Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On the Mullins-Sekerka model for phase transitions in mixtures

Author: Natasa Milic
Journal: Quart. Appl. Math. 49 (1991), 437-445
MSC: Primary 80A22; Secondary 80A15
DOI: https://doi.org/10.1090/qam/1121676
MathSciNet review: MR1121676
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Abstract: The Mullins-Sekerka model for dynamical phase transitions in two-component mixtures is considered. Global growth conditions for the phase regions and the interface are obtained from underlying conservation laws. A quasi-static model is formulated and the solutions are discussed for totally isolated mixtures.

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  • [1] J. W. Gibbs, On the equilibrium of heterogeneous substances, Trans. Connecticut Acad. 3, 108-248 (1876), 343-524 (1878). Reprinted in The Scientific Papers of J. Willard Gibbs, Vol. 1, Dover, New York, 1961
  • [2] W. W. Mullins and R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34, 323-329 (1963)
  • [3] R. F. Sekerka, Morphological stability, J. Crystal Growth (3) 4, 71-81 (1968)
  • [4] R. F. Sekerka, Morphological stability, Crystal Growth: an Introduction, North-Holland, Amsterdam, 1973
  • [5] N. Weck, Uber das Prinzip der eindeutigen Fortsetzbarkeit in der Kontrolltheorie, Optimization and Optimal Control, Lecture Notes in Math., vol. 477, Springer-Verlag, Berlin, 1975, pp. 276-284 MR 0394363
  • [6] E. J. P. Georg Schmidt and N. Weck, On the boundary behavior of solutions to elliptic and parabolic equations--with application to boundary control for parabolic equations, SIAM J. Control Optim. 16, 593-598 (1978) MR 497464
  • [7] R. F. Sekerka, Morphological instabilities during phase transformations, Phase Transformations and Material Instabilities in Solids (M. E. Gurtin, ed.), Academic Press, New York, 1984 MR 802224
  • [8] M. E. Gurtin, On the theory of phase transitions with interfacial energy, Arch. Rational Mech. Anal. 87 187-212 (1985) MR 768066
  • [9] M. E. Gurtin, On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199-241 (1986) MR 855304
  • [10] M. E. Gurtin, Multiphase thermomechanics with interfacial structure: Heat conduction and capillary balance law (forthcoming) MR 1017288
  • [11] N. Milic, On the non-equilibrium phase-transitions in mixtures with interfacial structure, Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1988 MR 2637228
  • [12] M. E. Gurtin, A. Struthers, and W. O. Williams, A transport theorem for moving interfaces (forthcoming)

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Additional Information

DOI: https://doi.org/10.1090/qam/1121676
Article copyright: © Copyright 1991 American Mathematical Society

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