A mean free path kinetic theory of void diffusion in a porous medium with surface diffusion. Asymptotic expansion in the Knudsen number

A mean free path kinetic theory of void transport with Fickian diffusion on the pore walls has been developed for diffusion in a porous medium. A variational upper bound expression for the effective dissusion coefficient for a bed of overlapping solid spheres is expanded asymptotically including terms to third order in the Knudsen number. The effects of tortuosity are rigorously considered by explicitly including the flux of diffusing material around obstructions in its path in the trial functions. Parallel addition of void and surface diffusivities appears to be a good approximation of the variational effective diffusivity equation for all porosities less than 0.70 and small Knudsen number. For small void fractions, the terms of the asymptotic expansion can be summed to give the simple parallel in surface, but series in Knudsen and bulk diffusivities combination in analytical form. (AIP)