Selection criterion of a stable dendrite growth in rapid solidification / Alexandrov D.V., Danilov D.A., Galenko P.K. // International Journal of Heat and Mass Transfer. - 2016. - V. 101, l. . - P. 789-799.

ISSN:
00179310
Type:
Article
Abstract:
We present an analysis of a free dendrite growing in a binary mixture under non-isothermal conditions. The stable growth mode is analyzed through the solvability condition giving the stability criterion for the dendrite tip as a function of the thermal Péclet number, PT, and ratio, W=V/VD, of the dendrite velocity V and solute diffusion speed VD in bulk liquid. We extend previous studies limited to small values of the Péclet numbers, by considering the effect of the anisotropy of surface energy for the needle-like dendrite growing at arbitrary Péclet numbers and under local non-equilibrium solute diffusion described by a hyperbolic type of transport equation. Transitions in growth regimes, namely, from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are derived and revealed. Limiting cases of known criteria for anisotropic dendrite growing at small and high growth Péclet numbers are provided. A comparison with the previously obtained criterion of marginal stability of rapidly growing dendrite is made. © 2016 Elsevier Ltd. All rights reserved.
Author keywords:
Crystal; Dendrite; Interface; Non-Fickian diffusion; Solidification; Solute
Index keywords:
Anisotropy; Binary mixtures; Crystals; Dendrites (metallography); Diffusion; Interfaces (materials); Interfacial energy; Ordinary differential equations; Rapid solidification; Solidification; Stabilit
DOI:
10.1016/j.ijheatmasstransfer.2
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Affiliations Ural Federal University, Department of Mathematical Physics, Ekaterinburg, Russian Federation; Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT), Eggenstein-Leopoldshafen, Germany; Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, Jena, Germany
Author Keywords Crystal; Dendrite; Interface; Non-Fickian diffusion; Solidification; Solute
Funding Details Ministry of Education and Science of the Russian Federation
Funding Text AcknowledgmentsD. V. A. acknowledges support from the Russian Foundation for Basic Research (Project No. 16-08-00932), from the Ministry of Education and Science of the Russian Federation (Project No. 315) and from the Government of the Russian Federation under the contract No. 02.A03.21.0006 (act 211). D. A. D. acknowledges the partial support of the Russian Foundation for Basic Research (RFBR Project No. 14-29-10282ofi-m). P. K. G. acknowledges the partial support from German Research Foundation (DFG Project RE 1261/8-2).
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Correspondence Address Danilov, D.A.; Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT)Germany; email: denis.danilov@kit.edu
Publisher Elsevier Ltd
CODEN IJHMA
Language of Original Document English
Abbreviated Source Title Int. J. Heat Mass Transf.
Source Scopus