Thermo-solutal and kinetic regimes of an anisotropic dendrite growing under forced convective flow / Alexandrov D.V., Galenko P.K. // Physical Chemistry Chemical Physics. - 2015. - V. 17, l. 29. - P. 19149-19161.

ISSN:
14639076
Type:
Article
Abstract:
A thermo-diffusional problem of a free dendrite growing in a binary mixture is considered analytically. Effects of the anisotropy and convective flow on the stable mode of the dendrite with four-fold crystal symmetry are studied. Special analysis is given for the parabolic dendrite growing at arbitrary Péclet numbers and with small anisotropy of surface energy and atomic kinetics. The stable growth mode is analyzed through the solvability condition giving the stability criterion for the dendrite tip velocity V and dendrite tip diameter ρ as a function of growth Péclet number, Pg, flow Péclet number, Pf, and Reynolds number, Re. Using the obtained criterion of stability, a complete sequence of transitions in growth regimes (namely, from solute diffusion-limited to thermally controlled and further to kinetically-limited regimes) of the anisotropic dendrite is derived and revealed. Limiting cases to known criteria for small and high growth Péclet numbers of the solidifying system with and without convective fluid flow are found. Two-dimensional solidification regimes and scalings obtained are discussed for their extension to three-dimensional dendritic growth. This journal is © the Owner Societies.
Author keywords:
Index keywords:
нет данных
DOI:
10.1039/c5cp03018h
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Affiliations Ural Federal University, Department of Mathematical Physics, Ekaterinburg, Russian Federation; Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, Jena, Germany
Funding Details 02.A03.21.0006, Russian Foundation for Basic Research; 13-01-96013-Ural, RFBR, Russian Foundation for Basic Research; 14-29-10282ofi-m, RFBR, Russian Foundation for Basic Research; 315, Russian Foundation for Basic Research
References Langer, J.S., Hong, D.C., (1986) Phys. Rev. A: At., Mol., Opt. Phys., 34, p. 1462; Kessler, D.A., Koplik, J., Levine, H., (1988) Adv. Phys., 37, p. 255; Barbieri, A., (1987) Phys. Rev. A: At., Mol., Opt. Phys., 36, p. 5353; Saville, D.A., Beaghton, J.P., (1988) Phys. Rev. A: At., Mol., Opt. Phys., 37, p. 3423; Pelcé, P., (1988) Dynamics of Curved Fronts, , Academic Press, Boston; Ben Amar, M., Brener, E.A., (1993) Phys. Rev. Lett., 71, p. 589; Brener, E.A., (1990) J. Cryst. Growth, 99, p. 165; Brener, E., Mel'nikov, V.I., (1991) Adv. Phys., 40, p. 53; Tong, X., Beckermann, C., Karma, A., Lee, Q., (2001) Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 63, p. 061601; Jeong, J.-H., Goldenfeld, N., Dantzig, J.A., (2001) Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 64, p. 041602; Herlach, D.M., Galenko, P.K., Holland-Moritz, D., (2007) Metastable Solids from Undercooled Melts, , Elsevier, Amsterdam; Aryanfar, A., Brooks, D.J., Colussi, A.J., Merinov, B.V., Goddard, W.A., Hoffmann, M.R., (2015) Phys. Chem. Chem. Phys., 17, p. 8000; Bieker, G., Winter, M., Bieker, P., (2015) Phys. Chem. Chem. Phys., 17, p. 8670; Xiao, J.P., Xie, Y., Tang, R., Chen, M., Tian, X.B., (2001) Adv. Mater., 13, p. 1887; Xiao, J.P., Xie, Y., Tang, R., Luo, W., (2002) J. Mater. Chem., 12, p. 1148; Chow, A., Toomre, D., Garret, W., Mellman, I., (2002) Nature, 418, p. 988; Kuang, D., Xu, A., Fang, Y., Liu, H., Frommen, C., Fenske, D., (2003) Adv. Mater., 15, p. 1747; Zhang, Q., Liu, S.-J., Yu, S.