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Cellular Profiles in Directional Solidification: Is the Saffman-Taylor Branch of Solutions the Physically Relevant One?

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Growth and Form

Part of the book series: NATO ASI Series ((NSSB,volume 276))

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Abstract

We summarize the main results and implications of our work on the calculation of cellular shapes in directional solidification using the asymptotic matching method introduced by Dombre and Hakim. For cells with narrow grooves, the finite Péclet number corrections to the cellular profiles that reduce to the Saffman-Taylor solutions for Péclet number p → 0, turn out to be small. We argue that there are several discrepancies between the behavior of these Saffman-Taylor like cells and those observed in experiments as well as numerical studies that suggest that this branch of solutions is not always the physically relevant one for directional solidification.

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Author information

Author notes

  1. Wim van Saarloos

    Present address: Instituut-Lorentz, University of Leiden, P.O. Box 9506, 2300 RA, Leiden, The Netherlands

  2. John D. Weeks

    Present address: Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA

Authors and Affiliations

  1. AT&T Bell Laboratories, Murray Hill, New Jersey, 07974, USA

    Wim van Saarloos & John D. Weeks

Authors
  1. Wim van Saarloos
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  2. John D. Weeks
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Editor information

Editors and Affiliations

  1. Ecole Normale Supérieure, Paris, France

    M. Ben Amar  & P. Tabeling  & 

  2. Université de Provence-St. Jerome, Marseille, France

    P. Pelcé

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© 1991 Plenum Press, New York

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van Saarloos, W., Weeks, J.D. (1991). Cellular Profiles in Directional Solidification: Is the Saffman-Taylor Branch of Solutions the Physically Relevant One?. In: Amar, M.B., Pelcé, P., Tabeling, P. (eds) Growth and Form. NATO ASI Series, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1357-1_15

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  • DOI: https://doi.org/10.1007/978-1-4684-1357-1_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1359-5

  • Online ISBN: 978-1-4684-1357-1

  • eBook Packages: Springer Book Archive

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