Critical effects at complete wetting.

Abstract

The approach towards complete wetting is considered for adsorbed liquid layers and for gravity-thinned layers in binary mixtures. These layers are bounded by one or two fluid-fluid interfaces. The thermal fluctuations of those interfaces are studied in the framework of effective interfacial models. Their correlation function C(x) is calculated within the Ornstein-Zernike approximation and by transfer-matrix methods. For large distances x, C(x)\ensuremath{\propto}exp(-x/${\ensuremath{\xi}}_{?}$). Due to the divergence of the correlation length ${\ensuremath{\xi}}_{?}$, complete wetting can be regarded as a critical phenomenon. Two different scaling regimes have to be distinguished depending on the nature of the long-ranged forces and on the dimensionality. In the mean-field regime, the critical exponents depend on the long-ranged forces. In the fluctuation-dominated regime, they depend only on the dimensionality. It is also shown that these critical effects are characterized by one superuniversal feature: The critical exponent \ensuremath{\eta} which governs the decay of the correlation function C(x) for x\ensuremath{\ll}${\ensuremath{\xi}}_{?}$ is zero both in the mean-field and in the fluctuation-dominated regime. The result \ensuremath{\eta}=0 is expected to be valid for all types of wetting transitions. The experimental work which has focused on the thickness of the wetting layer is briefly reviewed. Furthermore, two types of experiments are proposed by which the correlation length ${\ensuremath{\xi}}_{?}$ could be observed: it should show up both in the intensity of the small-angle scattering of light from the interfaces and in experiments which measure the dispersion relation of the capillary waves. This relation is found to be ${\ensuremath{\omega}}^{2}$(q)\ensuremath{\propto}q(${q}^{2}$+${\ensuremath{\xi}}_{?}^{\mathrm{\ensuremath{-}}2}$), where \ensuremath{\omega} and q are the frequency and the wave number of such waves. It is also suggested that the regime of critical wetting could be obtained in binary mixtures by the addition of impurities.