimal bounds on the trapping constant and permeability of porous media

The evaluation of the void bounds on the trapping constant γ and fluid permeability k for the coated-sphere and coated-cylinder models of porous media was presented. It was shown that the void bounds were optimal in some cases as they coincide with the corresponding exact solutions of γ and k. The exact expressions for the relevant length scale that arises in the void bounds which depends on S₂(r) was obtained. It was suggested that the model microstructures have been found that exactly realize bounds on either the trapping constant or fluid permeability.