Resonance of a Bubble on an Infinite Rigid Boundary

Blue, Joseph E.

doi:10.1121/1.1910347

Cited by 30 publications

(26 citation statements)

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“…This is expected and confirms that the resonance response of the bubble has been detected by the hydrophone. Also, both the image theory and the experimental data lie below Minnaert's relationship, which is consistent with the data of previous investigators; [18][19][20] and from the present work, enough data points are now available for the functional form of the relation to be confirmed. According to the image theory, this can be reasoned as follows.…”

Section: A Single Bubble Arrangement With Varying Bubble Sizesupporting

confidence: 92%

Symmetric mode resonance of bubbles attached to a rigid boundary

Payne

Illesinghe

Ooi

et al. 2005

The Journal of the Acoustical Society of America

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Experimental results are compared with a theoretical analysis concerning wall effects on the symmetric mode resonance frequency of millimeter-sized air bubbles in water. An analytical model based on a linear coupled-oscillator approximation is used to describe the oscillations of the bubbles, while the method of images is used to model the effect of the wall. Three situations are considered: a single bubble, a group of two bubbles, and a group of three bubbles. The results show that bubbles attached to a rigid boundary have lower resonance frequencies compared to when they are in an infinite uniform liquid domain ͑referred to as free space͒. Both the experimental data and theoretical analysis show that the symmetric mode resonance frequency decreases with the number of bubbles but increases as the bubbles are moved apart. Discrepancies between theory and experiment can be explained by the fact that distortion effects due to buoyancy forces and surface tension were ignored. The data presented here are intended to guide future investigations into the resonances of larger arrays of bubbles on rigid surfaces, which may assist in surface sonochemistry, sonic cleaning, and micro-mixing applications.

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Section: A Single Bubble Arrangement With Varying Bubble Sizesupporting

confidence: 92%

Symmetric mode resonance of bubbles attached to a rigid boundary

Payne

Illesinghe

Ooi

et al. 2005

The Journal of the Acoustical Society of America

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“…The majority of the experiments have been performed with bubbles tethered to a wall, a wire, a fibre or a glass rod (Howkins 1965;Hullin 1977;Gorskii et al 1988;Leighton et al 1991Leighton et al , 1997Birkin et al 2004;Bremond et al 2005a). The dynamics of a tethered bubble differ from the behaviour of a free bubble (Blue 1967;Leighton 1994;Weninger et al 1997;Bremond et al 2005b;Maksimov 2005). Since the experimental observations reported here did not include significant translational motion (this will not necessarily be true for all tethered bubbles (Tho et al 2007; in press)), if the contact area is small compared with the total area of the bubble, the observed effect of tethering can be relatively weak.…”

Section: Derivation Of Amplitude Equationsmentioning

confidence: 99%

Pattern formation on the surface of a bubble driven by an acoustic field

Maksimov

Leighton

2011

Proc. R. Soc. A.

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The final stable shape taken by a fluid–fluid interface when it experiences a growing instability can be important in determining features as diverse as weather patterns in the atmosphere and oceans, the growth of cell structures and viruses, and the dynamics of planets and stars. An example which is accessible to laboratory study is that of an air bubble driven by ultrasound when it becomes shape-unstable through a parametric instability. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the breathing mode, regular patterns of surface waves are observed on the bubble wall. The existing theoretical models, which take account only of the interaction between the breathing and distortion modes, cannot explain the selection of the regular pattern on the bubble wall. This paper proposes an explanation which is based on the consideration of a three-wave resonant interaction between the distortion modes. Using a Hamiltonian approach to nonlinear bubble oscillation, corrections to the dynamical equations governing the evolution of the amplitudes of interacting surface modes have been derived. Steady-state solutions of these equations describe the formation of a regular structure. Our predictions are confirmed by images of patterns observed on the bubble wall.

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“…The resonant frequency [5,11,12] of bubbles in a liquid can be described as follows, using the bubble radius r: Figure 8 shows the resonant frequency at constant acoustic pressure with r ranging from 0.001 mm to 1 mm. The resonant frequency is 300 kHz or higher when r is smaller than 0.01 mm.…”

Section: Resonant Frequency Of Bubblesmentioning

confidence: 99%