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In this paper we revisit the derivation of a nonlocal interfacial Hamiltonianmodel for systems with short-ranged intermolecular forces. Starting from amicroscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabolapotential, we reformulate the derivation of the interfacial model using arigorous boundary integral approach. This is done for three scenarios: a singlefluid phase in contact with a nonplanar substrate (i.e., wall); a freeinterface separating coexisting fluid phases (say, liquid and gas); and finallya liquid-gas interface in contact with a nonplanar confining wall, as isapplicable to wetting phenomena. For the first two cases our approachesidentifies the correct form of the curvature corrections to the free energyand, for the case of a free interface, it allows us to recast these as aninterfacial self-interaction as conjectured previously in the literature. Whenthe interface is in contact with a substrate our approach similarly identifiescurvature corrections to the nonlocal binding potential, describing theinteraction of the interface and wall, for which we propose a generalized andimproved diagrammatic formulation.

Curvature corrections to the nonlocal interfacial model for short-ranged forces