Analysis of the Conditions of Mechanical Equilibrium on the Curved Surface of a Vapor–Liquid System in a Gravitational Field

A thermodynamic analysis of mechanical equilibrium conditions is performed for the curved interface of a vapor–liquid system in the gravitational field potential with regard to ratios of experimental times of relaxation of thermodynamic parameters (momentum, energy, and mass). In a kinetic analysis of the relaxation stage of reaching the equilibrium state, it is revealed that it is important to consider the physical nature of the boundary of separating phases. The mechanical model of the boundary is one with an intermediate foreign film preventing the attainment of chemical equilibrium between the neighboring phases. The real boundary of coexisting phases has a variable density profile corresponding to the condition of the constant chemical potential throughout the region of transition and in the neighboring coexisting phases. The absence of an intermediate film excludes the priority of the mechanical equilibrium over the chemical equilibrium and results in pressure being the function of local temperature and chemical potential values (excluding the application of the Laplace equation). Considering times of relaxation is found to change the familiar Gibbs expression for the pressure jump between coexisting vapor and fluid as functions of the boundary in the gravitational field potential. A consequence of considering the correct ratio of momentum and mass times of relaxation is discussed: the phase equilibrium conditions of a separating vapor–liquid system in combined gravitational and surface force fields must be analyzed in order to solve problems of the capillary theory.