Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems / Alexandrov D.V., Nizovtseva G. // Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. - 2014. - V. 470, l. 2162.

ISSN:
13645021
Type:
Article
Abstract:
An exact analytical solution of an integro-differential model describing the transient nucleation of solid particles (nuclei) and their growth with fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems is constructed. Two important cases of the Weber-Volmer-Frenkel-Zel'dovich and Mier nucleation kinetics are detailed for supercooled melts and supersaturated solutions. © 2013 The Author(s) Published by the Royal Society. All rights reserved.
Author keywords:
Crystal growth; Kinetics; Nucleation; Phase transitions
Index keywords:
Crystal growth; Engineering; Enzyme kinetics; Phase transitions; Bulk phase transition; Exact analytical solutions; Intermediate stage; Metastable systems; Nucleation kinetics; Supercooled melt; Super
DOI:
10.1098/rspa.2013.0647
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84890613178&doi=10.1098%2frspa.2013.0647&partnerID=40&md5=6958550d2e27c97e86ae3d6c6d13ebcd
Соавторы в МНС:
Другие поля
Поле Значение
Art. No. 20130647
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84890613178&doi=10.1098%2frspa.2013.0647&partnerID=40&md5=6958550d2e27c97e86ae3d6c6d13ebcd
Affiliations Department of Mathematical Physics, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russian Federation; Laboratoire des Sciences du Climat et de l'Environnement, Institut Pierre Simon Laplace (LSCE/IPSL CEA), L'Orme des Merisiers,Bat. 701, 91191, Gif-sur-Yvette-Cedex, France
Author Keywords Crystal growth; Kinetics; Nucleation; Phase transitions
References Galkin, O., Vekilov, P.G., Are nucleation kinetics of protein crystals similar to those of liquid droplets? (2000) J. Am. Chem. Soc., 122, pp. 156-163. , (doi:10.1021/ja9930869); Hamza, M.A., Berge, B., Mikosch, W., Rühl, E., Homogeneous nucleation of supersaturated KCl-solutions from single levitated microdroplets (2004) Phys. Chem. Chem. Phys., 6, pp. 3484-3489. , (doi:10.1039/B401807A); Barlow, D.A., Theory of the intermediate stage of crystal growth with applications to protein crystallization (2009) J. Cryst. Growth, 311, pp. 2480-2483. , (doi:10.1016/j.jcrysgro.2009.02.035); Kelton, K.F., Greer, A.L., (2008) Nucleation in Condensed Matter: Applications in Materials and Biology, , Amsterdam, The Netherlands: Elsevier; Hanhoun, M., Montastruc, L., Azzaro-Pntel, C., Biscans, B., Freche, M., Pibouleau, L., Simultaneous determination of nucleation and crystal growth kinetics of struvite using a thermodynamic modeling approach (2013) Chem. Eng. J., 215-216, pp. 903-912. , (doi:10.1016/j.cej.2012.10038); Buil, S., Delville, J.P., Ducasse, A., Nucleation and early stage growth in phase-separating liquid mixtures under weak time-dependent supersaturation (2000) Eur. Phys. J. E, 2, pp. 105-116. , (doi:10.1007/s101890050044); Zhang, T.H., Liu, X.Y., Nucleation: What happens at the initial stage? (2009) Angew. Chem. Int. Ed., 48, pp. 308-1312. , (doi:10.1002/anie.200804743); Madras, G., McCoy, B.J., Transition from nucleation and growth to Ostwald ripening (2002) Chem. Eng. Sci., 57, pp. 3809-3818. , (doi:10.1016/S0009-2509(02)00313-5); Shneidman, V.A., Early stages of Ostwald ripening (2013) Phys. Rev. E, 88, p. 010401. , doi:10.1103/PhysRevE.88.010401); Russel, W.B., Brownian motion of small particles suspended in liquids (1981) Annu. Rev. Fluid Mech., 13, pp. 425-455. , (doi:10.1146/annurev.fl.13.010181.002233); Zumstein, R.C., Rousseau, R.W., Growth rate dispersion by initial growth rate distributionsand growth rate fluctuations (1987) AIChE J, 33, pp. 121-129. , doi:10.1002/aic.690330114); Randolph, A., Larson, M., (1988) Theory of Particulate Processes, , San Diego, CA: Academic Press; Gardiner, C.W., (1983) Handbook on Stochastic Methods: For Physics, Chemistry and the Natural Sciences, , Berlin, Germany: Springer; Lifshitz, E.M., Pitaevskii, L.P., (1981) Physical Kinetics, , New York, NY: Pergamon Press; Buyevich Yu, A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , NewYork, NY: