Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabolaapproximation

Abstract

We derive a non-local effective interfacial Hamiltonian model for short-ranged wettingphenomena using a Green’s function method. The Hamiltonian is characterized by abinding potential functional and is accurate to exponentially small order in the radii ofcurvature of the interface and the bounding wall. The functional has an elegantdiagrammatic representation in terms of planar graphs which represent different classes oftube-like fluctuations connecting the interface and wall. For the particular cases of planar,spherical and cylindrical interfacial (and wall) configurations, the binding potentialfunctional can be evaluated exactly. More generally, the non-local functional naturallyexplains the origin of the effective position-dependent stiffness coefficient in thesmall-gradient limit.