Fluid Dynamics

, Volume 53, Issue 1, pp 119–126 | Cite as

Acoustic Waves of Various Geometry in Multi-Fraction Bubbly Liquids

  • R. N. Gafiyatov
  • D. A. Gubaidullin
  • D. D. Gubaidullina


The propagation of acoustic waves of various geometry in mixtures of a liquid and a disperse phase consisting of small bubbles which differ from one another by both the radii and the thermophysical properties is investigated. A systemof differential equations of motion of the mixture is written and the dispersion relation is derived. The dispersion curves are constructed and damping of the pressure pulses is compared for the plane, cylindrical, and spherical waves in the bubbly liquids considered. The theory is compared with the experimental data.

Key words

acoustic waves bubbly liquid heat-and-mass transfer dispersion relation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. I. Nigmatulin, Dynamics of Multiphase Media, Vols. 1 and 2 (Hemisphere,Washington, 1989; Nauka, Moscow, 1987).Google Scholar
  2. 2.
    V. E. Nakoryakov, B. G. Pokusaev, and I. R. Shreiber, Wave Propagation in Gas-and Vapor-LiquidMedia (ITF, Novosibirsk, 1983) [in Russian].Google Scholar
  3. 3.
    S. Temkin, Suspension Acoustics: An Introduction to the Physics of Suspensions (Cambridge Univ. Press, Cambridge, 2005).CrossRefzbMATHGoogle Scholar
  4. 4.
    A. A. Gubaidullin, A. I. Ivandaev, R. I. Nigmatulin, and N. S. Kabeev, “Waves in the Liquids with Bubbles,” Itogi Nauki i Tekhniki. Ser. MLG, VINITI 17, 160–249 (1982).Google Scholar
  5. 5.
    K. W. Commander and A. Prosperetti, “Linear Pressure Waves in Bubbly Liquids: Comparison between Theory and Experiments,” J. Acoustical Society of America 85 (2), 732 (1989).ADSCrossRefGoogle Scholar
  6. 6.
    D. A. Gubaidullin and A. A. Nikiforov, “Acoustic Disturbances in a Mixture of a Liquid with Vapor and Gas Bubbles,” Teplofiz. Vys. Temp. 48 (2), 170–175 (2010).Google Scholar
  7. 7.
    D. A. Gubaidullin, A. A. Nikiforov, and R. N. Gafiyatov, “Acoustic Waves in Two-Fraction Bubbly Liquids with Phase Transitions,” Teplofiz. Vys. Temp. 50 (2), 269–273 (2012).zbMATHGoogle Scholar
  8. 8.
    R. N. Gafiyatov, D. A. Gubaidullin, A. A. Nikiforov, “Propagation of AcousticWaves in Two-Fraction Bubbly Liquids with Account for Phase Transitions in Each Fraction,” Fluid Dynamics 48 (3), 366–373 (2013).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    R. I. Nigmatulin, A. A. Gubaidullin, and Yu. V. Fedorov, “Acoustic Waves of Various Geometry in Liquids with Polydisperse Gas Bubbles. Theory and Experiment,” Dokl. Ross. Akad. Nauk 450 (6), 665–669 (2013).Google Scholar
  10. 10.
    D. A. Gubaidullin and Yu. V. Fedorov, “Sound Waves in Liquids with Polydisperse Vapor-Gas and Gas Bubbles,” Fluid Dynamics 50 (1), 61–70 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    D. A. Gubaidullin, A. A. Nikiforov, and R. N. Gafiyatov, “AcousticWaves inMulti-Fraction Bubbly Liquids,” Teplofiz. Vys. Temp. 53 (2), 250–255 (2015).Google Scholar
  12. 12.
    R. I. Nigmatulin, V. Sh. Shagapov, and N. K. Vakhitova, “Manifestation of the Carrier Phase Compressibility in the Case ofWave Propagation in a BubblyMedium,” Dokl.Akad. Nauk SSSR 304 (5), 1077–1081 (1989).Google Scholar
  13. 13.
    V. A. Gaponov, “Software Package for the Fast Fourier Transform with Applications to the Simulation of Random Processes,” Preprint No. 14, Institute of Thermal Physics of the Siberian Branch of the Academy of Sciences of the USSR (Novosibirsk, 1976) [in Russian].Google Scholar
  14. 14.
    D. A. Gubaidullin, Dynamics of Two-Phase Vapor-Gas-Droplet Media (Kazan Mat. Soc., Kazan, 1998) [in Russian].Google Scholar
  15. 15.
    V. Duro, D. R. Rajaona, D. Decultot, and G. Maze, “Experimental Study of Sound Propagation through Bubbly Water: Comparison with Optical Measurements,” IEEE J. Oceanic Engineering 36 (1), 114–125 (2011).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • R. N. Gafiyatov
    • 1
  • D. A. Gubaidullin
    • 1
  • D. D. Gubaidullina
    • 1
  1. 1.Institute of Mechanics and EngineeringKazan Science Center of the Russian Academy of SciencesKazan’Russia

Personalised recommendations