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    McDougald, Neil K. and Leal, L.Gary 1999. Numerical study of the oscillations of a non-spherical bubble in an inviscid, incompressible liquid. Part I: free oscillations from non-equilibrium initial conditions. International Journal of Multiphase Flow, Vol. 25, Issue. 5, p. 887.

    Feng, Z. C. and Leal, L. G. 1997. NONLINEAR BUBBLE DYNAMICS. Annual Review of Fluid Mechanics, Vol. 29, Issue. 1, p. 201.

    Feng, Z. C. and Leal, L. G. 1995. Translational instability of a bubble undergoing shape oscillations. Physics of Fluids, Vol. 7, Issue. 6, p. 1325.

    Feng, Z. C. and Leal, L. G. 1994. Bifurcation and chaos in shape and volume oscillations of a periodically driven bubble with two-to-one internal resonance. Journal of Fluid Mechanics, Vol. 266, Issue. -1, p. 209.

    Leighton, T.G. 1994. The Acoustic Bubble.

    Yang, Seung-Man 1994. Dynamics of bubble oscillation and pressure perturbation in an external mean flow. Korean Journal of Chemical Engineering, Vol. 11, Issue. 4, p. 271.

    Kang, I. S. 1993. Dynamics of a conducting drop in a time-periodic electric field. Journal of Fluid Mechanics, Vol. 257, Issue. -1, p. 229.

    Yang, S. M. Feng, Z. C. and Leal, L. G. 1993. Nonlinear effects in the dynamics of shape and volume oscillations for a gas bubble in an external flow. Journal of Fluid Mechanics, Vol. 247, Issue. -1, p. 417.

    Feng, James Q. and Beard, Kenneth V. 1991. Resonances of a conducting drop in an alternating electric field. Journal of Fluid Mechanics, Vol. 222, Issue. -1, p. 417.

    Sangani, A. S. 1991. A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. Journal of Fluid Mechanics, Vol. 232, Issue. -1, p. 221.

    Kang, I. S. and Leal, L. G. 1990. Bubble dynamics in time-periodic straining flows. Journal of Fluid Mechanics, Vol. 218, Issue. -1, p. 41.

  • Journal of Fluid Mechanics, Volume 187
  • February 1988, pp. 231-266

Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)

  • I. S. Kang (a1) and L. G. Leal (a1)
  • DOI:
  • Published online: 01 April 2006

The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = ⅙π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω2 = ω00(1−0.31W), where ω0 is the oscillation frequency of a bubble in a quiescent fluid.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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