Stability and Selection of Dendritic Growth with Convective Flow

  • Jian-Jun Xu
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 7)


In the previous chapters, we have studied the basic steady state solutions for systems with different types of convective motion in the melt. Like the Ivantsov solutions, without taking into account the surface tension, the solutions obtained are not unique, under a given growth condition. Thus, the selection remains. To resolve the selection problem of dendritic growth with convective flow, one needs to take the surface tension into account and study the stability property of the steady state solutions. For this purpose, one may apply the approach of the Interfacial Wave Theory (IFW) (Xu, 1997) to find the neutrally stable mode solution and determine the stability and selection criterion ε *. For the system under study, the criterion ε * may be a function of the undercooling parameter T and a properly defined flow parameter F, which measures the strength of convective flow.


Convective Flow Dendritic Growth Peclet Number External Flow Interface Shape 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

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

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