Mean-field Density Functional Theory of a Three-Phase Contact Line

TL;DR

This paper models a three-phase contact line using mean-field density functional theory, deriving both analytical and numerical solutions, and calculates a negative line tension associated with the contact line.

Contribution

It introduces a variational approach and numerical methods to analyze the three-phase contact line within a mean-field density functional framework, including the calculation of line tension.

Findings

Analytic solutions in two-phase regions at large distances

Numerical solutions for equal interfacial tensions

Line tension is negative and related to line adsorption

Abstract

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.