Effect of Surface Diffusion on Adsorption–Desorption and Catalytic Kinetics in Irregular Pores. I. Local Kinetics

By using a mass balance equation, we deduce an effective equation for the concentration of adsorbed particles that considers the surface diffusion of the particles and an adsorption–desorption process inside a pore of irregular shape. This equation, together with the generalized Fick–Jacobs equation for the bulk diffusion, allows us to quantify the augment in the effective flux through a porous material due to the migration of the gas material along the surface. The equation for the surface concentration has a similar structure to the well-known Fick–Jacobs equation and it takes explicitly into account the shape of the pore through the width and length of the walls, making our model an important tool in the understanding of the interaction of diffusion and adsorption in porous materials where the length of the pores is greater than its width. In this work we predict the profile for the fractional surface coverage as a function of the geometry, the surface and bulk diffusion coefficients, and the isotherm of the process in several illustrative situations that permit us to prove that the effective diffusion coefficients augments with the surface diffusion, that the surface diffusion can give place to internal fluxes in opposite directions between bulk and surface particles, and finally that the diffusivity of adsorbed particles is greater in the narrow regions of the pore, in contrast with what happens to bulk particles. Our description predicts very interesting couplings between bulk and surface diffusion that occur locally and are regulated by the adsorption–desorption kinetics.