Line tension on approach to 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. A first order wetting transition is induced by varying a parameter that is the controlling field variable in the model. The surface tensions of the constituent two-phase interfaces are evaluated for a range of parameter values and used to locate the wetting transition. The behavior of the line tension upon approach to the wetting transition is then determined by numerical solution of the Euler-Lagrange equations for the full three-phase system at each value of the parameter. The line tension is found to converge to a finite value as the contact angle vanishes, with a derivative that is finite with respect to contact angle but divergent with respect to the field variable (parameter), apparently growing as the inverse square root of the difference between the field variable and its value at wetting. Except for a possible logarithmic factor, which could not be discerned at the present level of numerical precision, this would be in accord with the prediction from mean-field theory.