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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 12, Pages 2065–2078
DOI: https://doi.org/10.7868/S0044466917120031 (Mi zvmmf10654) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Generalized Boltzmann-type equations for aggregation in gases

S. Z. Adzhieva, V. V. Vedenyapinbc, Yu. A. Volkovbc, I. V. Melikhova

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b RUDN University, Moscow, Russia
c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (405 kB) Citations (12)
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DOI: https://doi.org/10.7868/S0044466917120031
Abstract: The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker–Döring-type equation). The transition to a continuum description is performed.
Key words: aggregation, coalescence-fragmentation equations, Boltzmann equation, Becker–Döring equations, principle of detailed balance, conservation laws, Fokker–Planck-type equation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Academy of Sciences - Federal Agency for Scientific Organizations 1.3.1
Received: 31.05.2016
Revised: 12.03.2017
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 12, Pages 2017–2029
DOI: https://doi.org/10.1134/S096554251712003X
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017), 2065–2078; Comput. Math. Math. Phys., 57:12 (2017), 2017–2029
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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