Gaseous Diffusion in Porous Media. II. Effect of Pressure Gradients

A previously proposed model for the diffusion of gases in porous media at uniform pressure is extended to allow for pressure gradients. The porous medium is visualized as a collection of ``dust'' particles constrained to remain stationary in space. As before, the entire range of intermediate mechanisms from the Knudsen to the normal diffusion region can be covered by varying the mole fraction of real gases. The effect of pressure gradients is to introduce into the fundamental kinetic theory equations both a pressure diffusion term and an external force term, which is needed to keep the porous medium from being pushed along by the pressure gradient. Somewhat surprisingly, there is a considerable cancellation of terms, and the final diffusion equation has the same form as in the uniform pressure case. No additional parameters beyond those necessary to define a diffusing system at uniform pressure are thus required to compute the diffusion rates when pressure gradients are present. The coefficients of the di...