Recent Progress in the Theory of the Growth of Needle Crystals

  • M. Ben Amar
  • Y. Pomeau
Part of the NATO ASI Series book series (NSSE, volume 183)


This presents a review of recent progress made in the theory of growth of needle crystal. We consider first the low undercooling limit and then the finite undercooling limit, where the result of a detailed calculation is compared with recent experiments. We review first the now classical Ivantsov solution and explain how to derive the proper scaling laws from simple boundary layer estimates. This allows us to consider then the effect of an imposed axial flow on the growth. We find by using scaling arguments several regimes of growth for a needle crystal under those conditions. The growth velocity and tip radius are derived, depending on the fluid velocity and undercooling. Finally we present results relevant for a finite dimensionless undercooling, including in particular kinetic effects, and we compare this with recent experiments on rapid solidification of metals and alloys.


Boundary Layer Peclet Number Thermal Boundary Layer Axial Flow Integrodifferential Equation 
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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • M. Ben Amar
    • 1
  • Y. Pomeau
    • 1
  1. 1.Laboratoire de Physique StatistiqueEcole Normale SupérieureParis Cedex 05France

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