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Dynamic stabilization of an asymmetric nonlinear bubble oscillator

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Abstract

The present study focuses on the possibilities of dynamic stabilization of a gas–vapour bubble below Blake’s critical threshold (Blake in the onset of cavitation in liquids, 1949) by harmonic forcing. In bubble dynamics, in terms of the ambient pressure, this threshold is known as a special limit where bubbles tend to grow infinity due to the non-strictly dissipative nature of the governing equations. The employed model is the harmonically excited Rayleigh–Plesset equation that is a nonlinear, second-order ordinary differential equation. Partial results have already been published in the literature (Hegedűs in Ultrasonics 54(4):1113, 2014), Hegedűs in Phys Lett A 380(9–10):1012, 2016). Throughout this paper, however, the investigated parameter space is significantly extended: excitation properties (pressure amplitude and frequency), ambient pressure, bubble size and liquid viscosity (amount of dissipation). The numerical results have indicated that domains where stable oscillations exist can always be found below Blake’s threshold. However, from application point of view, it is mandatory to raise the dissipation rate of the system to significantly increase the extent of these domains making the process of dynamic stabilization robust.

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Acknowledgements

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

    Ferenc Hegedűs & Csanád Kalmár

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  1. Ferenc Hegedűs
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Hegedűs, F., Kalmár, C. Dynamic stabilization of an asymmetric nonlinear bubble oscillator. Nonlinear Dyn 94, 307–324 (2018). https://doi.org/10.1007/s11071-018-4360-5

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