Shape Oscillations Of Bubbles Research Articles

Comment on ``Bubble Shape Oscillations and the Onset of Sonoluminescence''

A Comment on the Letter by Michael P. Brenner, Detlef Lohse, and T. F. Dupont, Phys. Rev. Lett. 75, 954 (1995). The author of the Letter offer a Reply.

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Free decay of shape oscillations of bubbles acoustically trapped in water and sea water

Asymptotic results for the free decay of shape oscillations of viscous liquid spheres have been extended to include higher-order terms in the ratios of the inner and outer viscous penetration lengths to the radius. The new expressions are shown to be important for studies in which the two fluids have dissimilar densities and viscosities such as air/liquid systems. The analysis also includes an expansion for the frequency of maximum response of driven oscillations. The calculations are supported by measurements of the small-amplitude quadrupole mode free decay of nearly spherical bubbles acoustically levitated in clean water. The bubble radii ranged from 400 μm to 1400 μm. The results are interpreted in light of the initial-value problem. The lack of excess damping suggests that the interface behaves ideally for times up to two hours after bubble injection. Measurements were also carried out on bubbles in 0.5 m NaCl solution and in sea water. Larger bubbles (radius > 800 μm) in clean water exhibit damping two to four times larger than predicted by theory. The transition from this anomalous damping to theoretical damping is a very abrupt function of radius. All observations were carried out with similar acoustic fields for counteracting buoyancy. The excess damping appears to be associated with some nonlinear response of the bubble.

Bubble Shape Oscillations and the Onset of Sonoluminescence

An air bubble trapped in water by an oscillating acoustic field undergoes either radial or nonspherical pulsations depending on the strength of the forcing pressure. Two different instability mechanisms (the Rayleigh--Taylor instability and parametric instability) cause deviations from sphericity. Distinguishing these mechanisms allows explanation of many features of recent experiments on sonoluminescence, and suggests methods for finding sonoluminescence in different parameter regimes.

An experimental investigation of bubble shapes from a nozzle in water

The shape oscillations of bubbles from a nozzle in water have been well investigated by Longuet-Higgins [M. S. Longuet-Higgins, J. Fluid Mech. 201, 543–565 (1989)]. In the present paper the elliptical deformation due to a bubble rising in water is introduced in the Longuet-Higgin’s theory. The bubble shape oscillations in water are also experimentally observed using a stroboscope photographic technique. The theory with an elliptical deformation condition well describes the experimental observation of bubble shape oscillations. The dependence of antipole time on bubble radius shows good agreement between the theoretical estimation and the experimental observation. [Work supported by the Korea Science and Engineering Foundation.]

Experiments and analysis of shape oscillations of bubbles levitated in water on the Earth

Levitation and excitation of shape oscillations for bubbles in water were demonstrated for the size range 1.6 to 12-mm diameter [T. J. Asaki, P. L. Marston, and E. H. Trinh, J. Acoust. Soc. Am. 93, 706–713 (1993)]. Novel methods of experimentation and analysis in the current research should complement experiments carried out in microgravity. Current research concerns the understanding of equilibriuim shape effects on steady-state and freely decaying shape oscillations. These oscillations were studied with an optical extinction method. The measurements probe the surface rheology of the bubble. The experimental method has been shown to be applicable to saline solution as well as to degassed but otherwise untreated sea water. [Research supported by ONR and DOE GAANN fellowship.]

Shape oscillations of bubbles in water driven by modulated ultrasonic radiation pressure: Observations and detection with scattered laser light

Steady-state quadrupole shape oscillations of air bubbles trapped in water were excited by amplitude modulation of the acoustic radiation pressure used for levitation. This method of exciting controlled shape oscillations may make possible noncontact dynamical measurements of the rheological properties of bubbles. Bubble sizes ranged from 1.6- to 12-mm diameter corresponding to observed quadrupole mode frequenices of 190 to 17 Hz. Small-amplitude oscillations were detected by interference of scattered laser light. Some larger amplitude oscillations were detected by the unaided eye or with a television camera. The structure of the acoustic field in the levitator needed for the levitation of large bubbles is discussed. In the absence of modulation the levitated bubbles had an oblate shape.

Shape oscillations of bubbles driven by modulated ultrasonic radiation pressure: The complex frequency response.

The shape of a bubble in water should change in response to the radiation pressure of an ultrasonic wave. Modulation of the radiation pressure at the resonance frequencies for shape oscillations should facilitate the stable excitation of such modes [P. L. Marston, J. Acoust. Soc. Am. 67, 15–26 (1980)]. Levitation and detection of shape oscillations were previously discussed for bubbles in the size range 1–5 mm diameter [P. L. Marston etal., J. Acoust. Soc. Am. 89, 1885(A) (1991)]. Levitator design improvements have allowed stable trapping and shape oscillation detection for bubbles in the size range 1–12 mm diameter. The quadrupole mode was observed with resonance frequencies in the range 400–15 Hz. Oscillations over a more limited range were studied with a laser light scattering method that allowed the response phase and amplitude to be measured. The phase is referenced to the amplitude modulation of the acoustic field. Further experiments have involved the effects of surfactants, levitation of thin liquid shells, splitting of bubbles, and surface instabilities. [Research supported by ONR and NASA.]

