Selection criterion for the growing dendritic tip at the inner core boundary / Alexandrov D.V., Galenko P.K. // Journal of Physics A: Mathematical and Theoretical. - 2013. - V. 46, l. 19.

ISSN:
17518113
Type:
Article
Abstract:
A free dendrite growth at the Earth's inner core boundary is analyzed using a sharp interface model. A new selection criterion of the dendrite tip's stable growth into non-isothermal binary melt with convection and pressure effects for the 2D and 3D axisymmetric models is derived. The criterion obtained combines known analytic results for the dendrite growth under forced convection in a pure system and dendrite growth in a stagnant binary system. The generalized selection criterion represents a condition connecting the main physical parameters of the Earth's inner core. © 2013 IOP Publishing Ltd.
Author keywords:
Index keywords:
нет данных
DOI:
10.1088/1751-8113/46/19/195101
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84877771684&doi=10.1088%2f1751-8113%2f46%2f19%2f195101&partnerID=40&md5=728e3486944d878052444fca9ae9a7e0
Соавторы в МНС:
Другие поля
Поле Значение
Art. No. 195101
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84877771684&doi=10.1088%2f1751-8113%2f46%2f19%2f195101&partnerID=40&md5=728e3486944d878052444fca9ae9a7e0
Affiliations Department of Mathematical Physics, Ural Federal University, Lenin ave. 51, Ekaterinburg, 620000, Russian Federation; Fridrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, Löbdergraben Strasse 32, D-07743 Jena, Germany; Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft-und Raumfahrt (DLR), D-51170 Köln, Germany
References Verhoogen, J., Heat balance of the Earth's core (1961) Geophys. J. Int., 4 (S0), pp. 276-281. , 10.1111/j.1365-246X.1961.tb06819.x 0956-540X; Braginsky, S.I., Structure of the F layer and reasons for convection in the Earth's core (1963) Dokl. Akad. Nauk SSSR, 149, pp. 8-10. , 0002-3264; Shimizu, H., Poirier, J.P., Le Mouel, J.L., On crystallization at the inner core boundary (2005) Physics of the Earth and Planetary Interiors, 151 (1-2), pp. 37-51. , DOI 10.1016/j.pepi.2005.01.001, PII S0031920105000269; Loper, D.E., A model of the dynamical structure of Earth's outer core (2000) Physics of the Earth and Planetary Interiors, 117 (1-4), pp. 179-196. , DOI 10.1016/S0031-9201(99)00096-5, PII S0031920199000965, Study of the Earths deep interior (voyage au centre de la Terre); Loper, D.E., Dynamo energetics and the structure of the outer core (1989) Geophys. Astrophys. Fluid Dyn., 49 (1-4), pp. 213-219. , 10.1080/03091928908243473 0309-1929; Bloxham, J., Jackson, A., Fluid flow near the surface of Earth's outer core (1991) Rev. Geophys., 29 (1), pp. 97-120. , 10.1029/90RG02470 8755-1209; Kurz, W., Fisher, D.J., (1986) Fundamentals of Solidification; Buyevich Yu, A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) International Journal of Heat and Mass Transfer, 49 (25-26), pp. 4903-4909. , DOI 10.1016/j.ijheatmasstransfer.2006.05.046, PII S001793100600411X; Alexandrov, D.V., Aseev, D.L., Directional solidification with a two-phase zone: thermodiffusion and temperature-dependent diffusivity (2006) Computational Materials Science, 37 (1-2), pp. 1-6. , DOI 10.1016/j.commatsci.2005.12.019, PII S0927025605003472; Alexandrova, I.V., Alexandrov, D.V., Aseev, D.L., Bulitcheva, S.V., Mushy layer formation during solidification of binary alloys from a cooled wall: The role of boundary conditions (2009) Acta Phys. Pol., 115, pp. 791-794. , 0587-4246 A; Loper, D.E., Roberts, P.H., On the motion of an iron-alloy core containing a slurry (1978) Geophys. Astrophys. Fluid Dyn., 9 (1), pp. 289-321. , 10.1080/03091927708242333 0309-1929; Loper, D.E., Roberts, P.H., A study of conditions at the inner core boundary of the Earth (1981) Phys. Earth Planet. Inter., 24 (4), pp. 302-307. , 10.1016/0031-9201(81)90117-5 0031-9201; Fearn, D.R., Loper, D.E., Roberts, P.H., Structure of the Earth's inner core (1981) Nature, 292 (5820), pp. 232-233. , 10.1038/292232a0 0028-0836; Deguen, R., Alboussiere, T., Brito, D., On the existence and structure of a mush at the inner core boundary of the Earth (2007) Physics of the Earth and Planetary Interiors, 164 (1-2), pp. 36-49. , DOI 10.1016/j.pepi.2007.05.003, PII S0031920107001021; Alexandrov, D.V., Malygin, A.P., Coupled convective and morphological instability of the inner core boundary of the Earth (2011) Phys. Earth Planet. Inter., 189 (3-4), pp. 134-141. , 10.1016/j.pepi.2011.08.004 0031-9201; Cao, A., Romanowicz, B., Hemispherical transition of seismic attenuation at the top of the earth's inner core (2004) Earth and Planetary Science Letters, 228 (3-4), pp. 243-253. , DOI 10.1016/j.epsl.2004.09.032, PII