Line and boundary tensions at the wetting transition: Two fluid phases on a substrate

We develop and analyze a mean-field model free energy that describes two fluid phases on a substrate in order to calculate the (numerically) exact line and boundary tensions, on approach to the first-order wetting transition. A theory based on the van der Waals theory of gas–liquid interfaces is used. We implement a multigrid algorithm to determine the two-dimensional spatial variation of the density across the three-phase and boundary regions, and hence, the line and boundary tensions. As the wetting transition is approached, the tensions approach the same, finite, positive limit with diverging slopes. We compare our results with those of recent related work.