Cellular and Dendritic Fronts in Directional Solidification: Experiments by the Light of Pattern Selection

  • B. Billia
  • H. Jamgotchian
  • L. Capella
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)


Based on the analogy between Saffman-Taylor fingers in a Hele-Shaw cell and directional solidification, a model is presented for structure selection during cellular or dendritic growth. Three distinct steps allow a direct comparison with experiments all along the analysis. By using dimensionless periodicity, tip radius and composition, a unified approach is made possible which depends only on the solute partition coefficient and either a parameter L or the relative magnitudes of the characteristic lengths of the problem. Conversely, a new formulation of experimental data can give some information on capillary selection. Finally, the influence of fluid flow in the melt on pattern selection is shortly discussed, as an example of effects that would be worth introducing into the theory.


Directional Solidification Peclet Number Marginal Stability Solidification Front Pattern Selection 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • B. Billia
    • 1
  • H. Jamgotchian
    • 1
  • L. Capella
    • 1
  1. 1.Laboratoire de Physique CristallineFaculté de St. JérômeMarseille Cedex 13France

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