Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics
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| Автор |
Titova, E. A.
Alexandrov, D. V. Toropova, L. V. |
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| Тематика |
BOUNDARY INTEGRAL EQUATION
CURVED SOLID–LIQUID INTERFACE PHASE TRANSITIONS UNDERCOOLED MELT |
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| Описание |
In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion problem of binary melt crystallization with convection. Analyzing this equation coupled with the selection criterion for a stationary dendritic growth in the form of a parabolic cylinder, we show that nonlinear effects stemming from the liquidus equation and atomic kinetics play a decisive role. Namely, the dendrite tip velocity and diameter, respectively, become greater and lower with the increasing deviation of the liquidus equation from a linear form. In addition, the dendrite tip velocity can substantially change with variations in the power exponent of the atomic kinetics. In general, the theory under consideration describes the evolution of a curvilinear crystallization front, as well as the growth of solid phase perturbations and patterns in undercooled binary melts at local equilibrium conditions (for low and moderate Péclet numbers). In addition, our theory, combined with the unsteady selection criterion, determines the non-stationary growth rate of dendritic crystals and the diameter of their vertices. © 2022 by the authors.
Ministry of Education and Science of the Russian Federation, Minobrnauka, (075-02-2022-877) Russian Science Foundation, RSF, (21-71-00044) The present research work consists of theoretical and computational parts, which were supported by different financial sources. E.A.T. acknowledges the Russian Science Foundation (Project No. 21-71-00044) for the development of the boundary integral method. L.V.T. is grateful to the financial support from the Ministry of Science and Higher Education of the Russian Federation (Project 075-02-2022-877 for the development of the regional scientific and educational mathematical center “Ural Mathematical Center”) for the development of the selection criteria, computer simulations, and numerical examples. |
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| Дата |
2024-04-08T11:08:05Z
2024-04-08T11:08:05Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Titova, EA, Alexandrov, DV & Toropova, LV 2022, 'Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics', Crystals, Том. 12, № 11, стр. 1657. https://doi.org/10.3390/cryst12111657
Titova, E. A., Alexandrov, D. V., & Toropova, L. V. (2022). Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics. Crystals, 12(11), 1657. https://doi.org/10.3390/cryst12111657 2073-4352 Final All Open Access; Gold Open Access https://www.mdpi.com/2073-4352/12/11/1657/pdf?version=1669023263 https://www.mdpi.com/2073-4352/12/11/1657/pdf?version=1669023263 http://elar.urfu.ru/handle/10995/131574 10.3390/cryst12111657 85149462293 000895256400001 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//21-71-00044
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
MDPI
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| Источник |
Crystals
Crystals |
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