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|Title:||Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation|
|Authors:||Alexandrov, D. V.|
Ivanov, A. A.
Alexandrova, I. V.
|Publisher:||Royal Society Publishing|
|Citation:||Alexandrov, D. V. Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation / D. V. Alexandrov, A. A. Ivanov, I. V. Alexandrova. — DOI 10.1098/rsta.2017.0217 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2018. — Vol. 2113. — Iss. 376. — 20170217.|
|Abstract:||The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: at + eZ1(t), where Z1(t) = ßt7/2 and Z1(t) = ßt2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters a, ß and e are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. 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.|
DENSITY DISTRIBUTION FUNCTIONS
PHASE TRANSITION INTERFACE
|metadata.dc.description.sponsorship:||Российский Фонд Фундаментальных Исследований (РФФИ), RFBR|
Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present research article. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by project no. 16-08-00932 from the Russian Foundation for Basic Research.
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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