Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid-Solid Interaction

TL;DR

This paper develops a random process-based theory to derive effective fluid-solid interaction potentials for heterogeneous surfaces, accounting for geometric roughness and applying it to amorphous and crystalline materials, with validation against simulations.

Contribution

It introduces a general random process approach to model and approximate fluid-solid interactions on rough surfaces, including analytical solutions for small irregularities.

Findings

Effective potentials differ significantly with lattice spacing.

Good qualitative agreement with Monte-Carlo simulations.

Applicable to both amorphous and crystalline materials.

Abstract

Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarse-grained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations shows good qualitative agreement with the theory predictions. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.