Pattern selection in a boundary-layer model of dendritic growth in the presence of impurities

Alain Karma, B Kotliar

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We have analyzed, in the context of a boundary-layer model, the problem of pattern selection in dendritic growth in a situation where impurities are present in the undercooled liquid. We find that the tip-velocity selection criterion that has been proposed recently for the geometrical model and the boundary-layer model of a pure substance can be extended, in a nontrivial way, to this more complex situation where two coupled diffusion fields (temperature and solute) determine the interface dynamics. Our model predicts a sharp enhancement of tip velocity in good qualitative agreement with experiment. This agreement is consistent with the conjecture that a solvability condition can be used to determine the operating point of the dendrite in the full nonlocal problem.

Original languageEnglish (US)
Pages (from-to)3266-3275
Number of pages10
JournalPhysical Review A
Volume31
Issue number5
DOIs
StatePublished - Jan 1 1985

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boundary layers
impurities
dendrites
solutes
temperature distribution
augmentation
liquids

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

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Pattern selection in a boundary-layer model of dendritic growth in the presence of impurities. / Karma, Alain; Kotliar, B.

In: Physical Review A, Vol. 31, No. 5, 01.01.1985, p. 3266-3275.

Research output: Contribution to journalArticle

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