Diffusion, dead-end pores, and linearized absorption in aggregated media

Abstract

Transient diffusion in a porous medium containing dead-end pores will not behave as simple diffusion if local disequilibria of concentration (between neighbouring active and dead-end porosity) are significant. The problem of the diffusion consequent on a step-function change of concentration at the surface of a semi-infinite column of such a medium is solved by means of the Laplace transformation. The solution, simpler than those already in the literature, is well adapted to the detection of dead-end porosity by diffusion observations, a matter of current interest in soil physics. The diffusion initially follows a (time)) law and, at sufficiently large times, follows a second law of this type. The ratio of the two coefficients is a simple function of the ratio of dead-end porosity to active porosity. A study of the characteristic time of local equilibration indicates, however, that deviations from simple diffusion are limited to a small initial period, during which the diffusion process penetrates into the medium no further than a few pore dimensions. It therefore appears that, in systems of interest in soil physics, the existence of dead-end porosity will be difficult to confirm experimentally and is, in any case, of little practical importance. The experiments of Goodknight, Klikoff, and Fatt were not for molecular diffusion but for the physically different process (better fitted to exhibit significant local disequilibria) of the flow of a compressible gas. In any case, since their 'dead-end porosity' consisted of orifices and chambers of large dimensions, their experiments are not evidence that dead-end porosity produces significant deviations from simple diffusion behaviour (even for the process they studied) in real media. The formalism developed to solve this problem applies also to the linearized model of absorption of water into an unsaturated aggregated medium. The connections between the two problems are established, but details of this application are given in Philip (1968a). Two further applications are indicated: transient diffusion of soluble gases in porous media, and transient heat conduction in composite media.