A Numerical Analysis of Surface Diffusion in a Binary Adsorbed Film

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Abstract
Based on the assumptions that the adsorption of a binary gas mixture may be described by Langmuir isotherms and that the rate of diffusion into the interior of the adsorbent is proportional to the gradient in chemical potential, equations are developed to describe the adsorption of a binary mixture by a slab and by a sphere. The equations describing the concentration changes of each component are coupled nonlinear second-order partial differentials and were solved numerically for the following boundary conditions (normalized concentrations θ of the components at the surface): θA:θB=0.05:0.90, 0.05:0.05, 0.475:0.475, and 0.875:0.095 and ratios of diffusivities, L A/L B=2, 10, and 200. Profiles of concentration against distance into a slab or sphere and also curves of total uptake against time (all in dimensionless form) were obtained. The distinctive feature of the results is that the component of higher diffusivity advances ahead of the second component and tends to attain temporary local concentrations much higher than the equilibrium values at the boundary. Consequently, the total uptake of the more-mobile component may pass through a maximum. These effects are most pronounced when the difference in diffusivities is large, when the equilibrium concentration of the component of higher diffusivity is small, and when the total equilibrium concentration of the two components is large. The calculations were applied to previously reported results of the adsorption of nitrogen-methane mixtures by zeolite A and were found to give reasonable correlations between the behavior of mixtures and that of the individual pure components. In the case of near saturation (θA+θB → 1 at the boundary), the fit with experiment is particularly sensitive to the exact value of (1 − θA − θB).