Advertisement

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

  • S. P. Levitskii
  • A. T. Listrov
Article

Abstract

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].

Keywords

Mathematical Modeling Mechanical Engineer Exact Solution Industrial Mathematic Pressure Change 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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).Google Scholar
  2. 2.
    I. Tanasawa and W. J. Yang, “Dynamic behavior of a gas bubble in viscoelastic liquids,” J. Appl. Phys.,41, No. 11 (1970).Google Scholar
  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).Google Scholar
  4. 4.
    W. J. Yang and M. L. Lawson, “Bubble pulsation and cavitation in viscoelastic liquids,” J. Appl. Phys.,45, No. 2 (1974).Google Scholar
  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).Google Scholar
  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).Google Scholar
  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).Google Scholar
  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).Google Scholar
  9. 9.
    K. Walters, “The solution of flow problems in the case of materials with memory,” J. Méc.,1, No.4 (1962).Google Scholar
  10. 10.
    B. P. Demidovich, Lectures in Mathematical Stability Theory [in Russian], Nauka, Moscow (1967).Google Scholar
  11. 11.
    G. Houghton, “Theory of bubble pulsation and cavitation,” J. Acoust. Soc. Amer.,35, No. 9 (1963).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • S. P. Levitskii
    • 1
  • A. T. Listrov
    • 1
  1. 1.Voronezh

Personalised recommendations