Mean-field Density Functional Theory of Triple Junction

A triple junction 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 triple junction. 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 triple junction. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.