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

TL;DR

This paper extends the Fick Jacobs equation to better describe adsorption and desorption kinetics in irregular pores under non-equilibrium conditions, accounting for chemical reactions and pore geometry.

Contribution

It introduces a generalized Fick Jacobs model that incorporates chemical reactions, pore curvature, and non-equilibrium boundary conditions for improved accuracy.

Findings

The model accurately predicts concentration profiles in complex pore geometries.

Pore length and curvature are key factors in adsorption-desorption kinetics.

The approach offers detailed insights into transient and stationary states.

Abstract

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.