Unsteady Stefan problem with kinetic interface conditions for rarefied gas deposition

Abstract

The Stefan problem is a phase transition problem with a moving interface between two phases, originally established for solid and liquid. The influence of kinetic theory-based non-equilibrium thermodynamic models on the classical Stefan problem for deposition or sublimation processes is investigated. The gas phase is assumed to be in the rarefied slip regime, so default continuum and equilibrium models struggle. The results are dependent on the well-studied Knudsen and Mach numbers, defined at the phase transition interface. The differences from the classical model become significant as the Knudsen number, and correspondingly the level of rarefaction, increases. We observe influences on the temperature, pressure, phase transition speed and deviation from the saturation conditions.