Geodesic
On the unsteadiness time of primary dendritic growth
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 439-444 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : dendrites
Keywords: crystallization. 
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E. A. Titova; D. V. Alexandrov; P. K. Galenko. On the unsteadiness time of primary dendritic growth. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 3, pp. 439-444. http://geodesic.mathdoc.fr/item/VUU_2016_26_3_a10/

[1] Herlach D. M., Galenko P., Holland-Moritz D., Metastable solids from undercooled melt, Elsevier, Amsterdam, 2007, 432 pp.

[2] Kurz W., Fisher D. J., Fundamentals of solidification, Trans Tech Publications, Aedermannsdorf, 1992, 305 pp.

[3] Salhoumi A., Galenko P. K., “Gibbs–Thomson condition for the rapidly moving interface in a binary system”, Physica A: Statistical Mechanics and its Applications, 447 (2016), 161–171 | DOI | MR

[4] Celentano D., Cruchaga M., Romero J., El-Ganaoui M., “Numerical simulation of natural convection and phase-change in a horizontal Bridgman apparatus”, International Journal of Numerical Methods for Heat Fluid Flow, 21:4 (2011), 366–376 | DOI

[5] Koss M. B., LaCombe J. C., Tennenhouse L. A., Glicksman M. E., Winsa E. A., “Dendritic growth tip velocities and radii of curvature in microgravity”, Metallurgical and Materials Transactions A, 30:12 (1999), 3177–3190 | DOI

[6] Hultgren R., Desai P. D., Hawkins D. T., Gleiser M., Kelley K. K., Wagman D., Selected values of the thermodynamic properties of the elements, American Society for Metals, Metals Park, OH, 1973, 636 pp.