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arXiv · 0806.2915

Solid liquid phase changes with different densities

Michel Fremond·Elisabetta Rocca
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Abstract

In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container $Ω$ when we freeze the container. Since the density $\varrho_{2}$ of ice with volume fraction $β_{2}$, is lower than the density $\varrho_{1}$ of water with volume fraction $β_{1}$, experiments - for instance the freezing of a glass bottle filled with water - show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing may produce a non-homogeneous material, for instance water ice or sorbet. Here we describe a general class of phase transition processes including this example as particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved.

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Michel Fremond, Elisabetta Rocca. 2008-06-18. Solid liquid phase changes with different densities. https://arxiv.org/abs/0806.2915

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