Behavior of the line tension of a model three-phase fluid system approaching a wetting transition

The region of three-phase contact of a binary fluid system described by a model free-energy functional is studied using a mean-field density functional approach. The bulk density of a component in the wetting phase is used as a parameter to introduce a first-order wetting transition. The surface tensions of the constituent two-phase interfaces are evaluated for a range of parameter values (relative densities) and used with Antonov's rule to isolate the wetting transition. The behavior of the line tension upon approach to the wetting transition is then determined by numerically solving the Euler-Lagrange equations for the full, three-phase system at each value of the density parameter.