Molecular diffusion between walls with adsorption and desorption

TL;DR

This paper derives an explicit expression for the time-dependent diffusion coefficient between two walls considering adsorption and desorption, revealing their significant impact on diffusion behavior in porous media.

Contribution

It provides a novel analytical formula accounting for adsorption/desorption effects in simple geometries, aiding interpretation of diffusion measurements.

Findings

Adsorption and desorption significantly alter diffusion time-dependency.

Derived explicit expression for diffusion coefficient with surface interactions.

Applications include sorption rate measurement and benchmarking for complex models.

Abstract

The time dependency of the diffusion coefficient of particles in porous media is an efficient probe of their geometry. The analysis of this quantity, measured e.g. by nuclear magnetic resonance (PGSE-NMR), can provide rich information pertaining to porosity, pore size distribution, permeability and surface-to-volume ratio of porous materials. Nevertheless, in numerous if not all practical situations, transport is confined by walls where adsorption and desorption processes may occur. In this article, we derive explicitly the expression of the time-dependent diffusion coefficient between two confining walls in the presence of adsorption and desorption. We show that they strongly modify the time-dependency of the diffusion coefficient, even in this simple geometry. We finally propose several applications, from sorption rates measurements to the use as a reference for numerical implementations for more complex geometries.