(326b) Thermodynamics of Flat Thin Liquid Films

Thin liquid films play an important role in a number of interfacial phenomena, including the behavior of premelted ice, processing of polymer films for organic electronics, and wettability alteration in porous media by gases such as carbon dioxide and by low salinity waterflooding for improved oil recovery. We have studied the thermodynamics of a model system in which a thin liquid film of uniform thickness forms after a liquid droplet is placed on a flat, smooth, and chemically homogeneous solid surface. The film and the droplet are surrounded by a gas, and all of these non-reactive fluids are contained in an isothermal, non-deformable, closed container. We derive the conditions for thermodynamic equilibrium in our system and demonstrate that they are self-consistent and compatible with classical results like the augmented Young-Laplace equation. Our equilibrium conditions lead to an augmented Young equation that is different from existing results in the literature. In addition, we discuss discrepancies in the literature concerning the thermodynamic theory. We explain why a widely-used expression for the film tension is inconsistent with the fact that pressure in the film is generally different from the pressure in the corresponding bulk liquid. The film tension, in analogy with interfacial tension, is commonly thought to be an intensive variable; we show that it is neither an intensive nor an extensive variable. The literature derives thermodynamic functions of the film by treating them as being first-order Euler homogeneous. We demonstrate that this assumption may not be valid because the pressure-volume work terms of the film are second-order homogeneous. We propose an alternative and more general framework based on fundamental physical principles to derive thermodynamic relations like the Gibbs-Duhem equation and self-consistent expressions for the internal energy, Gibbs energy, and Helmholtz energy of the film. We combine our augmented Young equation with the Gibbs-Duhem equation to derive a widely-used relation between the disjoining pressure in the film and the contact angle.