Three-dimensional critical wetting and the statistical mechanics of fluids with short-range forces

Abstract

Statistical mechanical theory of inhomogeneous fluids is used to discuss the continuous growth of adsorbed fluids at wall-fluid interfaces. An ansatz for the form of the singular behaviour of the transverse surface structure factor leads to rederivations of all classes of continuous wetting behaviour expected in the absence of bulk critical phenomena, apart from the strong fluctuation regime of critical wetting, thereby providing one route by which previous results obtained from phenomenological interface hamiltonians and mean-field density functional theory may be based on a true many-body hamiltonian. Earlier reports dealt with systems involving power-law interactions. This paper discusses the complicated case of three dimensional systems in the absence of long-range forces. In particular, the relevant bulk correlation length, determining the appearance of various classes of behaviour, is identified with the asymptotic decay length of the bare profile of the fluctuating interface. This lends strong support to the view that continuous wetting systems can be viewed in terms of a delocalizing mean-field interface, renormalized by capillary-wave fluctuations. A discussion is given of the behaviour likely to be observed in three-dimensional systems involving liquid-vapour coexistence, with a view to possible experiments on liquid metal films.