Diffusion of hard sphere fluids in disordered porous media: Enskog theory description

TL;DR

This paper enhances the Enskog theory to better predict the self-diffusion of hard sphere fluids in disordered porous media by incorporating probe particle porosity, achieving improved agreement with simulations.

Contribution

The authors extend the Enskog theory by including probe particle porosity in the contact values, improving predictions of diffusion in porous media.

Findings

The modified theory aligns well with computer simulations.

Inclusion of probe particle porosity improves accuracy.

The model captures effects of density, size ratio, and matrix porosity.

Abstract

We use the Enskog theory for the description of the self-diffusion coefficient of hard sphere fluids in disordered porous media. Using the scaled particle theory previously developed by us for the description of thermodynamic properties of hard sphere fluids, simple analytical expressions for the contact values of the fluid-fluid and fluid-matrix pair distribution functions are obtained and used as the input of Enskog theory. The expressions obtained for the contact values are described only by the geometric porosity and do not include the dependence on other types of porosity that are important for the description of thermodynamic properties. It is shown that the application of such contact values neglects the effects of trapping of fluid particles by a matrix and at least the probe particle porosity $\phi$ should be included in the Enskog theory for a correct description of the matrix influence. In this paper we extend the Enskog theory by changing the contact values of the fluid-matrix and the fluid-fluid pair distribution functions with new properties which include the dependence not only on geometric porosity but also on probe particle porosity $\phi$. It is shown that such semi-empirical improvement of the Enskog theory corresponds to SPT2b1 approximation for the description of thermodynamic properties and it predicts correct trends for the influence of porous media on the diffusion coefficient of a hard sphere fluid in disordered porous media. Good agreement with computer simulations is illustrated. The effects of fluid density, fluid to matrix sphere size ratio, matrix porosity and matrix morphology on the self-diffusion coefficient of hard sphere fluids are discussed.