Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-03-31
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first re-examine the wetting properties of the model in the zero-curvature limit, i.e. for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharp-kink approximation (SKA). We obtain very good agreement with a mean-field density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the so called soft-interface approximation (SIA) originally formulated by Napi\'orkowski and Dietrich [Phys. Rev. B 34, 6469, (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, in this functional form SKA approximates surface tension with that of a sharp interface. This overestimates the liquid-gas surface tension and thus SKA is only qualitative rather than quantitative. On the other hand, by relaxing the assumption of a sharp interface, with e.g. even a simple "smoothing" of the density profile there, improves the predictive capability of the theory markedly, making it quantitative and showing that the liquid-gas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected mean-field critical exponent of the liquid-gas surface tension.
Kalliadasis Serafim
Malijevsky Alexandr
Nold Andreas
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