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Dynamics of Dendritic Growth Interacting with Convective Flow

Global Instabilities And Limiting State Selection
  • Jian-Jun Xu
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 1)

Abstract

Dendritic gorwth from under cooled melt is a fascinating, common phenomenon in crystal growth. It is also one of the most profound nonlinear pattern formation phenomena in complex dynamic systems far away from the equilibrium state. The essence and origin of dendritic structure formation; the selection of the limiting state of dendritic growth system have been the fundamental, key issues in the broad areas of material science and condensed matter physics for many years. These issues are now well understood on the basis of the so-called Interfacial Wave (IFW) theory. Dynamics of dendritic growth is an interdisciplinary subject. A realistic dendritic growth system unavoidably involves convective flow in the melt. The interplay between growth dynamics and fluid dynamics has been the subject of great significance and interest in the areas of material science, solidification physics, fluid mechanics and applied mathematics.

In this review article, I attempt to introduce this exciting, interdisciplinary subject to the readers in the broad areas of Mechanics and Mathematics. The article begins with the description of macroscopic, continuum approach for general solidification problems and a brief review on the IFW theory for typical dendritic growth without convective flow. This provides the readers with all the necessary background. The main body of the article is devoted to a systematic study of the interactive dynamics of dendritic growth with various types of convective flow in melt. In particular, it explores the effect of convection on the global stability and selection of pattern formation of the system.

Keywords

Dendritic growth convective flow interfacial wave theory selection mechanism of the limiting state global instability free boundary problem singular perturbations multiple variables asymptotic expansion. 
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© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Jian-Jun Xu
    • 1
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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