-H., (2009) J. Mater. Chem., 19, p. 207; Wen, X., Xie, Y.T., Mak, M.W.C., Cheung, K.Y., Li, X.Y., Renneberg, R., Yang, S., (2006) Langmuir, 22, p. 4836; Zhang, Q., Yao, W.T., Chen, X.Y., Zhu, L.W., Fu, Y.B., Zhang, G.B., Sheng, L.S., Yu, S.H., (2007) Cryst. Growth Des., 7, p. 1423; Cheng, Y., Wang, Y., Chen, D., Bao, F., (2005) J. Phys. Chem. B, 109, p. 794; Qin, Y., Song, Y., Sun, N., Zhao, N., Li, M., Qi, L., (2008) Chem. Mater., 20, p. 3965; Shi, L., Wang, A., Zhang, T., Zhang, B., Su, D., Li, H., Song, Y., (2013) J. Phys. Chem. C, 117, p. 12526; Binder, S., Galenko, P.K., Herlach, D.M., (2013) Philos. Mag. Lett., 93, p. 608; Binder, S., Galenko, P.K., Herlach, D.M., (2014) J. Appl. Phys., 115, p. 053511; Chernov, A.A., (1984) Modern Crystallography III, , Springer, Berlin; Tiller, W.A., (1991) The Science of Crystallization. Microscopic Interfacial Phenomena, , Cambridge University Press, Cambridge; Kreuer, K.D., (2003) Annu. Rev. Mater. Res., 33, p. 333; Shriver, D.F., Atkins, P.W., Overton, T.L., Rourke, J.P., Weller, M.T., Armstrong, F.A., (2006) Inorganic Chemistry, , ed. W. H. Freeman; Stuhrmann, C.H.J., Kreiterling, H., Funke, K., (2002) Solid State Ionics, 66, p. 109; Scheel, H.J., Capper, P., (2008) Crystal Growth Technology: From Fundamentals and Simulation to Large-scale Production, , Wiley-VCH, Weinheim; Tanveer, S., (1989) Phys. Rev. A: At., Mol., Opt. Phys., 40, p. 4756; Kruskal, M., Segur, H., (1987) Phys. D, 28, p. 228; Ben Amar, M., Bouissou, Ph., Pelcé, P., (1988) J. Cryst. Growth, 92, p. 97; Von Kurnatowski, M., Grillenbeck, T., Kassner, K., (2013) Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 87, p. 042405; Dash, S.K., Gill, W.N., (1984) Int. J. Heat Mass Transfer, 27, p. 1345; Bouissou, P., Pelcé, P., (1989) Phys. Rev. A: At., Mol., Opt. Phys., 40, p. 6673; Alexandrov, D.V., Galenko, P.K., (2013) Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 87, p. 062403; Pelcé, P., Bensimon, D., (1987) Nucl. Phys. B, 2, p. 259; Brener, E.A., Mel'nikov, V.I., (1990) J. Phys., 51, p. 157; Alexandrov, D.V., Galenko, P.K., (2014) Phys.-Usp., 57 (8), p. 771; Ben Amar, M., Pelcé, P., (1989) Phys. Rev. A: At., Mol., Opt. Phys., 39, p. 4263; Müller-Krumbhaar, H., Abel, T., Brener, E., Hartmann, M., Eissfeldt, N., Temkin, D., (2002) JSME Int. J., Ser. B, 45, p. 129; Brener, E.A., (1993) Phys. Rev. Lett., 71, p. 3653; Bragard, J., Karma, A., Lee, Y.H., Plapp, M., (2002) Interface Sci., 10 (2-3), p. 121; Nestler, B., Danilov, D., Galenko, P.K., (2005) J. Comput. Phys., 207, p. 221; Galenko, P.K., Herlach, D.M., (2006) Complexus Mundi: Emergent Patterns in Nature, pp. 199-208. , ed. M. M. Novak, World Scientific, Singapore; Schwarz, M., Karma, A., Eckler, K., Herlach, D.M., (1994) Phys. Rev. Lett., 73, p. 1380; Schick, M., Brillo, J., Egry, I., (2009) Int. J. Cast Met. Res., 22, p. 82; Asta, M., Hoyt, J.J., Karma, A., (2002) Phys. Rev. B: Condens. Matter Mater. Phys., 66, p. 100101; Steinbach, I., (2009) Modell. Simul. Mater. Sci. Eng., 17, p. 073001; Galenko, P.K., Danilov, D.A., (1997) Phys. Lett. A, 235, p. 271; Hartmann, H., Galenko, P.K., Holland-Moritz, D., Kolbe, M., Herlach, D.M., Shuleshova, O., (2008) J. Appl. Phys., 103, p. 073509; Galenko, P.K., Kolbe, M., Herlach, D.M., Rettenmayr, M., (2014) Metall. Res. Technol., 111, p. 295; Lin, T.-H., Lin, C.-W., Liu, H.-H., Sheub, J.-T., Hung, W.-H., (2011) Chem. Commun., 47, p. 2044; Zhang, Y., Sun, S., Zhang, X., Tang, L., Song, X., Yang, Z., (2014) Phys. Chem. Chem. Phys., 16, p. 18918; Barbieri, A., Langer, J.S., (1989) Phys. Rev. A: At., Mol., Opt. Phys., 39, p. 5314; Kochin, N.E., Kibel, I.A., Roze, N.V., (1964) Theoretical Hydromechanics, , Interscience, New York; Ben-Jackob, E., Godbey, R., Goldenfeld, N.D., Koplik, J., Levin, H., Mueller, T.E., Sander, L.M., (1985) Phys. Rev. Lett., 55, p. 1315; Dougherty, A., Gollub, J., (1988) Phys. Rev. A: At., Mol., Opt. Phys., 38, p. 3043; Chan, S.-K., Reimer, H.-H., Kahlweit, M., (1976) J. Cryst. Growth, 32, p. 303; Brener, E., Levin, H., (1991) Phys. Rev. A: At., Mol., Opt. Phys., 43, p. 883; Kantorovich, L., Akilov, G., (1964) Functional Analysis in Normed Spaces, , Macmillan, New York; Rudin, W., (1973) Functional Analysis, , McGraw Hill, New York; Fischaleck, T., Kassner, K., (2008) Europhys. Lett., 81, p. 54004; Von Kurnatowski, M., Kassner, K., (2014) J. Phys. A: Math. Theor., 47, p. 325202
Correspondence Address Galenko, P.K.; Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische FakultätGermany
Publisher Royal Society of Chemistry
CODEN PPCPF
Language of Original Document English
Abbreviated Source Title Phys. Chem. Chem. Phys.
Source Scopus