Shape oscillations of bubbles driven by modulated ultrasonic radiation pressure: Experiments

The shape of a bubble in water should change in response to the radiation pressure of an ultrasonic wave. Furthermore, modulation of the radiation pressure at the resonance frequencies for shape oscillations should facilitate the stable excitation of such modes [P. L. Marston, J. Acoust. Soc. Am. 67, 15–26 (1980)]. Recently this method of driving oscillations has been demonstrated by employing a novel ultrasonic levitator developed at Jet Propulsion Laboratory which traps bubbles in the size range of 1- to 5-mm diameter. The quadrupole mode was observed with resonance frequencies in the range from 400 to 40 Hz. Oscillations were detected with the unaided eye and with television and laser light scattering methods. These experiments suggest methods for investigating the nonlinear dynamics of bubbles, effects of surfactants, and the dynamics of bubbles in low gravity. Some comparisons with the dynamics of drops will be noted. [Research supported by ONR and NASA.]

Resonance in nonlinear bubble oscillations

In two recent papers (Longuet-Higgins 1989a,b) the author showed that the shape oscillations of bubbles can emit sound like a monopole source, at second order in the distortion parameter ε. In the second paper (LH2) it was predicted that the emission would be amplified when the second harmonic frequency 2σn of the shape oscillation approaches the frequency ω of the breathing mode. This ‘resonance’ would however be drastically limited by damping due to acoustic radiation and thermal diffusion. The predictions were confirmed by further numerical calculations in Longuet-Higgins (1990a).Ffowcs Williams & Guo (1991) have questioned the conclusions of LH2 on the grounds that near resonance there is a slow (secular) transfer of energy between the shape oscillation and the volumetric mode which tends to diminish the amplitude of the shape oscillation and hence falsify the perturbation analysis. They have also argued that the volumetric mode never grows sufficiently to produce sound of the stated order of magnitude. In the present paper we show that these assertions are unfounded. Ffowcs Williams & Guo considered only undamped oscillations. Here we show that when the appropriate damping is included in their analysis the secular transfer of energy becomes completely insignificant. The resulting pressure pulse (figure 5 below) is found to be essentially identical to that calculated in LH2, figure 3. Moreover, in the initial-value problem considered in LH2, the excitation of the volumetric mode takes place not by a secular energy transfer but by a resonance during the first few cycles of the shape oscillation. This accounts for the amplification near resonance found in Longuet-Higgins (1990a). Finally, it is pointed out that the initial energy of the shape oscillations is far greater than is required to produce the O(ε2) volume pulsations that were studied in LH2, and which were used for a comparison with field data. This acoustic radiation was not calculated by Ffowcs Williams & Guo.

Bubble Noise

The natural mechanisms for generating underwater sound at the sea surface have recently been the subject of renewed interest. † Oceanic noise at frequencies from 1 to 50 kHz are known to be associated with breaking waves, presumably through the sound emitted by newly formed bubbles. The precise mechanism of sound generation has remained unclear. The present paper reviews some recent contributions by the author and others, which have shown that the shape oscillations of bubbles produce a monopole radiation of sound at second order, and may contribute sigru6cantly to the noise spectrum. This suggestion is supported by field observations and laboratory experiments.

Bubble noise spectra

When bubbles are formed by the enclosure of pockets of air, they must first undergo extreme distortions before settling down into a spherical shape. In two recent papers [M. S. Longuet-Higgins, J. Fluid Mech. 201, 525–541 (1989); 201, 543–565 (1989)] it has been shown that the shape oscillations of bubbles will, at second order, contain radially symmetric ‘‘monopole’’ terms, having double the fundamental frequency. These terms can resonate with the radial, ‘‘breathing’’ mode to produce significant levels of sound in the ocean. In the present paper it is shown that any broad spectrum of bubble-generated sound may be expected to show peaks at the corresponding resonance frequencies. A first examination of the available oceanic data does indeed show evidence of such resonances, particularly at the even-numbered mode frequencies. The same mechanism may also help to explain certain resonances observed in laboratory experiments by Medwin and Beaky [J. Acoust. Soc. Am. 86, 1124–1130 (1989)].

Note on shape oscillations of bubbles

By use of a virial equation introduced in a recent paper (Benjamin 1987), the main results of a second-order perturbation theory developed by Longuet-Higgins (1989a) are recovered in comparatively simple fashion. Asymmetric capillary vibrations of a gas bubble in an infinite incompressible liquid are confirmed to generate an increase in the volume of the bubble, a lowering of the mean pressure of the gas and a monopole component in the motion of the liquid. It is shown that the second effect remains when the bubble is incompressible.