Mean-field density-functional model of a second-order wetting transition

First- and second-order wetting transitions are contrasted. A mean-field density-functional model that leads to a second-order transition is introduced. The way in which it differs from an earlier, otherwise similar model in which the transition is first order is noted. The interfacial and line tensions in the model are obtained numerically and their behavior on approach to the transition is determined. The spatial variation of the model's densities in the neighborhood of the contact line near the wetting transition is also found and seen to be characteristically different at a second-order transition from what it is at a first-order transition. The results for the line tension and for the spatial variation of the densities are in accord with those from an earlier interface-displacement model of the same phenomena.