Liquid-vapor isotherm in a closed single-component system with curved interfaces

A thermodynamic model to obtain the radius of bubbles or droplets in a single-component system for a given temperature, total volume, and phase distribution is developed. The general formulation of the model includes bubbles or droplets in the form of spheres, truncated spheres on a flat solid surface or inside conical walls. In these three geometries the liquid-vapor curvature radius is positive but in the case of conical walls it can be also negative. States with different dispersed-phase distributions are compared using the total free energy of the system. When the curvature radius is positive, it has a minimum nonvanishing value and the occurrence of the Ostwald ripening is energetically favorable. On the other hand, when the curvature radius is negative, it is energetically more favorable to find the dispersed phase even in the expected single-phase region, and the occurrence of an anti-ripening phenomenon. The PV isotherms obtained from the model and the applicability of the results to the nucleation process are discussed.