A transient distribution of particle assemblies at the concluding stage of phase transformations / Alexandrov D. V. // JOURNAL OF MATERIALS SCIENCE. - 2017. - V. 52, l. 12. - P. 6987-6993.

ISSN/EISSN:

0022-2461 / 1573-4803

Type:

Article

Abstract:

There are a number of experimental and theoretical papers testifying that the large-time behavior of the particle-size distribution function heavily depends on the initial conditions at the final stages of phase transformation processes. However, still now there is no theoretically derived distribution confirming these conclusions. The present paper is concerned with a new theoretical approach verifying the fact that the large-time distribution can actually be dependent on the details of the initial data. The concluding stage of evolution of a particulate ensemble as a result of coalescence and coagulation processes is considered. The transient kinetic and balance equations for the particle-size distribution function are modified into a single nonlinear equation for arbitrary collision frequency factors. This integro-differential equation is solved analytically in the limit of large times. The obtained particle-size distribution function depends on the initial condition and describes the concluding stages of transient phase transformation processes. The area of applicability of the present asymptotic solution for the large-time particle-size distribution is discussed. The obtained distribution function is in agreement with experiments.

Author keywords:

MASS-TRANSFER MECHANISMS; SELF-SIMILAR SOLUTIONS; ASYMPTOTIC-BEHAVIOR; COAGULATION; EQUATION; GROWTH; COALESCENCE; NUCLEATION; KINETICS

DOI:

10.1007/s10853-017-0931-y

Web of Science ID:

ISI:000399093900009

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	JUN
Publisher	SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013 USA
Language	English
EISSN	1573-4803
Keywords-Plus	MASS-TRANSFER MECHANISMS; SELF-SIMILAR SOLUTIONS; ASYMPTOTIC-BEHAVIOR; COAGULATION; EQUATION; GROWTH; COALESCENCE; NUCLEATION; KINETICS
Research-Areas	Materials Science
Web-of-Science-Categories	Materials Science, Multidisciplinary
Author-Email	dmitri.alexandrov@urfu.ru
ResearcherID-Numbers	Alexandrov, Dmitri/D-2516-2016
ORCID-Numbers	Alexandrov, Dmitri/0000-0002-6628-745X
Funding-Acknowledgement	Russian Science Foundation {[}16-11-10095]
Funding-Text	This work was supported by the Russian Science Foundation (Grant No. 16-11-10095).
Number-of-Cited-References	49
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	1
Journal-ISO	J. Mater. Sci.
Doc-Delivery-Number	ER8ST