Numerical solution and verification of the local equilibrium for the flat interface in the two-phase binary mixture

TL;DR

This paper numerically analyzes the local equilibrium of a non-equilibrium surface in a binary mixture, confirming that surface excess quantities approximate equilibrium values under stationary conditions.

Contribution

It applies the square gradient model to a binary mixture to numerically verify the local equilibrium hypothesis for the surface in non-equilibrium stationary states.

Findings

Surface excess quantities are independent of dividing surface choice.

Non-equilibrium surface can be described by Gibbs excess densities.

Surface properties approximate equilibrium values at the surface temperature and chemical potential difference.

Abstract

In this paper we first apply the general analysis described in our first paper to a binary mixture of cyclohexane and $n$-hexane. We use the square gradient model for the continuous description of a non-equilibrium surface and obtain numerical profiles of various thermodynamic quantities in various stationary state conditions. In the second part of this paper we focus on the verification of local equilibrium of the surface as described with excess quantities. We give a definition of the temperature and chemical potential difference for the surface and verify that these quantities are independent of the choice of the dividing surface. We verify that the non-equilibrium surface can be described in terms of Gibbs excess densities which are in good approximation equal to their equilibrium values at the temperature and chemical potential difference of the surface.