Global Asymptotic Solution for Axisymmetric Dendrite Growth with Small Undercooling

  • Jian-Jun Xu
Part of the NATO ASI Series book series (NSSE, volume 125)


Stationary non-isothermal growth of a needle-like crystal is considered. When the undercooling parameter is very small, the dendrite will always be slender. Hence slender body theory is applicable. We obtain a self consistent uniformly valid asymptotic solution to the problems. Our results show that as long as the surface tension parameter is small enough there always exists a smooth needle like solution for a given undercooling temperature. This non-isothermal needle is close to the Ivantsov parabaloid.


Growth Speed Interface Shape Phase Plane Analysis Needle Shape Slender Body Theory 
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Copyright information

© Martinus Nijhoff Publishers, Dordrecht 1987

Authors and Affiliations

  • Jian-Jun Xu
    • 1
  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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