Comments on the compositional boundary condition for diffuse interface model of contact line

TL;DR

This paper proposes a modification to the boundary conditions in the diffuse interface model for contact line dynamics, accounting for surface contributions to free energy, improving accuracy near solid surfaces.

Contribution

It introduces a new compositional boundary condition derived from surface free energy minimization for better modeling contact lines.

Findings

Modified boundary conditions improve contact line modeling accuracy.

Results are applicable to both single-component and binary mixtures.

The approach is valid under local thermodynamic equilibrium assumptions.

Abstract

The diffuse interface model of Cahn-Hilliard-van der Waals is often used to study various aspects of multi-phase flows such as droplets coalescence and contact line dynamics. The original model of Cahn-Hilliard-van der Waals uses an approximation which neglects some surface contributions to the free energy of the system and is justified by the large distance between the region of observation and the outer surface of the system. This is not a priori accurate when considering the dynamics of the contact line on a solid surface. A modification of the so called natural compositional boundary conditions obtained by minimization of the surface contribution to the free energy of the system is proposed for the vapor-liquid interface of a single component and for a quasi-incompressible binary mixture of partially miscible liquids. The results are obtained for a stagnant fluid in thermodynamic equilibrium but should be valid in a flow if local thermodynamic equilibrium can be assumed.