Nonspherical sub-millimeter gas bubble oscillations: Parametric forcing and nonlinear shape mode coupling

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Abstract

The nonspherical oscillations of a gas bubble being forced by a sinusoidal pressure field in an axisymmetric geometry are considered using an asymptotic model, which accounts for nonlinear shape mode interactions to third order, the effects of viscosity (in the absence of vorticity) to the same order, and weak compressibility. In particular, conditions by which a parametrically forced sub-millimeter sized bubble can achieve stable oscillatory shape deformation are studied in detail. It is found that a combination of the transfer of energy from the parametrically forced shape mode to the other modes through nonlinear shape mode coupling and viscous damping is key. Two transition regions in the spherical oscillations of the bubble are identified, the first being a consequence of the damping effects of compressibility and viscosity (with compressibility acting on a faster time scale) and the second due to nonlinear shape mode interactions. During this second transition time interval, the parametrically forced shape mode grows rapidly and nonlinearly excites other shape modes. For the moderate driving pressures considered, this growth is shown to peak and following a stabilizing transition region (only observed for the n ≥ 3 shape modes), the bubble thereafter undergoes stable, oscillatory shape deformation. Though the resultant shape deformation is dominated by the parametrically forced mode n = i, it is found to be a combination of a number of shapes modes, where the next most important mode is the second harmonic, n = 2i shape mode.

Original languageEnglish
Article number122103
JournalPhysics of Fluids
Volume29
Issue number12
DOIs
Publication statusPublished - 1 Dec 2017

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