Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Conditions of compatibility for the solid-liquid interface


Authors: F. Baldoni and K. R. Rajagopal
Journal: Quart. Appl. Math. 55 (1997), 401-420
MSC: Primary 80A22; Secondary 73B30
DOI: https://doi.org/10.1090/qam/1466140
MathSciNet review: MR1466140
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Abstract: The seminal theory of singular surfaces propounded by Hadamard and Thomas is examined within the context of the dynamics of a solid-liquid interface. It is shown that most of the hypotheses upon which Clapeyron's equation is based can be weakened and two generalized versions of it are derived: with and without curvature effects. The remaining part of the paper is mainly focused on the interface conditions for the classical Stefan problem. The counterpart of Clapeyron's equation for such a problem will give an explicit expression for the supercooling temperature without recourse to linearization procedures. Furthermore, a decay law for the latent heat of melting is given which shows, in an explicit way, its complex dependence upon the curvature and the normal speed of the interface. Finally, a transport equation for the interface temperature is derived and a qualitative solution of a simplified version of it is given for the particular case in which the jump in the Helmoltz free energies of the bulk phases is a conserved quantity throughout the field.


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DOI: https://doi.org/10.1090/qam/1466140
Article copyright: © Copyright 1997 American Mathematical Society


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