Cross-property relatigS for momentum and diffusional transport in porous media

Cross-property relations linking the fluid permeability k associated with viscous flow through a porous medium to effective diffusion properties of the medium have recently been derived. Torquato [Phys. Rev. Lett. 64,2644 (1990)] found that k<D4,7, where r is the “mean survival time” associated with steady-state diffusion of “reactants” in the fluid region of diffusion coefficient D and porosity #i of a porous medium containing absorbing walls (i.e., trap boundaries). Subsequently, Avellaneda and Torquato [Phys. Fluids A 3,2529 ( 1991)] related k to the electrical formation factor F (inverse of the dimensionless effective electrical conductivity) and the principal (largest) diffusion relaxation time T, associated withy the time-dependent trappingproblem, namely, k<DTl/F.. ‘In this study, we compute the aforementioned bounds, using an efficient first-passage-time algorithm, for grain-consolidation models of porous media and compare them to exact results for these models. We also conjecture a new relation connecting k to r and F for a wide class of porous media, namely, k<Dr/F, and show that it gives the sharpest permeability estimate among the existing bounds. The importance of this relation lies not only in its usefulness as an estimator of-the permeability but that it involves the diffusional parameters r and F which can be measured in situ. ; -