Nucleation and crystal growth kinetics during solidification: The role of crystallite withdrawal rate and external heat and mass sources / Alexandrov D.V. // Chemical Engineering Science. - 2014. - V. 117, l. . - P. 156-160.

ISSN:
00092509
Type:
Article
Abstract:
A complete analytical solution of the integro-differential model describing the transient nucleation and growth of the crystals at the intermediate stage of phase transitions is constructed. The roles of external heat/mass sources appearing in the balance equations and the crystallite withdrawal rate entering in the Fokker-Planck equation are detailed. An exact analytical solution of the Fokker-Planck equation is found for arbitrary nucleation mechanisms and growth kinetics. Two important cases of the Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetics are considered in some detail. A non-linear time-dependent integral equation with memory kernel for the metastability level is analytically solved on the basis of the saddle-point method for the Laplace integral in the case of mixed kinetic-diffusion regime of crystal growth, which is of frequent occurrence. It is shown that the desupercooling/desupersaturation rate decreases with increasing the crystal withdrawal rate and intensities of external sources. The density distribution function becomes more and more broad with time. In addition, this function increases with decreasing the crystallite withdrawal rate and with increasing intensities of external sources. © 2014 Elsevier Ltd.
Author keywords:
Crystal growth; Kinetics; Nucleation; Phase transitions
Index keywords:
Crystal growth; Crystallites; Enzyme kinetics; Kinetics; Nucleation; Phase transitions; Timing jitter; Balance equations; Density distribution functions; Exact analytical solutions; External sources;
DOI:
10.1016/j.ces.2014.06.012
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84904255059&doi=10.1016%2fj.ces.2014.06.012&partnerID=40&md5=4047d4f73ac6b11a42f9f7a66806d800
Affiliations Department of Mathematical Physics, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russian Federation
Author Keywords Crystal growth; Kinetics; Nucleation; Phase transitions
Funding Details 13-01-96013-ural, RFBR, Russian Foundation for Basic Research
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Correspondence Address Alexandrov, D.V.; Department of Mathematical Physics, Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russian Federation; email: Dmitri.Alexandrov@urfu.ru
Publisher Elsevier Ltd
CODEN CESCA
Language of Original Document English
Abbreviated Source Title Chem. Eng. Sci.
Source Scopus