Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Solid-liquid phase changes with different densities

Authors: Michel Frémond and Elisabetta Rocca
Journal: Quart. Appl. Math. 66 (2008), 609-632
MSC (2000): Primary 80A22, 34A34, 74G25
DOI: https://doi.org/10.1090/S0033-569X-08-01100-0
Published electronically: September 10, 2008
MathSciNet review: 2465138
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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 $ \Omega$ when we freeze the container. Since the density $ \varrho_{2}$ of ice with volume fraction $ \beta_{2}$ is lower than the density $ \varrho_{1}$ of water with volume fraction $ \beta_{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 nonhomogeneous material, for instance water, ice or sorbet. Here we describe a general class of phase transition processes, including this example as a 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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Additional Information

Michel Frémond
Affiliation: Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via del Politecnico, 1, I-00133 Roma, Italy
Address at time of publication: CMLA, ENS Cachan -Département de Mécanique, ENSTA, Paris
Email: fremond@cmla.ens-cachan.fr

Elisabetta Rocca
Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini, 50, I-20133 Milano, Italy
Email: rocca@mat.unimi.it

DOI: https://doi.org/10.1090/S0033-569X-08-01100-0
Keywords: Phase transitions with voids, singular and nonlinear PDE system, global existence of solutions.
Received by editor(s): February 26, 2007
Published electronically: September 10, 2008
Article copyright: © Copyright 2008 Brown University

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