Theory on Effective Diffusivities of Bi-disperse Porous Solids at Constant Pressure and Influence of an Inert Gas

Abstract

For predicting effective diffusivities of bi-disperse porous media, an improved model in which tortuosity factors of the macro- and micropores are taken into account is proposed on the basis of the Wakao and Smith random pore model. The diffusion fusion rates of binary gases at constant pressure and the effective diffusivity are derived according to the model.By the use of the experimental data of Wakao and Smith and of Henry et al., tortuosity factors of their porous solids are determined approximately on the basis of the model. The theoretical effective-diffusivities calculated by using the tortuosity factors agree better with the experimental ones over the pressure range 0.0006 to 12atm than those calculated on the basis of the random pore model.In order to examine the influence of an inert gas on the diffusion process, solutions to the Stefan-Maxwell equations for equimolar counter diffusion in a ternary gas mixture through a bi-disperse porous medium are derived on the basis of the model; the diffusion rate and the effective diffusivity in this system are determined reasonably.The expressions for the simple one-dimensional diffusion mentioned above are extended to those for the radial diffusion in a spherical shell.