Advertisement

Global Asymptotic Solution for Axisymmetric Dendrite Growth with Small Undercooling

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

Abstract

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.

Keywords

Growth Speed Interface Shape Phase Plane Analysis Needle Shape Slender Body Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. P. Ivantsov Dokl. Akad Nauk. SSSR 58, p. 567 (1974).Google Scholar
  2. 2.
    G. E. Nash and M. E. Glicksman: ACTA Metallurgica Vol. 22, Oct. p. 1283 (1974).CrossRefGoogle Scholar
  3. 3.
    J. S. Langer and H. Muller-Krumbhaar: Acta Matall 26, 1681 (1978).CrossRefGoogle Scholar
  4. 4.
    R. S. Brower, D. A. Kessler, J. Koplik, and H. Levine: Phys. Rev. Letter 51, 1111 (1983).CrossRefGoogle Scholar
  5. 5.
    R. Brower, D. A. Kessler, J. Koplik, and H. Levine: Phys. Rev. A29, 1335 (1984).Google Scholar
  6. 6.
    E. Ben-Jacob, N. D. Goldenfeld, B. G. Kotliar and J. S. Langer: Phys. Rev. Letters 53, 2110 (1984).CrossRefGoogle Scholar
  7. 7.
    D. A. Kessler, J. Koplik, H. Levine Schlumberger-Doll preprint Aug. 29 (1985).Google Scholar
  8. 8.
    Daniel I. Meiron (preprint) (1986).Google Scholar
  9. 9.
    J. S. Langer and D. C. Hong (preprint) (1986).Google Scholar
  10. 10.
    B. Caroli, C. Caroli, C. Misbah, B. Roulet (preprint) (1986).Google Scholar

Copyright information

© Martinus Nijhoff Publishers, Dordrecht 1987

Authors and Affiliations

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

Personalised recommendations