A continuum framework for modeling liquid-vapor interfaces out of local thermal equilibrium

Abstract

Continuum numerical methods modeling liquid-vapor phase change processes typically assume local thermal equilibrium at the liquid-vapor interface – continuity of temperature at phase interfaces, and a relation between interfacial saturation pressure and temperature based on phase co-existence curves. Several standard macroscopic problems have been solved accurately by adhering to this assumption. However, in micro-scale and certain non-standard macro-scale applications, significant jumps in temperature are observed at liquid-vapor interfaces during phase change, and vapor pressure can be far from equilibrium values. In this paper, we present a locally discontinuous arbitrary Lagrangian Eulerian finite element formulation with temperature discontinuities at interfaces. A penalty-based approach is used to weakly enforce the temperature jump condition. Furthermore, we use kinetic-theory-based Schrage relationship to evaluate the rate of phase change. We apply our methodology to solve the problem of flowing vapor in a planar heat pipe. The flow rates predicted by our continuum simulations are in excellent agreement with recently published molecular dynamics simulation results of the same problem. Interestingly, accounting for temperature discontinuities leads to only a slight improvement in the prediction of mass fluxes as compared to the case when temperature continuity is assumed. This is in contrast to the large improvement in the prediction of temperature profiles and is a consequence of a weak dependence of the evaporation/condensation rates on the vapor temperature.