A phase-field model for the isothermal solidification process of a binary alloy

  • Daniel Kessler Swiss Federal Institute of Technology
  • Olivier Kruger Swiss Federal Institute of Technology
  • Jacques Rappaz Swiss Federal Institute of Technology
  • Jean-Frangois Scheid Swiss Federal Institute of Technology

Abstract

We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical results are also presented.

Keywords

References

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[2] G. Caginalp. An analysis of a phase-field model for free boundary, Arch. Rational Mech. Anal., 92: 205-245, 1986.
[3] J.W. Cahn, J.E. Hilliard. Free energy of a uniform system. 1. Interfacial free energy, J. Chem. Phys., 28(2): 258-267, 1958.
[4] D. Kessler. Sharp-interface limits of a thermodynamically consistent solutal phase-field model, in preparation.
[5] D. Kessler, O. Krüger, J.F. Scheid. Construction d'un modele de champ-de-phase a temperature homogene pour la solidification d'un alliage binaire. Internal report DMA-EPFL, 1998.
Published
Mar 30, 2023
How to Cite
KESSLER, Daniel et al. A phase-field model for the isothermal solidification process of a binary alloy. Computer Assisted Methods in Engineering and Science, [S.l.], v. 7, n. 3, p. 279-288, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1235>. Date accessed: 21 nov. 2024.
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Issue
Vol 7 No 3 (2000)
Section
Articles
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