Thermodynamics of free and of interacting curved interfaces in liquid films

Publications on the thermodynamics of free and of interacting curved interfaces in liquid films are reviewed. The approaches of Gibbs, Boruvka–Neumann and others to the determination of the surface tension of free curved surfaces are compared. The dependences of differently defined interfacial tensions on the radius of curvature of the interface are obtained. The fundamental equilibrium equations for systems containing curved surfaces, including the transition region of the liquid film, are proposed. A generalised invariant of the profile of the liquid film is obtained, and used to derive all the known equilibrium equations for a liquid film with a bulk meniscus, including the equation for a liquid drop on a solid surface and precise analytical expressions describing the line tension for different thermodynamic models of the liquid film. The theory of the adhesion of fluid particles, which relates the adhesion force and the potential energy of the interaction between deformable particles to the parameters of the disjoining pressure isotherm, is discussed. The bibliography includes 88 references.