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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 3, Pages 439–444 (Mi vuu550)  

MECHANICS

On the unsteadiness time of primary dendritic growth

E. A. Titovaa, D. V. Alexandrova, P. K. Galenkob

a Department of Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia
b Faculty of Physics and Astronomy, Friedrich Schiller University, Jena, D-07743, Germany

Abstract: The evolution of the growth rate of a dendritic tip for nonisothermal crystal growth from the moment of crystal formation to the moment when the growth rate attains its steady-state value is considered. Gibbs–Thomson condition for highly nonequilibrium rapidly moving crystallization of a pure one-component liquid is used to determine the time dependence of the growth rate of a dendritic tip. It is shown that the dependence of the growth rate on overcooling has the form of an exponential law. Under the condition of constant overcooling an estimation of the time of reaching the steady-state regime of growth is obtained. The analytically derived velocity of growth as a function of time coincides with numerical calculations.

Keywords: dendrites, crystallization.

Funding Agency Grant Number
Russian Science Foundation 16-11-10095


DOI: https://doi.org/10.20537/vm160311

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Bibliographic databases:

Document Type: Article
UDC: 536.255+536.421
MSC: 76D07, 76M45
Received: 15.05.2016

Citation: E. A. Titova, D. V. Alexandrov, P. K. Galenko, “On the unsteadiness time of primary dendritic growth”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:3 (2016), 439–444

Citation in format AMSBIB
\Bibitem{TitAleGal16}
\by E.~A.~Titova, D.~V.~Alexandrov, P.~K.~Galenko
\paper On the unsteadiness time of primary dendritic growth
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 3
\pages 439--444
\mathnet{http://mi.mathnet.ru/vuu550}
\crossref{https://doi.org/10.20537/vm160311}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3558452}
\elib{http://elibrary.ru/item.asp?id=26726588}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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