Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Effect of viscoelastic properties of a liquid on the dynamics of small oscillations of a gas bubble

  • 26 Accesses

  • 3 Citations


A series of papers has been devoted to questions of gas bubble dynamics in viscoeiastic liquids. Of these papers we mention [1–4]. The radial oscillations of a gas bubble in an incompressible viscoeiastic liquid have been studied numerically in [1, 2] using Oldroyd's model [5]. Anexact solution was found in [3], and independently in [4], for the equation of small density oscillations of a cavity in an Oldroyd medium when there is a periodic pressure change at infinity. The analysis of bubble oscillations in a viscoeiastic liquid is complicated by properties of limiting transitions in the rheological equation of the medium. These properties are of particular interest for the problem under investigation. These properties are discussed below, and characteristics of the small oscillations of a bubble in an Oldroyd medium are investigated on the basis of a numerical analysis of the exact solution obtained in [3].

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    H. S. Fogler and J. D. Goddard, “Oscillations of a gas bubble in viscoelastic liquids subject to acoustic and impulsive pressure variations,” J. Appl. Phys.,42, No. 1 (1971).

  2. 2.

    I. Tanasawa and W. J. Yang, “Dynamic behavior of a gas bubble in viscoelastic liquids,” J. Appl. Phys.,41, No. 11 (1970).

  3. 3.

    S. P. Levitskii and A. T. Listrov, “Small oscillations of a gas-filled spherical cavity in viscoelastic polymer media,” Zh. Prikl. Mekh. Tekh. Fiz., No. 1 (1974).

  4. 4.

    W. J. Yang and M. L. Lawson, “Bubble pulsation and cavitation in viscoelastic liquids,” J. Appl. Phys.,45, No. 2 (1974).

  5. 5.

    J. G. Oldroyd, “Non-Newtonian effects in steady motion of some idealized elasticoviscous liquids,” Proc. Roy. Soc. Ser. A,245, No. 1241 (1958).

  6. 6.

    H. G. Flynn, “The physics of acoustic cavitation in liquids,” in: Physical Acoustics (edited by W. P. Mason), Vol. 1b, Academic Press (1964).

  7. 7.

    V. A. Gorodtsov and A. I. Leonov, “Kinematics, nonequilibrium thermodynamics, and rheological relations in the nonlinear theory of viscoelasticity,” Prikl. Mat. Mekh.,32, No. 1 (1968).

  8. 8.

    J. E. Dunn and R. L. Fosdick, “Thermodynamics, stability and boundedness of fluids of complexity 2, and fluids of second grade,” Arch. Rat. Mech. Anal.,56, No. 3 (1974).

  9. 9.

    K. Walters, “The solution of flow problems in the case of materials with memory,” J. Méc.,1, No.4 (1962).

  10. 10.

    B. P. Demidovich, Lectures in Mathematical Stability Theory [in Russian], Nauka, Moscow (1967).

  11. 11.

    G. Houghton, “Theory of bubble pulsation and cavitation,” J. Acoust. Soc. Amer.,35, No. 9 (1963).

Download references

Author information

Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 82–87, May–June, 1976.

The authors are grateful to V. N. Nikolaevskii for useful advice and for discussing the results.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Levitskii, S.P., Listrov, A.T. Effect of viscoelastic properties of a liquid on the dynamics of small oscillations of a gas bubble. J Appl Mech Tech Phys 17, 363–366 (1976). https://doi.org/10.1007/BF00853570

Download citation


  • Mathematical Modeling
  • Mechanical Engineer
  • Exact Solution
  • Industrial Mathematic
  • Pressure Change