Phase separation in a gravity field (Q631296)

A model for the solid-liquid phase transition of a medium inside a rigid container is extended for the case in which also gravity effects are considered. This model describes the evolution of the process which is driven by an energy balance, a quasistatic momentum balance, and a phase dynamics equation. The thermodynamic consistency of the model is verified, and the equilibria are studied. The main goal is to give a qualitative and quantitative description of the interaction between volume, pressure, phase, and temperature changes in the situation when the specific volume of the solid phase exceeds the specific volume of the liquid phase. The well-posedness of the corresponding system of evolution equations is proved and the convergence to equilibria for the solution trajectories associated with a model for solidification of the liquid content of a rigid container in a gravity field is confirmed. It has been observed that the gravity effects, which can be neglected without considerable changes of the process on finite time intervals, have a substantial influence on the long time behavior of the evolution system. Without gravity, a temperature interval is found, in which all phase distributions with a prescribed total liquid content are admissible equilibria, while, under the influence of gravity, the only equilibrium distribution in a connected container consists of two pure phases separated by one plane interface perpendicular to the gravity force.