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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering SciencesVolume 378, Issue 2171, 15 May 2020, Article number 0243

The shape of dendritic tips(Review)(Open Access)

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  • aDepartment of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federation
  • bPhysikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, Jena, 07743, Germany

Abstract

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. © 2020 The Author(s) Published by the Royal Society. All rights reserved.

Author keywords

Boundary integral methodDendritesDendritic tipsHeat and mass transferPhase transformations

Indexed keywords

Engineering uncontrolled termsBinary systemsDendritic growthFractional powerLimiting case
Engineering main heading:Engineering
EMTREE medical terms:articlecomputer simulationdendriteheat

Funding details

Funding sponsor Funding number Acronym
Russian Science Foundation16-11-10095RSF

  • 1

    Competing interests. We declare we have no competing interests. Funding. Authors thank Efim Brener and Mathis Plapp for the fruitful discussions. This work was supported by the Russian Science Foundation (grant no. 16-11-10095).

  • ISSN: 1364503X
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1098/rsta.2019.0243
  • PubMed ID: 32279631
  • Document Type: Review
  • Publisher: Royal Society Publishing

  Galenko, P.K.; Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, Russian Federation;
© Copyright 2020 Elsevier B.V., All rights reserved.

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