Abstract
Investigators of problems in nonlinear hydrodynamic stability theory are aware of the fact that their methods can be adapted so that they apply to a broad class of physical phenomena. The controlled unidirectional solidification of a pure substance or binary mixture under the influence of imposed temperature and/or solute gradients is an example of a phenomena of this sort. For the last twenty years, the morphological stability of freely growing interfacial boundaries between the liquid and solid phases during such transitions has been analyzed by means of linear stability theory. Typical problems involve diffusion-controlled growth of a precipitate from a solid solution or crystallization from the melt. Idealized (unperturbed) solutions usually exist for interfaces of simple shape, but under certain conditions these simple shapes are spontaneously unstable with respect to small disturbances. Growth subsequent to instability is no longer governed by linear stability theory and more complicated quasi-steady-state structures (e.g., nodes, bands, cells) or chaotic tree-like shapes (dendrites) can occur. This review will survey our current understanding of these nonlinear growth forms from the vantage point of those results obtained by a fluid mechanical stability method applied to a particular three-dimensional solidification model.
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© 1987 Martinus Nijhoff Publishers, Dordrecht
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Wollkind, D.J. (1987). Nonlinear Analyses of Phase Change and Crystal Growth Phenomena. In: Loper, D.E. (eds) Structure and Dynamics of Partially Solidified Systems. NATO ASI Series, vol 125. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3587-7_5
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DOI: https://doi.org/10.1007/978-94-009-3587-7_5
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