A theory of a curved vapor-liquid separation boundary: The lattice gas model

Abstract

Molecular theory of curved vapor-liquid interphase boundaries was considered in terms of the lattice gas model. The theory uses the quasi-thermodynamic concept of curved layers of a separation boundary with a large radius. The transition from a rectangular lattice to such layers is performed by the introduction of a variable number of the nearest neighbors. The problems (1) of the transition from distributed molecular models to layer models reflecting macroscopic symmetry of the interphase boundary and (2) of a minimum linear size of the surface region to which thermodynamic approaches are applicable were considered. Equations for the quasi-equilibrium distribution of molecules at the vapor-liquid boundary in a metastable system were constructed in the quasi-chemical approximation taking into account direct correlations between the nearest interacting molecules. A metastable state is maintained by a pressure jump described by the macro-scopic Laplace equation on a separation surface inside the interphase region. Equations for local mean pressure values and normal and tangential pressure tensor components inside the interphase region were constructed. These equations were used to obtain microscopic difference mechanical equilibrium equations for curved boundaries of spherical and cylindrical drops in the metastable state. The relation between the micro-scopic difference mechanical equilibrium equations and similar differential equations and the macroscopic Laplace equation, which described pressure jump in a metastable system, was considered. Various definitions of surface tension are discussed.