A theoretical model for mass transition rate at liquid-vapor sharp interface

Abstract

Phase change phenomena like evaporation and boiling have traditionally relied on accommodation coefficients, determined experimentally over centuries. This paper presents a new formula for the mass transition rate at a sharp interface, derived from the diffuse interface model in a two-phase system. The mass transition rate is proportional to the difference in chemical potentials between liquid and vapor which is consistent with the classical thermodynamic phase transition criteria. By using the saturation state at the interfacial temperature as a reference, unmeasurable parts of the chemical potentials are eliminated. The proposed model consists of two terms: the first accounts for the relative pressure between the liquid's vapor pressure and the vapor pressure at the interface, while the second reflects the contributions of surface tension and curvature. An alternative formulation expresses relative pressure as the temperature difference between the interfacial temperature and the saturation temperature corresponding to the vapor's interfacial pressure. Unlike traditional models, the proposed formula does not require accommodation coefficients, which typically vary by case. Validation against literature data for both flat and curved surfaces as well as micro-scale test setup shows reasonable agreement, demonstrating the model's effectiveness.