Density functional theory of long-range critical wetting

The wetting properties of a fluid adsorbed at a solid substrate are studied by means of density functional theory. Explicit calculations of the substrate-liquid and substrate-gas density profiles are carried out and used to evaluate the asymptotic expansion for the interface potential of a system with long-range interactions. The range of validity of the asymptotic expansion is checked by comparing it with the interface potential obtained numerically through the constrained minimization of the density functional free energy. Depending on the parameters of the fluid-fluid and substrate-fluid interactions we find first-order or critical wetting transitions. In a limited range of parameters, the critical wetting transition is preceded by a first-order transition between a microscopic and a mesoscopic film, thus corroborating previous calculations and experiments for alkanes on brine. We find that the behavior of the alkanes on brine is not universal, since it requires fine-tuning of the fluid-fluid and substrate-fluid interactions. Finally, we investigate the influence of the short- and long-range forces on the location of the first-order transition. We find that for the models studied, the long-range forces cannot be treated perturbatively. Thus for this type of model it is not possible to separate the effects of short- and long-range forces as done in Landau theories, where the long-range forces are treated perturbatively.