Generalized Fick Jacobs Approach for describing Adsorption Desorption Kinetics in Irregular Pores under Non Equilibrium Conditions

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We present a study exploring the range of applicability of a generalized Fick Jacobs equation in the case when diffusive mass transport of a fluid along a pore includes chemical reactions in the bulk and pore surface. The study contemplates nonequilibrium boundary conditions and makes emphasis on the comparison between the predictions coming from the projected Fick Jacobs description and the corresponding predictions of the original two dimensional mass balance equation, establishing a simple cuantitative criterion of validity of the projected description. For the adsorption desorption process, we demonstrate that the length and the local curvature of the pore are the relevant geometric quantities for its description, allowing for giving very precise predictions of the mass concentration along the pore. Some schematic cases involving adsorption and chemical reaction are used to quantify with detail the concentration profiles in transient and stationary states involving equilibrium and nonequilibrium situations. Our approach provides novel and important insights in the study of diffusion and adsorption in confined geometries.