Correlation functions in the approach to complete drying at a wall-liquid interface

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Abstract
Pairwise correlations in fluids adsorbed at structureless substrates (walls) are investigated by means of a simple density functional theory. In the approach to complete wetting or drying from off bulk coexistence capillary-wave-like fluctuations lead to singularities in the total correlation function h when one or both of the particles are located in the edge of the growing film far from the wall. However these singular contributions are damped out when both particles lie close to the wall. For a hard-wall the theory yields explicit results for the zeroth and second transverse moments of h which are consistent with the predictions of exact statistical mechanical sum rules. In particular h 2(0, 0), the second moment evaluated with both particles at the wall, is proportional to the wall-fluid surface tension σ. The implications of this result for the case of complete drying at a wall-liquid-interface, where σ acquires a gas-liquid contribution from the detaching edge of the gas film, are discussed in some detail. We give a new interpretation of the sum rule prediction for h 2(0, 0) in terms of a coherent fluctuation of the complete interface. This interpretation is different from that given in previous work.