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

Abstract

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.

Review on the Macro-Transport Processes Theory for Irregular Pores able to Perform Catalytic Reactions

“…In order to establish a one-dimensional description of the concentration of the adsorbed phase along the main transport coordinate, we will assume that the pore surface is non-twisted, i.e., it is independent of the azimuthal coordinate and therefore describable by a single parametric coordinate. This assumption allows us to write, in the limit of zero loading, the parametric coordinate [31]…”

“…The Equation 29quantifies the concentration distribution of the adsorbed phase as the result of the surface diffusion and the interchange of particles with the bulk phase. In the case when the projection of the dynamics is performed from a two dimensional channel [31], the corresponding mathematical form of the one-dimensional diffusion equation is very similar to the generalization of the Fick-Jacobs equation given in Equation (16). The difference is the form of quantifying the effective mass flux of both diffusive processes.…”

“…The presence of inhomogeneities on the surface concentration slaved to the form of the pore induce non-vanishing gradients, that is, induce bulk and diffusion currents developing in opposite directions along z. The result is the apparent formation of condensation-diffusion cells inside the pore [31]. shows that the adsorbed particles tend to segregate producing an accumulation in the wider regions of the pore.…”

“…For a previous discussion on this subject, see Ref. [18,31] An operational definition γ can be introduced in terms of the ratio between the reaction velocity constant inside the pore with respect to that of a flat surface. Thus, γ can be expressed in terms of the net bulk reaction velocityR = γ R, where R was defined through Equations (17) to (19).…”

“…The present article generalizes to three dimensionsa novel approach to this problem that was recently formulated for the case of non-regular domains in two dimensions [16,18,21,30,31]. In this alternative or generalized macrotransport process theory, the non-regularity of the geometry of the pores is explicitly taken into account when the description is contracted.…”