Wedge wetting by van der Waals fluids

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Abstract
Using a microscopic density-functional theory for inhomogeneous van der Waals fluids, we derive the equation for the shape of the interface between a liquidlike adsorbed film and the vapor phase in the bulk exposed to a long-range potential of a wedge-shaped substrate. This is a nonlinear and nonlocal integral equation associated with the line tension of the system. Within certain approximations it reduces to that equation which follows from the common phenomenological approach for bent interfaces between fluid phases. The asymptotic lateral behavior of the interfacial profile far away from the center of the wedge displays the presence of van der Waals tails; they are calculated analytically for the cases of complete and critical wetting. The full solutions of the integral equation are obtained numerically. They allow us to predict a scaling behavior of the excess coverage as a function of the thickness of the wetting layer far away from the center of the wedge.

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