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|Title:||Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection|
|Authors:||Alexandrov, D. V.|
Galenko, P. K.
Toropova, L. V.
|Publisher:||Royal Society Publishing|
|Citation:||Alexandrov, D. V. Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection / D. V. Alexandrov, P. K. Galenko, L. V. Toropova. — DOI 10.1098/rsta.2017.0215 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2018. — Vol. 2113. — Iss. 376. — 20170215.|
|Abstract:||Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers and n-fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity. A set of nonlinear equations consisting of the solvability criterion and undercooling balance is solved analytically for the tip velocity V and tip diameter ? of dendrites with n-fold symmetry in the absence of convective flow. The case of convective heat and mass transfer mechanisms in a binary mixture occurring as a result of intensive flows in the liquid phase is detailed. A selection criterion that describes such solidification conditions is derived. The theory under consideration comprises previously considered theoretical approaches and results as limiting cases. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.|
CONVECTIVE HEAT AND MASS TRANSFERS
FORCED CONVECTIVE FLOWS
|metadata.dc.description.sponsorship:||Russian Science Foundation, RSF: 16-11-10095|
Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present review paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (grant number 16-11-10095) and the German Space Center Space Management (under contract number 50WM1541).
|RSCF project card:||16-11-10095|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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