Begell House; Zettlemoyer, A.C., (1969) Nucleation, , NewYork, NY:Dekker; Mullin, J.W., (1972) Crystallization, , Oxford, UK: Butterworth & Co; Buyevich Yu, A., Ivanov, A.O., Kinetics of phase separation in colloids: 2. Non-linear evolution of metastable colloid (1993) Phys. A, 193, pp. 221-240. , (doi:10.1016/0378-4371(93)90027-2); Buyevich Yu, A., Mansurov, V.V., Kinetics of the intermediate stage of phase transition in batch crystallization (1990) J. Cryst. Growth, 104, pp. 861-867. , (doi:10.1016/0022-0248(90)90112-X); Volmer, M., Weber, A., Keimbildung in ubersattigen gebilden (1926) Z. Phys. Chem. A, 119, pp. 277-301; Zel'dovich, J.B., On the theory of formation of a new phase. Cavitation (1942) J. Exp. Theor. Phys., 12, pp. 525-536; Frenkel, J., (1955) Kinetic Theory of Liquids, , New York, NY: Dover; Shanmugham, M., Gnanam, F.D., Ramasamy, P., Nucleation studies in supersaturated potassium dihydrogen orthophosphate solution and the effect of soluble impurities (1984) J. Mater.Sci., 19, pp. 2837-2844. , (doi:10.1007/BF01026958); Ramesh, R., Mahadevan, C., Nucleation studies in supersaturated aqueous solutions of (NH 4)H2PO4 doped with (NH4) 2C2O4 H2O (1998) Bull. Mater. Sci., 21, pp. 287-290. , (doi:10.1007/BF02744954); Streets, A.M., Quake, S.R., Ostwald ripening of clusters during protein crystallization (2010) Phys. Rev. Lett., 104, p. 178102. , doi:10.1103/PhysRevLett.104.178102); Kirkaldy, J.S., Young, D.J., (1987) Diffusion in the Condensed State, , London, UK: Institute of Metals; Chernov, A.A., (1984) Modern Crystallography 3, , Berlin, Germany: Springer; Buyevich Yu, A., Natalukha, I.A., Unsteady processes of combined polymerization and crystallization in continuous apparatuses (1994) Chem. Eng. Sci., 49, pp. 3241-3247. , (doi:10.1016/0009-2509(94)E0052-R); Shneidman, V.A., Transient nucleation with a monotonically changing barrier (2010) Phys. Rev. E, 82, p. 031603. , (doi:10.1103/PhysRevE.82.031603); Enomoto, Y., Finite volume fraction effects on coarsening - 2. Interface-limited growth (1991) Acta Metall. Mater., 39, pp. 2013-2016. , (doi:10.1016/0956-7151(91)90170-6); Yao, J.H., Elder, K.R., Guo, H., Grant, M., Theory and simulation of Ostwald ripening (1993) Phys. Rev. B, 47, pp. 14110-14125. , (doi:10.1103/PhysRevB.47.14110); Caraballo, K.G., Baird, J.K., Ng, J.D., Comparison of the crystallization kinetics of canavalin and lysozyme (2006) Cryst. Growth Des., 6, pp. 874-880. , (doi:10.1021/cg058016u); Aseev, D.L., Alexandrov, D.V., Nonlinear dynamics for the solidification of binarymelt with a nonequilibrium two-phase zone (2006) Dokl. Phys., 51, pp. 291-295. , (doi:10.1134/S1028335806060024); Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) Int. J. Heat Mass Transf., 49, pp. 4903-4909. , (doi:10.1016/j.ijheatmasstransfer.200605046); Alexandrov, D.V., Malygin, A.P., Flow-induced morphological instability and solidification with the slurry and mushy layers in the presence of convection (2012) Int. J. Heat Mass Transf., 55, pp. 3196-3204. , (doi:10.1016/j.ijheatmasstransfer.2012.02.048); Solomatov, V.S., Stevenson, D.J., Kinetics of crystal growth in a terrestrialmagma ocean (1993) Int. J. Geophys. Res., 98, pp. 5407-5418. , (doi:10.1029/92JE02839); Alexandrov, D.V., Malygin, A.P., Coupled convective and morphological instability of the inner core boundary of the earth (2011) Phys. Earth Planet. Int., 189, pp. 134-141. , (doi:10.1016/j.pepi. 2011.08.004); Ivanov, A.O., Zubarev Ayu, Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid (1998) Phys A, 251, pp. 348-367. , (doi:10.1016/S0378-4371(97)00561-X); Uwaha, K., Koyama, K., Transition from nucleation to ripening in the classical nucleation model (2010) J. Cryst. Growth, 312, pp. 1046-1054. , (doi:10.1016/j.jcrysgro.2010.01.017)
Correspondence Address Alexandrov, D.V.; Department of Mathematical Physics, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russian Federation; email: dmitri.alexandrov@usu.ru
Publisher Royal Society
Language of Original Document English
Abbreviated Source Title Proc. R. Soc. A Math. Phys. Eng. Sci.
Source Scopus