Bubble Rebound Research Articles

Implosion of an underwater spark-generated bubble and acoustic energy evaluation using the Rayleigh model

The growth, collapse, and rebound of a vapor bubble generated by an underwater spark is studied by means of high-speed cinematography, simultaneously acquiring the emitted acoustic signature. Video recordings show that the growth and collapse phases are nearly symmetrical during the first two or three cycles, the bubble shape being approximately spherical. After 2-3 cycles the bubble behavior changes from a collapsing/rebounding regime with sound-emitting implosions to a pulsating regime with no implosions. The motion of the bubble wall during the first collapses was found to be consistent with the Rayleigh model of a cavity in an incompressible liquid, with the inclusion of a vapor pressure term at constant temperature within each bubble cycle. An estimate of the pressure inside the bubble is obtained measuring the collapse time and maximum radius, and the amount of energy converted into acoustical energy upon each implosion is deduced. The resulting value of acoustic efficiency was found to be in agreement with measurements based on the emitted acoustic pulse.

3D Jet Impact and Toroidal Bubbles

A three-dimensional model of collapsing bubble with jet formation and impact is presented in this paper. The strong instabilities of the jetting process, impact, and toroidal bubble rebound are dampened by a new smoothing scheme based on least squares, thus enabling a smooth transition from a singly connected bubble to a doubly connected toroidal bubble. A high order of mesh regularity is maintained by a mesh refinement procedure. The circulation of the flow around the gaseous tube of the toroidal bubble is modelled by a generalization of the vortex ring method of Q. X. Wang et al. (Comput. Fluids25, 607 (1996)). Although our results indicate some differences from previous axisymmetric results in terms of time to impact and fine features of the evolving toroidal bubble profiles, the essential physics associated with the jet impact, such as the circulation around the torus and the rebound of the toroidal bubble, are well captured in the new model. We also present, for the first time, results for fully three-dimensional bubbles in which buoyancy effects lead to oblique jetting.

Behavior of laser-induced cavitation bubbles in liquid nitrogen

Initial behavior and the subsequent motion of a bubble in liquid nitrogen are investigated experimentally using high-speed photography. A bubble is generated by focusing a pulsed ruby laser into liquid nitrogen at 78.0 K, changing the ambient pressures up to 253.2 kPa which corresponds to the applied pressure (or overpressure), Δp, being 147.1 kPa. When the energy level of the laser beam at the focus exceeds an irradiance threshold, for instance 5.4×1011 W/cm2 for Δp=4.9 kPa, the optical breakdown occurs in the liquid nitrogen, followed by a series of high-speed phenomena such as plasma formation, shock wave emission, and vapor bubble generation. It is found that during a very short period after the plasma formation a bubble grows nonspherically reflecting from the plasma shape, but the bubble volume itself varies with time in the same way for all cases performed in the present experiment. The liquid inertia is a dominant factor affecting the bubble growth, while the thermal effect becomes remarkable during the bubble collapse, resulting in the retardation of the bubble motion. The characteristic behavior of a laser-induced cavitation bubble in liquid nitrogen is significantly influenced by the phase change of vapor at the bubble surface as well as by the vapor pressure inside the bubble. Immediately after the bubble rebound, instabilities are amplified over the bubble surface similar to those caused in the water case.

Bubble dynamics, shock waves and sonoluminescence

Sound and light emission by bubbles is studied experimentally. Single bubbles kept in a bubble trap and single lasergenerated bubbles are investigated using ultrafast and highspeed photography in c...

Localized detection of cavitation generated by lithotripsy shock waves

Extracorporeal shock wave lithotripters generate intense cavitation which plays a role in both kidney stone destruction and tissue damage. The cavitation can be detected by listening for the characteristic ‘‘double-bang‘‘ acoustic emission, radiated by the bubbles during their rapid expansion and collapse phases. Previous workers have used a single focused transducer to detect the double-bang signature. However, the focal spot of the transducers is typcially 5 cm long and individual cavitation events can not be localized. A system has been developed that uses two confocal transducers (1 MHz, 20 cm radius of curvature, 10 cm diameter) to detect cavitation events in a localized volume. The system can be run in two modes: passive or active. In the passive mode both transducers listen to acoustic emissions generated by the cavitation field. In the active mode one transducer sends a tone and the second transducer listens to the sound scattered by any bubbles present in the focal region. In both cases the region to which the detectors are sensitive is approximately a sphere 5 mm in diameter. The passive system shows bubble rebound times far longer than predicted by theory for a single bubble. Scattering indicates that bubbles persist in the focal region for at least 6 ms. [Work supported by NIH.]

