Gaseous Diffusion in Porous Media at Uniform Pressure

Abstract

A model is presented for the diffusion of gases in porous media in the absence of pressure gradients, in which the porous medium is visualized as a collection of uniformly distributed ``dust'' particles which are constrained to be stationary. By formally considering the dust particles as giant molecules, it is possible to derive all the desired results very simply from rigorous kinetic theory as special cases of multicomponent mixtures. By formally varying the mole fractions of the real gas molecules, the entire pressure range from the Knudsen region to the normal diffusion region can be covered. This model permits the first satisfactory theoretical derivation of the experimentally discovered fact that the flux ratio for binary mixtures is equal to (m₂/m₁)^½ at all pressures (not just in the Knudsen region). It also permits a rigorous theoretical treatment of the entire transition region for the first time, from which is obtained the usual Bosanquet interpolation formula and a differential equation for diffusion which covers the entire range (and appears to be new). The model gives no quantitative a priori characterization of the porous medium itself, but if one gas mixture is measured in a given medium, then the behavior of other gas mixtures in the same medium can be predicted.