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## Archive of Issues

Germany; Russia Jena; Yekaterinburg
Year
2016
Volume
26
Issue
3
Pages
299-311
 Section Mathematics Title Influence of convective flow on the growth of pure and alloyed dendrite Author(-s) Kazak O.V.a, Galenko P.K.b, Alexandrov D.V.a Affiliations Ural Federal Universitya, University of Jenab Abstract The paper presents the model of anisotropic growth of dendritic crystallization of chemically pure and binary liquid (solution or melt) based on forced convection of the liquid phase. The dependencies of the growth rate and the radius of the top of a dendrite from under-cooling fluid in cases of a chemically pure material and alloys are presented. A comparative analysis of the influence of forced convection on the dendrite growth kinetics is carried out. Evaluation of growth rate and morphology of dendrite by high-speed crystal growth model was done. The contribution of convective flow and the anisotropic properties of the liquid-crystal boundary were taking into account. The model is also used hyperbolic diffusion equation to describe the non-equilibrium impurity capture by crystal surface, which occurs under the rapid crystals growth. Keywords crystallization, dendrite growth, numerical simulation, convection UDC 51-72 MSC 76D07, 76M45 DOI 10.20537/vm160301 Received 15 May 2016 Language Russian Citation Kazak O.V., Galenko P.K., Alexandrov D.V. Influence of convective flow on the growth of pure and alloyed dendrite, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 299-311. References Flemings M.C. Solidification processing, New York: McGraw-Hill, 1974. Chernov A.A. Modern crystallography III. Crystal growth, Berlin-Heidelberg: Springer, 1984. DOI: 10.1007/978-3-642-81835-6 Kurz W., Fisher D.J. Dendrite growth at the limit of stability: tip radius and spacing, Acta Metallurgica, 1981, vol. 29, issue 1, pp. 11-20. DOI: 10.1016/0001-6160(81)90082-1 Lipton J., Glicksman M.E., Kurz W. Dendritic growth into undercooled alloy metals, Materials Science and Engineering, 1984, vol. 65, issue 1, pp. 57-63. DOI: 10.1016/0025-5416(84)90199-X Boettinger W.J., Coriell S.R. Microstructure formation in rapidly solidified alloys, Science and Technology of the Undercooled Melt, Eds.: Sahm P.R., Jones H., Adam C.M. Springer, 1986, pp. 81-109. DOI: 10.1007/978-94-009-4456-5_5 Lipton J., Kurz W., Trivedi R. Rapid dendrite growth in undercooled alloys, Acta Metallurgica, 1987, vol. 35, issue 4, pp. 957-964. DOI: 10.1016/0001-6160(87)90174-X Trivedi R., Lipton J., Kurz W. Effect of growth rate dependent partition coefficient on the dendritic growth in undercooled melts, Acta Metallurgica, 1987, vol. 35, issue 4, pp. 965-970. DOI: 10.1016/0001-6160(87)90175-1 Boettinger W.J., Coriell S.R., Trivedi R. Application of dendritic growth theory to the interpretation of rapid solidification microstructures, Rapid Solidification Processing: Principles and Technologies IV, Eds.: Mehrabian R., Parrish P.A. Claitor, 1988. Herlach D.M., Matson D.M. (Eds.) Solidification of containerless undercooled melts, Wiley, 2012. DOI: 10.1002/9783527647903 Hoyt J.J., Asta M., Karma A. Atomistic and continuum modeling of dendritic solidification, Materials Science and Engineering: R: Reports, 2003, vol. 41, issue 6, pp. 121-163. DOI: 10.1016/S0927-796X(03)00036-6 Funke O., Phanikumar G., Galenko P.K., Chernova L., Reutzel S., Kolbe M., Herlach D.M. Dendrite growth velocity in levitated undercooled nickel melts, Journal of Crystal Growth, 2006, vol. 297, issue 1, pp. 211-222. DOI: 10.1016/j.jcrysgro.2006.08.045 Binder S., Galenko P.K., Herlach D.M. Faceting of a rough solid-liquid interface of a metal induced by forced convection, Philosophical Magazine Letters, 2013, vol. 93, issue 10, pp. 608-617. DOI: 10.1080/09500839.2013.830201 Langer J.S., Hong D.C. Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy, Physical Review A, 1986, vol. 34, issue 2, pp. 1462-1471. DOI: 10.1103/PhysRevA.34.1462 Pelcé P., Bensimon D. Theory of dendrite dynamics, Nuclear Physics B - Proceedings Supplements, 1987, vol. 2, pp. 259-270. DOI: 10.1016/0920-5632(87)90022-3 Ben Amar M., Pelcé P. Impurity effect on dendritic growth, Physical Review A, 1989, vol. 39, issue 8, pp. 4263-4269. DOI: 10.1103/PhysRevA.39.4263 Brener E.A. Effects of surface energy and kinetics on the growth of needle-like dendrites, Journal of Crystal Growth, 1990, vol. 99, issues 1-4, pp. 165-170. DOI: 10.1016/0022-0248(90)90505-F Galenko P.K., Danilov D.A. Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt, Physics Letters A, 1997, vol. 235, issue 3, pp. 271-280. DOI: 10.1016/S0375-9601(97)00562-8 Galenko P.K., Danilov D.A. Model for free dendritic alloy growth under interfacial and bulk phase nonequilibrium conditions, Journal of Crystal Growth, 1999, vol. 197, issue 4, pp. 992-1002. DOI: 10.1016/S0022-0248(98)00977-4 Yang Y., Humadi H., Buta D., Laird B.B., Sun D., Hoyt J.J., Asta M. Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts, Physical Review Letters, 2011, vol. 107, issue 2, 025505, 4 p. DOI: 10.1103/PhysRevLett.107.025505 Jou D., Galenko P. Coarse graining for the phase-field model of fast phase transitions, Physical Review E, 2013, vol. 88, issue 4, 042151, 8 p. DOI: 10.1103/PhysRevE.88.042151 Herlach D.M. Non-equilibrium solidification of undercooled metallic metls, Materials Science and Engineering: R: Reports, 1994, vol. 12, issues 4-5, pp. 177-272. DOI: 10.1016/0927-796X(94)90011-6 Herlach D., Galenko P., Holland-Moritz D. Metastable solids from undercooled melts, Amsterdam: Elsevier, 2007. Alexandrov D.V., Danilov D.A., Galenko P.K. Selection criterion of a stable dendrite growth in rapid solidification, International Journal of Heat and Mass Transfer, 2016, vol. 101, pp. 789-799. DOI: 10.1016/j.ijheatmasstransfer.2016.05.085 Galenko P.K., Danilov D.A., Reuther K., Alexandrov D.V., Rettenmayr M., Herlach D.M. Effect of convective flow on stable dendritic growth in rapid solidification of a binary alloy, Journal of Crystal Growth, 2016. DOI: 10.1016/j.jcrysgro.2016.07.042 Barbieri A., Langer J.S. Predictions of dendritic growth rates in the linearized solvability theory, Physical Review A, 1989, vol. 39, issue 10, pp. 5314-5325. DOI: 10.1103/PhysRevA.39.5314 Alexandrov D.V., Galenko P.K. Selection criterion of stable dendritic growth at arbitrary Peclét numbers with convection, Physical Review E, 2013, vol. 87, 062403, 5 p. DOI: 10.1103/PhysRevE.87.062403 Alexandrov D.V., Galenko P.K. Dendrite growth under forced convection: analysis methods and experimental tests, Physics-Uspekhi, 2014, vol. 57, issue 8, pp. 771-786. DOI: 10.3367/UFNe.0184.201408b.0833 Galenko P. Solute trapping and diffusionless solidification in a binary system, Physical Review E, 2007, vol. 76, issue 3, 031606, 9 p. DOI: 10.1103/PhysRevE.76.031606 Galenko P. Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy, Physical Review B, 2002, vol. 65, issue 14, 144103, 11 p. DOI: 10.1103/PhysRevB.65.144103 Hartmann H., Galenko P.K., Holland-Moritz D., Kolbe M., Herlach D.M., Shuleshova O. Nonequilibrium solidification in undercooled $Ti_{45}Al_{55}$ melts, Journal of Applied Physics, 2008, vol. 103, issue 7, 073509. DOI: 10.1063/1.2903920 Alexandrov D.V., Galenko P.K. Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow, Physical Chemistry Chemical Physics, 2015, vol. 17, pp. 19149-19161. DOI: 10.1039/C5CP03018H Ben Amar M. Theory of needle-crystal, Physica D: Nonlinear Phenomena, 1988, vol. 31, issue 3, pp. 409-423. DOI: 10.1016/0167-2789(88)90006-1 Brener E., Melnikov V.I. Velocity selection and instability spectrum in 3D dendritic growth, Journal of Experimental and Theoretical Physics, 1995, vol. 80, no. 2, pp. 341-345. http://www.jetp.ac.ru/cgi-bin/dn/e_080_02_0341.pdf Bouissou P., Pelcé P. Effect of a forced flow on dendritic growth, Physical Review A, 1989, vol. 40, issue 11, pp. 6673-6680. DOI: 10.1103/PhysRevA.40.6673 Müller-Krumbhaar H., Abel T., Brener E., Hartmann M., Eissfeldt N., Temkin D. Growth-morphologies in solidification and hydrodynamics, JSME International Journal Series B, 2002, vol. 45, no. 1, pp. 129-132. DOI: 10.1299/jsmeb.45.129 Full text