On the nonspherical collapse and rebound of a cavitation bubble

The behavior of a cavitation bubble adjacent to a rigid wall is studied numerically with the boundary integral method described in Zhang, Duncan, and Chahine [J. Fluid Mech. 257, 147 (1993)]. In the previous work, the pressure inside the bubble was held constant (this is referred to herein as the empty bubble case). In the present calculations, an internal gas pressure, which is a function of the bubble volume, is included in the model. The present results are qualitatively similar to those in the empty bubble case in several ways: a wall-directed reentrant jet is formed in the later phase of the collapse; this jet impacts with the side of the bubble closest to the wall creating a toroidal-shaped bubble; and a shear layer develops along the impact interface. However, unlike the empty bubble, whose volume decreases monotonically to zero at the end of the collapse, the present gas-filled bubble reaches a minimum volume and then, due to its high internal gas pressure, begins to grow again (rebound). In the empty bubble case, the hydrodynamic pressure on the wall rises rapidly at the end of the calculation making it impossible to compute the maximum value of the pressure. In the present calculations, the pressure on the wall is found to reach a maximum value when the bubble starts to rebound. This timing of the pressure peak is in agreement with the experimental data of Tomita and Shima [J. Fluid Mech. 169, 535 (1986)] and Kimoto [International Symposium on Cavitation Research Facilities and Techniques (American Society of Mechanical Engineers, New York, 1987), Vol. 57, pp. 535–564], as are the orders of magnitude of the maximum pressures. Direct comparison with the numerical results of Best [J. Fluid Mech. 251, 79 (1993)] are also presented. Large differences in bubble shapes and flow fields are found.

Numerical study of single-vapor-bubble dynamics in insulating liquids initiated by electrical current pulses

In this paper we present a study of the dynamics (growth, collapse, and rebound) of a single bubble (typical radius 1–10 μm) as a function of various parameters: injected energy, hydrostatic pressure (for a wide range 0.1–12 MPa), and several liquid hydrocarbons of different physical properties. It appears that between two rebounds the dominant role is played by liquid inertia. However, rapid damping occurs, and we examine here the influence of both liquid viscosity and acoustic radiation on this mechanism, discarding heat and mass transfers. Two simple models are proposed: the first one, based on a Herring modified model, and the second one, based on the Rayleigh–Plesset equation. The discrepancy with experimental results suggests that further insight must be achieved, taking into account the neglected transfers between vapor and liquid.

Direct observation of the pressure developed in a liquid during cavitation-bubble collapse

A Mach–Zehnder interferometer with a pulsed dye-laser light source is used to observe the collapse of laser-produced cavitation bubbles in water near a rigid transparent polymeric boundary. Vapor bubbles with a maximum radius of about a millimeter are formed using a Q-switched Nd:YAG laser operating at 1.06 μm with a pulse energy of 4.6 mJ and a pulse duration of 8 ns. The pressure in the liquid around the bubbles is determined directly from the resulting interferograms using a fringe tracing method. Prior to bubble rebound, a region of compressed water develops adjacent to the cavity and a weak acoustic wave is directed towards the rigid boundary.

Secondary cavitation due to interaction of a collapsing bubble with a rising free surface

An experimental investigation was made of the motion of a cavitation bubble in the vicinity of a free surface in order to study an induced secondary cavitation during the bubble rebound. A bubble was produced by focusing a ruby laser into water, and its subsequent behavior was observed with a high-speed camera. The deformable nature of both a bubble and a free surface becomes significant as the mutual distance between them is decreased. Immediately after bubble rebound, a secondary cavitation occurs at around zero dynamic pressure region which is developed in water between a rising free surface and a collapsing bubble, due to the local pressure reduction mainly caused by the interaction of expansion waves originated from the surface.

An Investigation of the Motion of a Bubble near a Free Surface.

