Wetting transitions. II. First order or second order?

We resolve a controversial difference between two recently proposed theories of the equilibrium contact angle, the angle at which a fluid interface meets a solid surface, by investigating integral and gradient theories of fluid at a solid. van der Waals integral theory, of which Sullivan’s model is a special case, in fact admits either a first- or second-order transition from a nonzero contact angle to perfect wetting as a critical point is approached. So also does gradient theory, of which the constant coefficient version we examined previously is a special case.