The square gradient model in a two-phase mixture I. \\Equilibrium properties

TL;DR

This paper extends the square gradient model to multi-component systems, providing a systematic approach to describe equilibrium properties of nonuniform mixtures with interfaces, building on van der Waals and Cahn-Hilliard theories.

Contribution

It introduces a systematic extension of the gradient theory to three-dimensional multi-component mixtures for equilibrium analysis.

Findings

Extended gradient model for multi-component systems

Applicable to three-dimensional interfacial phenomena

Provides a theoretical framework for nonuniform mixtures

Abstract

In order to describe a nonuniform equilibrium mixture with an interface between two coexisting phases it is necessary to consider contributions to the Helmholtz energy which depend on the gradients of for instance the density. Van der Waals \cite{vdW/sg, vdW/translation} was the first to introduce such a term, which is very important in the interfacial region for a one-component system. Cahn & Hilliard \cite{cahnhilliard/fens/I} extended this analysis to a binary mixture by introducing gradient terms of the mol fraction. We give an systematic extension of the gradient theory to three-dimensional multi-component systems.