Abstract
Before we begin the study of dendritic growth, it is appropriate to examine a simple case first: the instability of a planar interface in unidirectional solidification. Mullins and Sekerka were the first, in 1963, to perform a systematic analysis of this system. Their linear stability analysis is now called the Mullins-Sekerka instability [2.1].
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References
W. W. Mullins, and R. F. Sekerka, “Morphological Stability of a Particle Growing by Diffusion or Heat Flow”, J. Appl. Phys. 34, pp. 323–329, (196S).
J. Kevorkian and J. D. Cole, ‘Multiple Scale and Singular Perturbation Methods’, Applied Mathematical Sciences, Vol. 114(Springer, Berlin, Heidelberg 1996).
J. W. Rutter, and B. Chalmers, “A Prismatic Substructure Formed During Solidification of Metals”, Can. J. Phys. 31, pp. 15–39, (1953).
W. W. Mullins, and R. F. Sekerka, “Stability of a Planar Interface during Solidification of a Dilute Binary Alloy”, J. Appl. Phys. 35, pp. 444–451, (1964).
S. H. Davis, “Hydrodynamic Interactions in Directional Solidification”, J. Fluid Mech. 212, pp. 241–262, (1990).
S. H. Davis, “Effect of Flow on Morphological Stability”, in ‘Handbook of Crystal Growth, Volume 1: Fundamentals, Part B: Transport and Stability’ Ed. by D.T.J. Hude, (Elsevier Science, North-Holland, Amsterdam 1993).
B. Caroli, C. Caroli and B. Roulet, “Instability of Planar Solidification Fronts” in ‘Solids Far from Equilibrium’ Ed. by C. Godreche, (Cambridge University Press, Cambridge, New York 1991).
B. Billia and R. Trivedi, “Pattern Formation in Crystal Growth”, Chapter 14, in ‘Handbook of Crystal Growth, Volume 1: Fundamentals, Part B: Transport and Stability’ Ed. by D.T.J. Hude, (Elsevier Science, North-Holland, Amsterdam, 1993).
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Xu, JJ. (1998). Unidirectional Solidification and the Mullins-Sekerka Instability. In: Interfacial Wave Theory of Pattern Formation. Springer Series in Synergetics, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80435-9_2
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DOI: https://doi.org/10.1007/978-3-642-80435-9_2
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