Relationship between permeability and diffusion-controlled trapping constant of porous media

For anisotropic porous media of arbitrary topology, it is shown that there exists a rigorous relation between the fluid permeability tensor k and the diffusion-controlled trapping constant, namely, k-1I. It is demonstrated that the equality is achieved for a certain class of microstructures and that the bound can be relatively sharp for other media. The important fundamental as well as practical implications of this relation are discussed.