Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/89988
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dc.contributor.authorAlexandrov, D. V.en
dc.contributor.authorIvanov, A. A.en
dc.contributor.authorAlexandrova, I. V.en
dc.date.accessioned2020-09-29T09:45:32Z-
dc.date.available2020-09-29T09:45:32Z-
dc.date.issued2018-
dc.identifier.citationAlexandrov, 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.en
dc.identifier.issn1364-503X-
dc.identifier.otherhttps://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0217pdf
dc.identifier.other1good_DOI
dc.identifier.other2ce494e1-224d-4644-817b-0e6ffeb4c305pure_uuid
dc.identifier.otherhttp://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85040632971m
dc.identifier.urihttp://hdl.handle.net/10995/89988-
dc.identifier.urihttps://elar.urfu.ru/handle/10995/89988en
dc.description.abstractThe 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.en
dc.description.sponsorshipРоссийский Фонд Фундаментальных Исследований (РФФИ), RFBRen
dc.description.sponsorshipData 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.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherRoyal Society Publishingen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourcePhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.subjectCRYSTAL GROWTHen
dc.subjectMOVING BOUNDARIESen
dc.subjectMUSHY LAYERen
dc.subjectNUCLEATIONen
dc.subjectPHASE TRANSITIONSen
dc.subjectCRYSTAL GROWTHen
dc.subjectDISTRIBUTION FUNCTIONSen
dc.subjectKINETICSen
dc.subjectLIQUIDSen
dc.subjectPHASE TRANSITIONSen
dc.subjectSUPERCOOLINGen
dc.subjectDENSITY DISTRIBUTION FUNCTIONSen
dc.subjectDIFFERENTIAL MODELSen
dc.subjectMOVING BOUNDARIESen
dc.subjectMUSHY LAYERen
dc.subjectPHASE TRANSITION INTERFACEen
dc.subjectPHASE-TRANSITION BOUNDARYen
dc.subjectSUPERCOOLED LIQUIDSen
dc.subjectSUPERSATURATED SOLUTIONSen
dc.subjectNUCLEATIONen
dc.titleAnalytical solutions of mushy layer equations describing directional solidification in the presence of nucleationen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.1098/rsta.2017.0217-
dc.identifier.scopus85040632971-
local.affiliationDepartment of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federationen
local.contributor.employeeAlexandrov, D.V., Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federationru
local.contributor.employeeIvanov, A.A., Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federationru
local.contributor.employeeAlexandrova, I.V., Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russian Federationru
local.issue376-
local.volume2113-
dc.identifier.wos000419529400014-
local.identifier.pure6432333-
local.description.order20170217-
local.identifier.eid2-s2.0-85040632971-
local.fund.rffi16-08-00932-
local.identifier.wosWOS:000419529400014-
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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