Continuous and first-order wetting transition from the van der Waals theory of fluids

The transition between incomplete wetting and complete wetting of an attractive substrate in contact with a gas at gas-liquid coexistence is studied. Within the framework of the systematic van der Waals (mean-field) theory of fluids, it is shown that both a continuous wetting transition, as found by Sullivan, and a first-order transition with a prewetting line, previously found by other methods, are possible. The relative magnitude of the various characteristic lengths in the problem is shown to be of relevance in this context. Beyond the model calculations, purely thermodynamic arguments show that in general the prewetting line, if it exists, joins the bulk coexistence line tangentially in the T- phase plane. The manner in which the difference in slope vanishes as bulk coexistence is approached is closely related to the nature of the forces.