S0012821X04005862; Ivantsov, G.P., Temperature field around spheroidal, cylindrical, and acicular crystal growing in a supercooled melt (1947) Dokl. Akad. Nauk SSSR, 58, pp. 567-569. , 0002-3264; Horvay, G., (1960) General Electric Research Report; Horvay, G., Cahn, J.W., Dendritic and spheroidal growth (1961) Acta Metall., 9 (7), pp. 695-705. , 10.1016/0001-6160(61)90008-6 0001-6160; Pelce, P., Bensimon, D., Theory of dendrite dynamics (1987) Nucl. Phys., 2, pp. 259-270. , 10.1016/0920-5632(87)90022-3 0920-5632 B; Pelce, P., (1988) Dynamics of Curved Fronts; Bouissou, P., Pelce, P., Effect of a forced flow on dendritic growth (1989) Phys. Rev., 40 (11), pp. 6673-6680. , 10.1103/PhysRevA.40.6673 0556-2791 A; Ben Amar, M., Pelce, P., Impurity effect on dendritic growth (1989) Phys. Rev., 39 (8), pp. 4263-4269. , 10.1103/PhysRevA.39.4263 0556-2791 A; Dash Sachindra Kumar, Gill William, N., Forced convection heat and momentum transfer to dendritic structures (parabolic cylinders and paraboloids of revolution) (1984) International Journal of Heat and Mass Transfer, 27 (8), pp. 1345-1356. , DOI 10.1016/0017-9310(84)90062-0; Benamar, M., Ph, B., Pelce, P., An exact solution for the shape of a crystal growing in a forced flow (1988) J. Cryst. Growth, 92 (1-2), pp. 97-100. , 10.1016/0022-0248(88)90439-3 0022-0248; Saville, D.A., Beaghton, J.P., Growth of needle-shaped crystals in the presence of convection (1988) Phys. Rev., 37 (9), pp. 3423-3430. , 10.1103/PhysRevA.37.3423 0556-2791 A; Boehler, R., Temperatures in the Earth's core from melting-point measurements of iron at high static pressures (1993) Nature, 363 (6429), pp. 534-536. , DOI 10.1038/363534a0; Sumita, I., Bergman, M.I., Inner-core dynamics (2007) Treatise on Geophysics, 8, pp. 299-318. , 10.1016/B978-044452748-6.00132-2; Officer, C.B., A conceptual model of core dynamics and the Earth's magnetic field (1986) J. Geophys., 59, pp. 89-97. , 0340-062X; Melchior, P., (1986) The Physics of the Earth's Core; De Wijs, G.A., Kresse, G., Vocadlo, L., Dobson, D., Alfe, D., Gillan, M.J., Price, G.D., The viscosity of liquid iron at the physical conditions of the Earth's core (1998) Nature, 392 (6678), pp. 805-807. , DOI 10.1038/33905; Kessler, D.A., Koplik, J., Levine, H., Pattern selection in fingered growth phenomena (1988) Adv. Phys., 37 (3), pp. 255-339. , 10.1080/00018738800101379 0001-8732; Saffman, P.G., Taylor, G.I., The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid (1958) Proc. R. Soc. Lond., 245 (1242), pp. 312-329. , 10.1098/rspa.1958.0085 1364-5021 A; Davies, R.M., Taylor, G.I., The mechanics of large bubbles rising through extended liquids and through liquids in tubes (1950) Proc. R. Soc. Lond., 200 (1062), pp. 375-390. , 10.1098/rspa.1950.0023 1364-5021 A; Zel'dovich, Ya.B., Istratov, A.G., Kidin, N.I., Librovich, V.B., Flame propagation in tubes: Hydrodynamics and stability (1980) Combustion science and technology, 24 (1-2), pp. 1-13; Caroli, B., Caroli, C., Roulet, B., Langer, J.S., Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification (1986) Phys. Rev., 33 (1), pp. 442-452. , 10.1103/PhysRevA.33.442 0556-2791 A; Dombre, T., Hakim, V., Pomeau, Y., Séléction de la largeur des doigts dans l'instabilité de Saffman-Taylor (1986) C. R. Acad. Sci., 302, pp. 803-808. , 1620-7742; Mullins, W.W., Sekerka, R.F., Stability of a planar interface during solidification of a dilute binary alloy (1964) J. Appl. Phys., 35 (2), pp. 444-451. , 10.1063/1.1713333 0021-8979; Alexandrov, D.V., Galenko, P.K., Herlach, D.M., Selection criterion for the growing dendritic tip in a non-isothermal binary system under forced convective flow (2010) J. Cryst. Growth, 312 (14), pp. 2122-2127. , 10.1016/j.jcrysgro.2010.03.036 0022-0248; Bouissou, P., Perrin, B., Tabeling, P., Influence of an external flow on dendritic crystal growth (1989) Phys. Rev., 40 (1), pp. 509-512. , 10.1103/PhysRevA.40.509 0556-2791 A; Brener, E., Melnikov, V.I., Pattern selection in two-dimensional dendritic growth (1991) Adv. Phys., 40 (1), pp. 53-97. , 10.1080/00018739100101472 0001-8732; Tong, X., Beckermann, C., Karma, A., Li, Q., Phase-field simulations of dendritic crystal growth in a forced flow (2001) Phys. Rev., 63 (6). , 10.1103/PhysRevE.63.061601 1063-651X E 061601; Jeong, J.-H., Goldenfeld, N., Dantzig, J.A., Phase field model for three-dimensional dendritic growth with fluid flow (2001) Phys. Rev, 64 (4). , 10.1103/PhysRevE.64.041602 1063-651X E 041602
Correspondence Address Department of Mathematical Physics, Ural Federal University, Lenin ave. 51, Ekaterinburg, 620000, Russian Federation
Language of Original Document English
Abbreviated Source Title J. Phys. Math. Theor.
Source Scopus