Wetting problem for multi-component fluid mixtures

TL;DR

This paper extends the Cahn method to binary fluid mixtures to analyze wetting phenomena near critical points, deriving density profiles and boundary conditions without assuming specific intermolecular potentials.

Contribution

It introduces a generalized approach for binary mixtures, compares it with previous models, and provides explicit density profile expressions and criteria for phase transitions.

Findings

Derived density profiles near solid walls for binary mixtures.

Established a criterion for first-order wetting transitions.

Proposed explicit expressions for component adsorption at surfaces.

Abstract

In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method and later works by Sullivan, Evans et al is made. By using an expression of the energy of interaction between solid surface and liquids proposed recently by Gouin, we obtain the equations of density profiles and the boundary conditions on a solid surface. In the case of a convex free energy, a one-dimensional solution of a linear problem is proposed for the density profiles between a bulk and on a solid wall. A non-linear model of binary mixtures extending Cahn's results for simple fluids is also studied. For the case of a purely attractive wall we have established a criterion of a first order transition in terms of the structure of the level set of the homogeneous part of the free energy. Additively, explicit expressions of density profiles near the wall are proposed. They allow one to consider the adsorption of mixture components by a solid wall.