An investigation was made of the motion of a cavitation bubble in the vicinity of a free surface experimentally as well as theoretically. A bubble was produced by focusing a ruby laser into water, and subsequent behavior was observed with a high speed camera. The deformable nature of both a bubble and a free surface becomes significant when a bubble behaves relatively close to the surface. Immediately after the bubble rebound a secondary cavitation occurs, at around zero dynamic pressure region, which was developed in water between a rising free surface and a re-expanding bubble due to lower pressure caused by the interaction of reflected expansion waves from the surface. Some aspects of the bubble motion were compared with image theory with good agreement.

Collapse and rebound of a gas-filled spherical bubble immersed in a diagnostic ultrasonic field

This work is concerned with the influence of the finite-amplitude distortion of a driving diagnostic ultrasonic field on the collapse and rebound of a gas-filled spherical microbubble, present in the exposed compressible liquid. Such an analysis is especially important since one of the mechanisms for cavitation damage comes from the very large gas pressures generated at bubble collapse and in the subsequent pressure wave formed by bubble rebound. Gilmore's model [F.R. Gilmore, "The growth or collapse of a spherical bubble in a viscous compressible liquid," Hydrodynamics Lab. Rep. No. 26-4, California Institute of Technology, Pasadena, CA (1952)] for bubble dynamics is used to obtain the motion of the bubble interface when subjected to a pulsed diagnostic ultrasonic field of large amplitude. Knowledge of the bubble motion allows one to derive the pressure distribution around the bubble. Numerical results over a range of initial bubble sizes, acoustic pressures, and frequencies relevant to medical use show that the strength of the pressure spikes radiated by the rebounding bubble depends upon (i) the acoustic frequency (f), (ii) the initial bubble size (R0), and (iii) the magnitude of the pressure amplitude of the fundamental (PF) in a Fourier series description of the distorted pulse. As the pressure spikes propagate outward from the bubble wall, their strength is attenuated as the reciprocal of the distance from the center of collapse.

An experimental study of the behavior of bubbles and shock waves generated by laser focusing in water.

This paper deals with an experimental study on the collapsing process of bubbles produced by a focused ruby laser beam in water. The behavior of the collapsing bubbles, and propagation of shock waves induced in the process were observed using double a exposure holographic interferometer and an Ima-Con Camera. The impact pressure was measured by changing the distance between the focusing point of the laser beam and a pressure gauge. Results indicated that the impact pressure induced at the instant of bubble rebound was more intense than that induced at bubble initiation due to the laser focusing, and showed how the impact pressure was attenuated with the distance.

Experimental Study of the Shock Generation at the Collapse of Cavitation Bubble

Using a photoelastic apparatus or Schlieren interferometer, we experimentally studied the mechanism of the impulsive force generation by a spark-induced cavitation bubble, collapsing near the solid boundary. The experimental results indicate that the cause of the impulsive force is classified by the parameter l, where l= (maximum bubble center distance from the solid boundary) / (maximum bubble radius). In case of lg1.35, the shock waves are dominant and in case of l ), both the shock waves and the water microjet are supposed to impact against the solid boundary. Even when an asymmetrically collapsing bubble rebounds, the shock waves are observed.

Experimental Investigations of Cavitation Bubble Collapse by a Water Shock Tube

This paper deals experimentally with the mechanism of an impulsive pressure generated by a collapsing bubble. In a water filled shock tube, an expansion wave and a subsequent compression wave are applied to single, twin and triadic bubbles. The growth, collapse and rebound of bubbles situated at various distances from a solid boundary are observed by means of high-speed photography and in-line Fraunhofer holography using a pulsed dye laser. The results indicate that the impulsive pressure is caused by a shock wave radiated at the instant of the rebound of a collapsing bubble, and that the subsequent jet impingement does not produce any detectable effects. The pressure pulse is found to be of the order 104 ∼ 105 atm, and its duration 2 ∼ 3 μsec.

On the Behavior of a Spherical Bubble and the Impulse Pressure in a Viscous Compressible Liquid

With the help of the PLK coordinate perturbation technique the equation of motion of a spherical bubble in a viscous compressible liquid is derived by taking account of the gas density inside the bubble, and the effects of the liquid compressibility on the variations of the bubble radius, bubble wall velocity and bubble wall pressure with time and the maximum impulse pressure accompanying the bubble collapse are investigated. Further, by considering the liquid compressibility. the pressure distributions in the liquid during the collapse and rebound of bubble are numerically obtained, and natural frequency of bubble is analytically obtained. As a result, the relation between the maximum impulse pressure and the bubble natural frequency is numerically clarified.

