Fluid Dynamics

, Volume 53, Issue 2, pp 248–254 | Cite as

Acoustic Waves in a Liquid with Solid Particles and Gas Bubbles

  • D. A. GubaidullinEmail author
  • Yu. V. Fedorov


The mathematical model which determines acoustic wave propagation in a mixture of liquid with gas bubbles and solid particles is proposed. A system of differential equations is written and the dispersion relation is derived. Low- and high-frequency asymptotics of the phase velocity in the mixture considered are found and illustrated. The effect of solid particles and gas bubbles on acoustic wave dispersion and dissipation is indicated. For the mixture of fluid with solid particles considered the speed of sound is compared with available experimental data.


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  1. 1.
    A. Prosperetti, “Vapor Bubbles,” Annu. Rev. Fluid Mech. 49, 221–248 (2017).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    D. A. Gubaidullin, A. A. Nikiforov, and Yu. V. Fedorov, “A Review on Bubbly Liquid Acoustics,” in: Topical Problems of ContinuumMechanics. To 25th Anniversary of the Institute ofMechanics and Engineering of Kazan Science Center of the Russian Academy of Sciences (Izd-vo “Fen” ANR, Kazan, 2016) [in Russian], pp. 30–47.Google Scholar
  3. 3.
    S. M. Rytov, V. V. Vladimirskii, and M. D. Galanin, “Sound Propagation in Disperse Systems,” Zh. Eksp. Teor. Fiz. 8, No. 5, 614–621 (1938).Google Scholar
  4. 4.
    V. V. Vladimirskii and M. D. Galanin, “Ultrasound Absorption in a Water-Mercury Emulsion,” Zh. Eksp. Teor. Fiz. 9, 233–236 (1939).Google Scholar
  5. 5.
    R. J. Urick, “A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances,” J. Appl. Phys. 18, 983–987 (1947).ADSCrossRefGoogle Scholar
  6. 6.
    M. A. Isakovich, “Propagation of Sound in Emulsions,” Zh. Eksp. Teor. Fiz. 18, No. 10, 907–912 (1948).Google Scholar
  7. 7.
    I. A. Ratinskaya, “Attenuation of Sound in Emulsions,” Akust. Zh. 8, No. 2, 210–215 (1962).Google Scholar
  8. 8.
    L. D. Hampton, “Acoustic Properties of Sediments,” J. Acoust. Soc. Amer. 42, No. 4, 882–890 (1967).ADSCrossRefGoogle Scholar
  9. 9.
    J. R. Allegra and S. A. Hawley, “Attenuation of Sound in Suspensions and Emulsions: Theory and Experiments,” J. Acoust. Soc. Amer. 51, No. 5, 1545–1564 (1972).ADSCrossRefGoogle Scholar
  10. 10.
    A. H. Harker and J. A. G. Temple, “Velocity and Attenuation of Ultrasound in Suspensions of Particles in Fluids,” J. Phys. D:Appl. Phys. 21, 1576–1588 (1988).ADSCrossRefGoogle Scholar
  11. 11.
    C. M. Atkinson and H. K. Kytömaa, “Acoustic Wave Speed and Attenuation in Suspensions,” Int. J. Multiphase Flo. 18, No. 4, 577–592 (1992).CrossRefzbMATHGoogle Scholar
  12. 12.
    H. K. Kytömaa, “Theory of Sound Propagation in Suspensions: a Guide to Particle Size and Concentration Characterization,” Powder Technol. 82, 115–121 (1995).CrossRefGoogle Scholar
  13. 13.
    J.M. Evans and K. Attenborough, “Coupled Phase Theory for Sound Propagation in Emulsions,” J. Acoust. Soc. Amer. 102, No. 1, 278–282 (1997).ADSCrossRefGoogle Scholar
  14. 14.
    J.M. Evans and K. Attenborough, “Sound Propagation in Concentrated Emulsions: Comparison of Coupled PhaseModel and Core-ShellModel,” J. Acoust. Soc. Amer. 112, No. 5, 1911–1917 (2002).ADSCrossRefGoogle Scholar
  15. 15.
    V. E. Dontsov, V. E. Nakoryakov, and B. G. Pokusaev,” Reflection of Pressure Waves on the Boundary between a Liquid and a Three-PhaseMedium,” Akust. Zh. 42, No. 6, 783–788 (1996).Google Scholar
  16. 16.
    V. E. Dontsov and B. G. Pokusaev,” Reflection of a Shock Waves from the Rigid Wall in a Suspension of a Liquid with Solid Particles and Gas Bubbles,” Akust. Zh. 45, No. 2, 215–222 (1999).Google Scholar
  17. 17.
    L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. 6. Fluid Mechanics (Pergamon, Oxford, 1987; Nauka, Moscow, 1986).Google Scholar
  18. 18.
    V. S. Fedotovskii, Hydrodynamic Forces Exerted on Vibrating Spherical and Cylindrical Inclusions. Preprint No. 1473 (FEI, Obninsk, 1983) [in Russian].Google Scholar
  19. 19.
    R. I. Nigmatulin, “Small-Scale Flows and Surface Effects in Hydrodynamics of Multiphase Media,” Prikl. Mat. Mekh. 35, No. 3, 451–463 (1971).Google Scholar
  20. 20.
    R. I. Nigmatulin, Dynamics of Multiphase Media, Vol. 1 (Hemisphere, Washington, 1989; Nauka, Moscow, 1987).Google Scholar
  21. 21.
    D. A. Gubaidullin and Yu. V. Fedorov, “Sound Waves in Two-Fraction Polydisperse Bubbly Media,” Appl. Mat. Mech. 77, No. 5, 532–540 (2013).CrossRefGoogle Scholar
  22. 22.
    A. G. Petrov, Analytic Hydrodynamics (Fizmatlit, Moscow, 2010) [in Russian].Google Scholar
  23. 23.
    D. A. Gubaidullin, Dynamics of Two-Phase Vapor-Gas-Droplet Media (Kazan Mat. Soc., Kazan, 1998) [in Russian].Google Scholar
  24. 24.
    M. A. Pakhomov and V. I. Terekhov, “Turbulent Flow Structure and Bubble Distribution in an Axisymmetric Nonisothermal Impinging Gas–Liquid Jet,” Fluid Dynamic. 52, No. 2, 288–298 (2017).MathSciNetCrossRefzbMATHGoogle Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Mechanics and EngineeringKazan Science Center of the Russian Academy of SciencesKazan, TatarstanRussia

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