Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/90059
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.
Issue Date: 2018
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.
Keywords: CRYSTALLINE ANISOTROPY
DENDRITIC GROWTH
FORCED CONVECTION
KINETICS
PHASE TRANSITIONS
SELECTION THEORY
ANISOTROPY
BINARY MIXTURES
CRYSTAL SYMMETRY
CRYSTALLINE MATERIALS
ENZYME KINETICS
FORCED CONVECTION
GROWTH (MATERIALS)
GROWTH KINETICS
KINETICS
MASS TRANSFER
NONLINEAR EQUATIONS
PHASE TRANSITIONS
VORTEX FLOW
CONVECTIVE HEAT AND MASS TRANSFERS
CRYSTALLINE ANISOTROPY
DENDRITIC GROWTH
FORCED CONVECTIVE FLOWS
SELECTION CRITERIA
SELECTION THEORY
SOLIDIFICATION CONDITION
THEORETICAL APPROACH
HEAT CONVECTION
URI: http://hdl.handle.net/10995/90059
https://elar.urfu.ru/handle/10995/90059
metadata.dc.rights: info:eu-repo/semantics/openAccess
SCOPUS ID: 85040558527
WOS ID: 000419529400012
PURE ID: 6432458
ISSN: 1364-503X
DOI: 10.1098/rsta.2017.0215
metadata.dc.description.sponsorship: Russian Science Foundation, RSF: 16-11-10095
50WM1541
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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