On the Behavior of a Spherical Bubble and the Impulse Pressure in a Viscous Compressible Liquid

With the help of the PLK coordinate perturbation technique the equation of motion of a spherical bubble in a viscous compressible liquid is derived by taking account of the gas density inside the bubble, and the effects of the liquid compressibility on the variations of the bubble radius, bubble wall velocity and bubble wall pressure with time and the maximum impulse pressure accompanying the bubble collapse are investigated. Further, by considering the liquid compressibility. the pressure distributions in the liquid during the collapse and rebound of bubble are numerically obtained, and natural frequency of bubble is analytically obtained. As a result, the relation between the maximum impulse pressure and the bubble natural frequency is numerically clarified.

Spherical vapour bubble collapse

An experimental study of spherical vapour bubble collapse in uniformly subcooled water has been performed, and data have been obtained on bubble radius and pressure histories for subcoolings up to 60°C. A theoretical incompressible equilibrium model of spherical collapse in an infinite sea geometry utilising a finite difference technique to solve the heat conduction equations has been developed, and the predictions are shown to agree with the experimental radius and pressure histories to within 30 per cent, subject to the bubble pressure not exceeding the critical pressure of water. The discrepancies are accounted for in terms of the restricted geometry of the experimental vessel. The noise spectra generated by bubble rebound are shown to extend to beyond 100 kHz in water subcoolings above 40°C.

Laser-Induced Cavitation

When intense laser light is focused into liquids, bubbles can be prod need in the vicinity of the focal point. The dynamics of these bubbles is investigated by high-speed photography with picture repetition rates up to 106 frames/sec. Single spherical bubbles can be produced. In water, they can be said to be the experimental realization of the Rayleigh bubble model. Results on both spherical and nonspherical bubble collapse, rebound, and subsequent collapses and rebounds will be reported showing the sequence of events leading to the cloud of minute bubbles often observed after the collapse of a big bubble. Repeated jet formation of the same bubble seems to be the major suicide mechanism. Shedding of minute bubbles occurs by gas entrainment into the jet. Spherical undisturbed collapsing bubbles remain spherical down to very small radii being heavily distorted a few microseconds later during rebound. Nonlinear spherical bubble oscillations are investigated in silicone oils. The stability of the spherical shape seems to be enhanced by viscosity. A comparison is made with calculated nonlinear bubble oscillations damped by viscosity.

Sonoluminescence and the Acoustic Cavitation of Water

The emission of sonoluminescence from aqueous solutions cavitated at 16 and 500 kHz is discussed in terms of the bubble motion with which it is associated and the mechanism by which the light is produced. It is shown from measurements of the phases of the sound pressure cycle at which the sonoluminescence flashes occur that bubble nuclei must grow to over half their resonant size before being capable of imploding to produce a sonoluminescence flash and that the secondary flash is probably due to a bubble rebound. Spectra of the sonoluminescence from different solutions show continua of various shapes, OH bands, and, in cases where there are salts in solution, spectral lines which may be quenched by the presence of some dissolved gases. From these data a model is postulated which suggests that part of the light emitted is due to an incandescence of the bubble contents and part to chemiluminescent reactions within the bubble. It is shown that no feature of the spectrum can give much useful information about conditions within the bubble during its implosion, although other authors have suggested the contrary.

Cavitation Bubble Collapse Observations in a Venturi

Bubbles collapsing in water in a cavitating venturi are photographically observed. The large pressure gradient in the venturi causes the bubbles to collapse by flattening in the direction of flow. In many cases a torus is formed, implying the existence of a central jet which, as has been suggested by other investigators, may well be the primary damaging mechanism in cavitating flows. The effect of adjacent bubbles upon each other is visually observed. Numerous bubble rebounds, even in relatively degassed water, are noted. A comparison of observed collapse rates with incompressible theory for a spherical bubble indicates that the slowing down of collapse herein observed at small bubble radii probably results primarily from the asymmetry of the collapse and perhaps also from metastable compression of vapor within the bubble.