Unidirectional Solidification and the Mullins-Sekerka Instability
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].
KeywordsDispersion Relation Asymptotic Solution Planar Interface Mode Solution Unidirectional Solidification
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- 2.2J. Kevorkian and J. D. Cole, ‘Multiple Scale and Singular Perturbation Methods’, Applied Mathematical Sciences, Vol. 114(Springer, Berlin, Heidelberg 1996).Google Scholar
- 2.6S. 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).Google Scholar
- 2.7B. 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).Google Scholar
- 2.8B. 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).Google Scholar