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

Holovko Holovko,Korvatska Korvatska

doi:10.5488/cmp.23.23605

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.

Highlights

The properties of fluids confined in disordered porous media substantially differ from those of bulk fluids [1]
We show in this paper that the application of such contact values neglects the effects of fluid particles being trapped by the matrix, and at least the probe particle porosity φ should be included in the Enskog theory for a correct description of the matrix effect
We modelled a hard sphere fluid in a disordered porous medium by an equilibrium two-component mixture in the limit m0 → ∞ for the species corresponding to the matrix particles

Summary

Introduction

The properties of fluids confined in disordered porous media substantially differ from those of bulk fluids [1]. In order to solve this problem, Holovko and Dong [11] proposed to extend the classical scaled particle theory (SPT) [12, 13] for the description of thermodynamic properties of hard sphere fluids in disordered porous media. They considered a fluid in a disordered matrix as a mixture of two components one of which is quenched in space and was treated as the particles with the infinite mass In such an approach, the contact values of fluid-fluid and fluidmatrix pair-distribution functions are introduced as the input of theory. We propose such an improvement in a manner similar to the description of thermodynamic properties We show that such semi-empirical improvement of the Enskog equation predicts correct trends for the effect of porous media on the diffusion coefficient of hard sphere fluids in disordered porous media. We present some comparison with computer simulation data obtained by the group of Yethiraj [3]

The Enskog theory

Conclusions