A phase-field model for the isothermal solidification process of a binary alloy
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.
References
[1] M. Brokate, J. Sprekels. Hysteresis and phase transitions, in AMS, vol. 121, Springer-Verlag, New York, 1996.
[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.
[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
2023-03-30
Issue
pp. 279-288
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Kessler, D., Kruger, O., Rappaz, J., & Scheid, J.-F. (2023). A phase-field model for the isothermal solidification process of a binary alloy. Computer Assisted Methods in Engineering and Science, 7(3), 279-288. https://cames3.ippt.pan.pl/index.php/cames/article/view/1235
