Critical behaviour of the contact angle within nonwetting gaps

Recent density functional theory and simulation studies of fluid adsorption near planar walls in systems where the wall-fluid and fluid-fluid interactions have different ranges, have shown that critical point wetting may not occur and instead nonwetting gaps appear in the surface phase diagram, separating lines of wetting and drying transitions, that extend up to the critical temperatureT. Here we clarify the features of the surface phase diagrams that are common, regardless of the range and balance of the forces, showing, in particular, that the lines of temperature driven wetting and drying transitions, as well as lines of constant contact angleπ>θ>0, always converge to an ordinary surface phase transition atT. When nonwetting gaps appear the contact angle either vanishes or tends toπast≡(Tc-T)/Tc→0. More specifically, when the wall-fluid interaction is long-ranged (dispersion-like) and the fluid-fluid short-ranged we estimateπ-θ∝t0.16, compared withθ∝t0.77when the wall-fluid interaction is short-ranged and the fluid-fluid dispersion-like, allowing for the effects of bulk critical fluctuations. The universal convergence of the lines of constant contact angle implies that critical point filling always occurs for fluids adsorbed in wedges.