Kinetic theory approach to simultaneous gas and surface diffusion in capillaries

Abstract

Momentum balances are derived for the isothermal, isobaric counterdiffusion of two gases within a capillary, with one of the gases adsorbed in a mobile phase on the surface of the capillary. Interactions between the gases and the mobile adsorbed phase result in equations for describing the gaseous diffusion behavior which are significantly different from the equations derived when these interactions are ignored. Simplification of these equations for low surface coverage by the adsorbate is possible; the simplification eliminates the need for adsorption isotherms in the low-coverage situation. The momentum balances derived here are applied to data from two systems which had earlier defied satisfactory description of the diffusion behavior. The diffusion behavior of helium, from nitrogen and helium counterdiffusing through pelleted Graphon, is described satisfactorily by an equation resulting from manipulation of the low-surface-coverage momentum balances. However, the diffusion behavior of helium from propane and helium counterdiffusing through pelleted Graphon is not described satisfactorily by an equation resulting from the general momentum balances. It is suspected that the principal cause for failure in the latter case is an overly naive model for the gas-adsorbate interactions. The momentum balances derived here can be used to calculate surface fluxes within the adsorbed phase. Values calculated for the nitrogen and propane surface fluxes in the above systems can be drastically different from those calculated when the gas-mobile surface phase interactions are ignored.