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General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids

Published online by Cambridge University Press:  22 May 2007

DANIEL M. ANDERSON ,
PAOLO CERMELLI ,
ELIOT FRIED ,
MORTON E. GURTIN  and
GEOFFREY B. MCFADDEN
DANIEL M. ANDERSON
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030-4422, USA
PAOLO CERMELLI
Affiliation:
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
ELIOT FRIED
Affiliation:
Department of Mechanical and Aerospace Engineering, Washington University in St Louis, St Louis, MO 63130-4899, USA
MORTON E. GURTIN
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
GEOFFREY B. MCFADDEN
Affiliation:
Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, USA
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Abstract

We develop a complete set of equations governing the evolution of a sharp interface separating two fluid phases undergoing transformation. In addition to the conventional balances for mass, linear momentum and energy these equations include also a counterpart of the Gibbs–Thomson equation familiar from theories for crystal growth. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. Although the notion of configurational forces is well-developed and understood for the description of materials, such as crystalline solids, that possess natural reference configurations, little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the bulk phases and the interface and for viscous and thermal dissipation in the bulk phases and for viscous dissipation on the interface. Because of the complexity of these equations, we provide a reduced system of equations based on simplified constitutive assumptions and approximations common in the literature on phase transformations. Using these reduced equations, we apply the theory to the radially symmetric problem for the condensation of a liquid drop into the vapour phase.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007 , pp. 323 - 370
Copyright
Copyright © Cambridge University Press 2007

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