Fluid Dynamics

, Volume 53, Issue 2, pp 189–199 | Cite as

Steady Flows in an Oscillating Spheroidal Cavity with Elastic Wall

  • V. G. KozlovEmail author
  • R. R. Sabirov
  • S. V. Subbotin


The steady flow arising in a spheroidal cavity with periodically-deformed elastic wall is studied experimentally. It is found that average flows whose intensities and structures depend on the wall oscillation frequency and amplitude can develop in the fluid. The average flow is generated in the Stokes boundary layer whose relative thickness is characterized by the dimensionless frequency of the vibrational action. Flow in the form of a pair of toroidal vortices which occupy the entire cavity volume can be observed over the range of low dimensionless frequencies when the boundary layer thickness is comparable with the characteristic cavity dimension. Increase in the dimensionless frequency (decrease in the relative thickness of the Stokes layers) leads to a displacement of the primary vortices towards the cavity boundary. In this case secondary vortices with opposite swirling are formed in the central part of the cavity above the primary vortices. The further increase in the dimensionless frequency leads to development of the secondary vortices and growth of the flow intensity. The large-scale secondary vortices occupy almost the entire cavity volume over the range of high dimensionless frequencies. The dependences of the regimes of average flows and their intensities on the control dimensionless parameters, the oscillation amplitude and frequency, are found on the basis of the results of the investigation.


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  1. 1.
    W. L.M. Nyborg, “Acoustic Streaming,” in: Physical Acoustics, W.P.Mason, Ed., Vol. II B (Academic, New York, 1965), p. 265.Google Scholar
  2. 2.
    N. Riley, “Steady Streaming,” Annu. Rev. Fluid Mech. 33, 43–65 (2001).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1979).zbMATHGoogle Scholar
  4. 4.
    M. Wegener, N. Paul, and M. Kraume, “Fluid Dynamics and Mass Transfer at Single Droplets in Liquid/Liquid Systems,” Int. J. HeatMass Transfer 71, 475–495 (2014).CrossRefGoogle Scholar
  5. 5.
    T.-B. Liang and M. J. Slater, “Liquid-Liquid Extraction Drop Formation: Mass Transfer and the Influence of Surfactant,” Chem. Eng. Sci. 45 (1), 97–105 (1990).CrossRefGoogle Scholar
  6. 6.
    S. K. Chung and E. H. Trinh, “Internal Flow of an Electrostatically Levitated Droplet Undergoing Resonant Shape,” Phys. Fluids 12, 249 (2000).ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    S. M. Lee, D. J. Im, and I. S. Kang, “Circulating Flows Inside a Drop under Time-Periodic Nonuniform Electric Fields,” Phys. Fluids 12, 1899–1910 (2000).ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    D. Zang, Y. Yu, Z. Chen, X. Li, H. Wu, and X. Geng, “Acoustic Levitation of Liquid Drops: Dynamics, Manipulation, and Phase Transitions,” Adv. Colloid Interface Sci. 243, 77–85 (2017).CrossRefGoogle Scholar
  9. 9.
    H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1932; Gostekhizdat, Moscow, Leningrad, 1947).zbMATHGoogle Scholar
  10. 10.
    E. Trinh, A. Zwern, and T. G. Wang, “An Experimental Study of Small-Amplitude Drop Oscillations in Immiscible Liquid Systems,” J. FluidMech. 115, 463–474 (1982).ADSCrossRefGoogle Scholar
  11. 11.
    E. Trinh and T. G. Wang, “Large-Amplitude Free and Driven Drop-Shape Oscillations: Experimental Observations,” J. FluidMech. 122, 315–338 (1982).ADSCrossRefGoogle Scholar
  12. 12.
    Y. Yamamoto, Y. Abe, A. Fujiwara, K. Hasegawa, and K. Aoki, “Internal Flow of Acoustically Levitated Droplet,” Microgravity Sci. Technol. 20, 277–280 (2008).ADSCrossRefGoogle Scholar
  13. 13.
    C. L. Shen, W. J. Xie, Z. L. Yan, and B. Wei, “Internal Flow of Acoustically Levitated Drops Undergoing Sectorial Oscillations,” Phys. Lett. A 374, 4045–4048 (2010).ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    Z. L. Yan, W. J. Xie, and B. Wei, “Vortex Flow in Acoustically Levitated Drops,” Phys. Lett. A. 375, 3306–3309 (2011).ADSCrossRefGoogle Scholar
  15. 15.
    A. L. Yarin, “Stationary D.C. Streaming due to Shape Oscillations of a Droplet and Its Effect on Mass Transfer in Liquid-Liquid Systems,” J. FluidMech. 444, 321–342 (2001).ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    B.D. Doré, OnMass Transport Induced by InterfacialOscillations at a Single Frequency,” Proc. Camb. Phil. Soc. 74, 333–347 (1973).ADSCrossRefGoogle Scholar
  17. 17.
    V. A. Murtsovkin and V. M. Muller, “Steady-State Flows Induced by Oscillations of a Drop with an Adsorption Layer,” J. Colloid Interface Sci. 151(1), 150–156 (1992).ADSCrossRefGoogle Scholar
  18. 18.
    A. Saha, S. Basu, and R. Kumar, “Particle Image Velocimetry and Infrared Thermography in a Levitated Droplet with Nanosilica Suspensions,” Exp. Fluids 52, 795–807 (2012).CrossRefGoogle Scholar
  19. 19.
    A. Saha, S. Basu, and R. Kumar, “Velocity and RotationMeasurements in Acoustically Levitated Droplets,” Phys. Lett. A. 376, 3185–3191 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    A. Saha, S. Basu, and R. Kumar, “Effects of Acoustic-Streaming-Induced Flow in Evaporating Nanofluid Droplets,” J. FluidMech. 692, 207–219 (2012).ADSCrossRefzbMATHGoogle Scholar
  21. 21.
    V. G. Kozlov, N. V. Kozlov, and V. D. Schipitsyn, “Steady Flows in an Oscillating Deformable Container. Effect of the Dimensionless Frequency,” Phys. Rev. Fluids 2, 094501 (2017).ADSCrossRefGoogle Scholar
  22. 22.
    W. Thielicke and E. J. Stamhuis, PIVlab "—Time-Resolved Digital Particle Image Velocimetry Tool for MATLAB (Version: 1.41) (2014).Google Scholar
  23. 23.
    G. Z. Gershuni and D. V. Lyubimov, Thermal Vibrational Convection (Wiley, New York, 1998).Google Scholar
  24. 24.
    A. A. Ivanova and V. G. Kozlov, “Vibrational Convection in a Nontranslationally Oscillating Cavity (Isothermal Case),” Fluid Dynamic. 38, No. 2, 186–192 (2003).CrossRefzbMATHGoogle Scholar
  25. 25.
    A. A. Ivanova, V. G. Kozlov, and N. V. Selin, “Average Fluid Flow in the End Regions of a Long Channel Subjected to Rotational Vibration,” Fluid Dynamic. 40, No. 3, 369–375 (2005).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. G. Kozlov
    • 1
    Email author
  • R. R. Sabirov
    • 2
  • S. V. Subbotin
    • 1
  1. 1.Perm State Humanitarian-Pedagogical UniversityVibrational Hydromechanics LaboratoryPermRussia
  2. 2.Perm National Research Polytechnic UniversityApplied Physics DepartmentPermRussia

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