Pressure-temperature effects in planar Stefan problems with density change

An extension of the classical thermal Stefan problem by incorporating the dependence of the phase transition temperature on pressure generated by the flow of the liquid phase due to a density change in the transition process is presented. Two prototypical planar situations are considered. The first is the onset of freezing in an incompressible liquid layer of finite thickness in a gravity field. Asymptotic solutions developed for this problem demonstrate that the initial singularities of the interface velocity and acceleration, typical for the solutions of the classical Stefan problem with an instantaneous temperature drop at the fixed boundary, are regularized by the dynamic pressure effect. The second problem addressed is the freezing or melting of a saturated porous half-space with a flow governed by the Darcy law. Exact similarity solutions (accounting for compressibility of the fluid in the case of freezing) are developed. They indicate that the pressure dependence of the transition temperature may affect significantly the propagation of the phase-change front.