Abstract
Some examples of the motion of a disperse mixture in which regions of unbounded growth of the particle concentration arise are considered. It is shown that integrable and nonintegrable singularities of the concentration can exist. The distribution function for the distances between the particles found by Chernyshenko [9] is used to determine the conditions for the absence of interaction of the particles. It is shown that in the case of integrable singularities of the concentration the model of noninteracting particles is valid in a wide range of the determining parameters, since, despite the infinite value of the concentration, the distance between the particles remains much greater than the particle diameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Literature cited
R. I. Nigmatulin, Fundamentals of the Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1978).
F. Marble, “Dynamics of dusty gases,” in: Mekhanika [Periodical of Russian Translations], No. 6, 48 (1971).
A. P. Vasil'kov, “Neighborhood of the stagnation point of a blunt body in a hypersonic two-phase flow,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 121 (1975).
A. N. Osiptsov, “Structure of the laminar boundary layer of a disperse mixture on flat plate,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 48 (1980).
A. N. Osiptsov, “Flow of a disperse mixture past bodies,” Report No. 2376 [in Russian], Institute of Mechanics, Moscow State University (1980).
I. M. Zheleva and V. P. Stulov, “Helical motion of dusty gas,” in: Gas Dynamics of Nonequilibrium Processes [in Russian], Institute of Theoretical and Applied Mathematics, Novosibirsk (1981), pp. 96–105.
Ya. B. Zel'dovich and A. D. Myshkis, Elements of Mathematical Physics. Media of Noninteracting Particles [in Russian], Nauka, Moscow (1973), p. 352.
A. N. Kraiko, “Discontinuity surfaces in media without self-pressure,” Prikl. Mat. Mekh.,43, 500 (1979).
S. I. Chernyshenko, “On the average distance between particles in a dusty gas in the presence of singularities of the “smeared” density of the particle medium,” Vestn. Mosk. Univ. Ser. Mat. Mekh., No. 1, 69 (1984).
I. S. Men'shov, “Propagation of strong blast waves in a disperse mixture,” Dokl. Akad. Nauk SSSR,267, 808 (1982).
V. M. Voloshchuk, Introduction to the Hydrodynamics of Coarse Disperse Aerosols [in Russian], Gidrometeoizdat, Leningrad (1971).
N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydrodynamics, New York (1964).
J. M. Burgers, “A mathematical model illustrating the theory of turbulence,” in: Advances in Applied Mechanics, Vol. 1, Academic Press, New York (1948), pp. 197–199.
Yu. A. Rozanov, Random Processes [in Russian], Nauka, Moscow (1977).
M. V. Fedoryuk, The Method of Steepest Descent [in Russian], Nauka, Moscow (1977).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 46–52, May–June, 1984.
I thank V. P. Stulov and S. I. Chernyshenko for helpful discussions.
Rights and permissions
About this article
Cite this article
Osiptsov, A.N. Investigation of regions of unbounded growth of the particle concentration in disperse flows. Fluid Dyn 19, 378–385 (1984). https://doi.org/10.1007/BF01093900
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01093900