Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/89988
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.
Issue Date: 2018
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.
Keywords: CRYSTAL GROWTH
MOVING BOUNDARIES
MUSHY LAYER
NUCLEATION
PHASE TRANSITIONS
CRYSTAL GROWTH
DISTRIBUTION FUNCTIONS
KINETICS
LIQUIDS
PHASE TRANSITIONS
SUPERCOOLING
DENSITY DISTRIBUTION FUNCTIONS
DIFFERENTIAL MODELS
MOVING BOUNDARIES
MUSHY LAYER
PHASE TRANSITION INTERFACE
PHASE-TRANSITION BOUNDARY
SUPERCOOLED LIQUIDS
SUPERSATURATED SOLUTIONS
NUCLEATION
URI: http://hdl.handle.net/10995/89988
https://elar.urfu.ru/handle/10995/89988
metadata.dc.rights: info:eu-repo/semantics/openAccess
SCOPUS ID: 85040632971
WOS ID: 000419529400014
PURE ID: 6432333
ISSN: 1364-503X
DOI: 10.1098/rsta.2017.0217
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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