The thermodynamic principle determining the interface temperature during phase change

Abstract

What is the interface temperature during phase transition (for instance, from liquid to vapor)? This question remains fundamentally unresolved. In the modeling of heat transfer problems with no phase change, the temperature and heat flux continuity conditions lead to the interface temperature. However, in problems with phase change, the heat flux condition is used to determine the amount of mass changing phase. This makes the interface temperature indeterminate unless an additional condition is imposed. A common approach in the modeling of boiling is to assume that the interface attains the saturation temperature according some measure of pressure at the interface. This assumption is usually applied even under highly non-equilibrium scenarios where significant temperature gradients and mass transport occur across the interface. In this work, an ab-initio thermodynamic principle is introduced based on the entropy production at the interface that fully specifies the associated temperature under non-equilibrium scenarios. Physically, the thermodynamic principle provides a theoretical limit on the space of possible phase change rates that can occur by associating the mass flux with a corresponding interfacial entropy production rate; a stronger statement is made that a system with sufficient degrees of freedom selects the maximum entropy production, giving the observed phase change rate and associated interface properties. This entropic principle captures experimental and computational values of the interface temperature that can deviate by over $50\%$ from the assumed saturation values. It also accounts for temperature jumps (discontinuities) at the interface whose difference can exceed 15 degrees Celcius. This thermodynamic principle is found to appropriately complete the phase change problem.