Mathematical modelling of nucleation and growth of crystals with buoyancy effects / Alexandrov D.V. // Philosophical Magazine Letters. - 2016. - V. 96, l. 4. - P. 132-141.

ISSN:

09500839

Type:

Article

Abstract:

A complete analytical solution of the integro-differential model describing the nucleation of crystals and their subsequent growth in a binary system with allowance for buoyancy forces is constructed. An exact analytical solution of the Fokker-Planck-type equation for the three-parameter density distribution function is found for arbitrary nucleation kinetics. Two important cases of the Weber–Volmer–Frenkel–Zel’dovich and Meirs kinetics are considered in some detail. It is shown that the solute concentration decreases and the distribution function increases with increasing the melt supercooling (with increasing the depth of a metastable system). It is demonstrated that the distribution function attains its minimum at a certain size of crystals owing to buoyancy forces. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Author keywords:

buoyancy; crystal growth; Nucleation

Index keywords:

Crystal growth; Distribution functions; Fokker Planck equation; Nucleation; Density distribution functions; Differential models; Exact analytical solutions; Melt supercooling; Metastable systems; Nucl

DOI:

10.1080/09500839.2016.1177222

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84964573644&doi=10.1080%2f09500839.2016.1177222&partnerID=40&md5=f3c78c362d3040d6bba079e2dbb75a34

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Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84964573644&doi=10.1080%2f09500839.2016.1177222&partnerID=40&md5=f3c78c362d3040d6bba079e2dbb75a34
Affiliations	Department of Mathematical Physics, Ural Federal University, Ekaterinburg, Russian Federation
Author Keywords	buoyancy; crystal growth; Nucleation
References	Aseev, D.L., Alexandrov, D.V., (2006) Dokl. Phys., 51, p. 291; Alexandrov, D.V., Malygin, A.P., (2012) Int. J. Heat Mass Trans., 55, p. 3196; Chuntonov, K.A., Fedorov, V.M., (1986) Izv. Akad. Nauk SSSR. Neorganich. Materialy, 22, p. 949; Stabel, H.-H., (1986) Limnol. Oceanogr., 31, p. 1081; Morse, S.A., (2002) Geochim. Cosmochim. Acta, 66, p. 2155; Snell, E.H., Helliwell, J.R., (2005) Rep. Prog. Phys., 68, p. 799; Kelton, K.F., Greer, A.L., (2010) Nucleation in Condensed Matter: Applications in Materials and Biology, , Elsevier, Amsterdam:; Alexandrov, D.V., Malygin, A.P., (2011) Phys. Earth Planet. Inter., 189, p. 134; Dimitrov, I., (2012) J. Sci. Rev., 4, p. 189; Alexandrov, D.V., Malygin, A.P., (2014) Modelling Simul. Mater. Sci. Eng., 22, p. 015003; Alexandrov, D.V., (2014) Phys. Lett. A, 378, p. 1501; Buyevich, Y.A., Mansurov, V.V., (1990) J. Crystal Growth, 104, p. 861; Solomatov, V.S., Stevenson, D.J., (1993) J. Geophys. Res., 98, p. 5407; Ivanov, A.O., Zubarev, A.Y., (1998) Physica A, 251, p. 348; Barlow, D.A., (2009) J. Crystal Growth, 311, p. 2480; Alexandrov, D.V., Malygin, A.P., (2013) J. Phys. A: Math. Theor., 46, p. 455101; Alexandrov, D.V., (2014) Phil. Mag. Lett., 94, p. 786; Mullin, J.W., (1961) Crystallization, , Plenum Press, New York:; Randolph, A., Larson, M., (1988) Theory of Particulate Processes, , Academic Press, New York:; Zheng, L., Yapa, P.D., (2000) J. Hydraulic Eng., 126, p. 852; Mansurov, V.V., Postovalov, V.G., Chuntonov, K.A., (1993) Rasplavy, 5, p. 68; Skripov, V.P., (1974) Metastable Liquids, , Wiley, New York:; Herlach, D.M., Galenko, P.K., Holland-Moritz, D., (2007) Metastable Solids from Undercooled Melts, , Elsevier, Amsterdam:; Herlach, D.M., (2008) Phase Transformations in Multicomponent Melts, , Wiley-VCH, Weinheim:; Nanev, C.N., Penkova, A., Chayen, N., (2004) Ann. N.Y. Acad. Sci., 1027, p. 1; Li, J., Wu, M., Ludwig, A., Kharicha, A., (2012) IOP Conf. Series: Mater. Sci. Eng., 33, p. 012091; Gavira, J.A., García-Ruiz, J.M., (2009) Cryst. Growth Des, 9, p. 2610; Alexandrov, D.V., Nizovtseva, I.G., Malygin, A.P., Huang, H.-N., Lee, D., (2008) J. Phys.: Condens. Matter, 20, p. 114105; Martin, S., Kauffman, P., (1974) J. Fluid Mech., 64, p. 507; Alexandrov, D.V., (2014) Chem. Eng. Sci., 117, p. 156
Correspondence Address	Alexandrov, D.V.; Department of Mathematical Physics, Ural Federal UniversityRussian Federation; email: dmitri.alexandrov@urfu.ru
Publisher	Taylor and Francis Ltd.
CODEN	PMLEE
Language of Original Document	English
Abbreviated Source Title	Philos Mag Lett
Source	Scopus