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Classification of the bifurcation structure of a periodically driven gas bubble

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Abstract

The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia et al. (Ultrasonics 49(8):605, 2009) revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that \(R_\mathrm{E} \omega \) is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller–Miksis equation, are presented. It is shown that the validity range of Behnia’s condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately \(5\,\upmu \mathrm {m}\).

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Acknowledgments

The research described in this paper was supported by the Hungarian Scientific Research Fund—OTKA, Grant No. K81621. This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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  1. Department of Hydrodynamic Systems, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary

    Roxána Varga & Ferenc Hegedűs

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  1. Roxána Varga
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Correspondence to Roxána Varga.

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Varga, R., Hegedűs, F. Classification of the bifurcation structure of a periodically driven gas bubble. Nonlinear Dyn 86, 1239–1248 (2016). https://doi.org/10.1007/s11071-016-2960-5

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