Pairwise correlations at a fluid-fluid interface

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Abstract
Density-density correlations in a planar interface of a neutral, multi-component fluid mixture are analysed. For a ‘normal’ liquid-gas or liquid-liquid interface the transverse (parallel to the interface) correlations exhibit Ornstein-Zernike behaviour with a common correlation length ξT = (σ/b)1/2, where σ is the surface tension and b is determined by the external fields. If, however, the interface corresponds to a near complete wetting situation so that a thick film of a third fluid phase (β) intrudes between the two bulk phases α and γ, the transverse correlations do not, in general, exhibit Ornstein-Zernike behaviour. Rather they exhibit more complex structure for small transverse wave numbers which depends on the ‘stiffness’ of the wetting film. In the limit of a very thick film Ornstein-Zernike behaviour occurs in both edges, the correlation length depending on the value of σ and b appropriate to the individual interface so that ξαβ T = (σαβ/b αβ)1/2 and ξβγ T = (σβγ/b βγ)1/2. The theoretical analysis is supported by the results of density functional calculations for a model binary fluid mixture, the parameters of which are chosen to mimic the experimentally observed situation in which the liquid phase (β) with the larger mass density forms a wetting film that intrudes between the less dense liquid phase (γ) and the gas (α). The resulting transverse correlation functions depend sensitively on the thickness of the film. Possible destabilization mechanisms for wetting films in gravitational fields are mentioned.