Abstract
In this paper a class of models of continuous media is constructed whose free energy depends on the density, the rate of change of density, and the temperature. Conditions at discontinuities in such models are found. A Kogarko model for a mixture of liquid with gas bubbles is obtained. Moreover, the propagation of small disturbances is investigated. In the third and fourth sections exact solutions are found for the problems of nonsteady and steady motion of a mixture of liquid and bubbles in a tube.
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L. I. Sedov, “Mathematical methods for the construction of new models of continuous media,” Usp. Matem. Nauk,20, No. 5 (1965).
L. I. Sedov, “Models of continuous media with internal degrees of freedom,” Prikl. Matem. i Mekh.,32, No. 5 (1968).
L. I. Sedov, Mechanics of Solid Media, Vols. 1, 2 [in Russian], Nauka, Moscow (1970).
B. S. Kogarko, “A model of a cavitating liquid,” Dokl. Akad. Nauk SSSR,137, No. 6 (1961).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–116, November–December, 1971.
The author thanks L. I. Sedov for guidance and valuable advice.
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Khanna, S.S.B. Motion of a liquid containing gas bubbles. Fluid Dyn 6, 1005–1009 (1971). https://doi.org/10.1007/BF01019811
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DOI: https://doi.org/10.1007/BF01019811