Werner Lauterborn

Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary

The dynamics of laser-produced cavitation bubbles near a solid boundary and its dependence on the distance between bubble and wall are investigated experimentally. It is shown by means of high-speed photography with up to 1 million frames/s that jet and counterjet formation and the development of a ring vortex resulting from the jet flow are general features of the bubble dynamics near solid boundaries. The fluid velocity field in the vicinity of the cavitation bubble is determined with time-resolved particle image velocimetry. A comparison of path lines deduced from successive measurements shows good agreement with the results of numerical calculations by Kucera & Blake (1988). The pressure amplitude, the profile and the energy of the acoustic transients emitted during spherical bubble collapse and the collapse near a rigid boundary are measured with a hydrophone and an optical detection technique. Sound emission is the main damping mechanism in spherical bubble collapse, whereas it plays a minor part in the damping of aspherical collapse. The duration of the acoustic transients is 20-30 ns. The highest pressure amplitudes at the solid boundary have been found for bubbles attached to the boundary. The pressure inside the bubble and at the boundary reaches about 2.5 kbar when the maximum bubble radius is 3.5 mm. The results are discussed with respect to the mechanism of cavitation erosion.

Numerical investigation of nonlinear oscillations of gas bubbles in liquids

Forced oscillations of a spherical gas bubble in an incompressible, viscous liquid (water) are calculated numerically. The information gathered is mainly displayed in the form of frequency response curves of the steady‐state solutions showing the harmonics, subharmonics, and ultraharmonics. Bubbles oscillating ultraharmonically at frequencies below the main resonance may emit half the driving frequency. This fact gives rise to a new explanation for the occurrence of the first subharmonic in the spectrum of the cavitation noise in ultrasonic cavitation.Subject Classification: [43]30.70, [43]30.75.

Physics of bubble oscillations

Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.

Collapse and rebound of a laser-induced cavitation bubble

A strong laser pulse that is focused into a liquid produces a vapor cavity, which first expands and then collapses with subsequent rebounds. In this paper a mathematical model of the spherically symmetric motion of a laser-induced bubble is proposed. It describes gas and liquid dynamics including compressibility, heat, and mass transfer effects and nonequilibrium processes of evaporation and condensation on the bubble wall. It accounts also for the occurrence of supercritical conditions at collapse. Numerical investigations of the collapse and first rebound have been carried out for different bubble sizes. The results show a fairly good agreement with experimental measurements of the bubble radius evolution and the intensity of the outgoing shock wave emitted at collapse. Calculations with a small amount of noncondensable gas inside the bubble show its strong influence on the dynamics.

Acoustic transient generation by laser-produced cavitation bubbles near solid boundaries

The acoustic transients emitted after breakdown and cavitation bubble collapse upon focusing a Q‐switch laser pulse into a liquid are investigated with special emphasis on their modifications induced by a solid boundary. For measuring the form p(t)/pmax of the pressure pulses an optical technique with a resolution of 10 ns has been developed. When p(t)/pmax is known, the pressure amplitude can be determined even when a transducer with a rise time much longer than the pulse duration is used. The duration of the transients (20–30 ns) and their pressure are nearly the same after breakdown and spherical bubble collapse. During spherical collapse, a maximum pressure of about 60 kbar is developed inside a bubble with Rmax=3.5 mm, and on average 73% of the bubble energy loss is transformed into acoustic energy. The sound emission near a solid boundary strongly depends on the normalized distance γ between the bubble and the boundary. The highest pressures at the boundary are achieved for γ→0; for γ=0.2 and Rmax =...

Cavitation bubble dynamics.

The dynamics of cavitation bubbles on water is investigated for bubbles produced optically and acoustically. Single bubble dynamics is studied with laser produced bubbles and high speed photography with framing rates up to 20.8 million frames per second. Examples for jet formation and shock wave emission are given. Acoustic cavitation is produced in water in the interior of piezoelectric cylinders of different sizes (up to 12 cm inner diameter). The filementary structure composed of bubbles is investigated and their light emission (sonoluminescence) studied for various driving strengths.

Bubble dynamics, shock waves and sonoluminescence

Sound and light emission by bubbles is studied experimentally. Single bubbles kept in a bubble trap and single laser–generated bubbles are investigated using ultrafast and high–speed photography in combination with hydrophones. The optical observation at 20 million frames per second of the shock waves emitted has proven instrumental in revealing the dynamic process upon bubble collapse. When jet formation is initiated by a non–spherically symmetric environment, several distinct shock waves are emitted within a few hundred nanoseconds, originating from different sites of the bubble. The counterjet phenomenon is interpreted in this context as a secondary cavitation event. Furthermore, the light emission of laser–generated cavities (termed cavitation bubble luminescence) is studied with respect to the symmetry of collapse. The prospects of optical cavitation and multibubble trapping in the study of few–bubble systems and bubble interactions are briefly discussed. Finally, the behaviour of bubble clouds, their oscillations, acoustic noise and light emission are described. Depending on the strength of the driving sound field, period doubling and chaotic oscillations of the collective bubble dynamics are observed.

Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt)

Abstract Resonance curves, bifurcation diagrams, and phase diagrams of the Duffing equation x + d x + x + x 3 = f cos (ωt) are presented. They show a periodic recurrence of a specific fine structure in the bifurcation set, which is closely connected with the nonlinear resonances of the system.

Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall

Collapse and rebound of a cavitation bubble near a wall are revisited with modern experimental means. The bubble is generated by the optical breakdown of the liquid when a strong laser pulse is focused into water. Observations are made with high-speed cinematography; framing rates range between several thousand and 100 million frames per second, and the spatial resolution is in the order of a few micrometres. After formation the bubble grows to a maximum size with a radius of 1.5 mm at the pulse energy used, and in the subsequent collapse a liquid jet evolves on the side opposite the wall and penetrates through the bubble. Using a shadowgraph technique and high framing rates, the emission of shock waves, which is observed at minimum bubble size, is resolved in detail. For a range of stand-off distances between the bubble centre and the wall, a counterjet forms during rebound. The counterjet is clearly resolved to consist of cavitation micro-bubbles, and a quantitative measure of its height evolution is given. Its emergence might be caused by a shock wave, and a possible connection of the observed shock wave scenario with the counterjet formation is discussed. No counterjets are observed when the stand-off distance is less than the maximum bubble radius, and the bubble shape becomes toroidal after the jet hits the wall. The jet impact on the wall produces a pronounced splash, which moves radially outwards in the space between the bubble and the wall. The volume compression at minimum bubble size is found to depend strongly on the stand-off distance. Some of the results are compared to numerical simulations by Tong et al. (1999), and the material presented may also be useful for comparison with future numerical work.

Bifurcation structure of bubble oscillators

Methods from chaos physics are applied to a model of a driven spherical gas bubble in water to determine its dynamic properties, especially its resonance behavior and bifurcation structure. The dynamic properties are described in a growing level of abstraction by radius‐time curves, trajectories in state space, strange attractors in the Poincare plane, basins of attraction, bifurcation diagrams, winding number diagrams, and phase diagrams. A sequence of bifurcation diagrams is given, exemplifying the recurrent pattern in the bifurcation set and its relation to the resonances of the system. Period‐doubling cascades to chaos and back (‘‘period bubbling’’) are a prominent recurring feature connected with each resonance (demonstrated for period‐1, period‐2, and period‐3 resonances, and observed for some higher‐order resonances). The recurrent nature of the bifurcation set is most easily seen in the phase diagrams given. A similar structure of the bifurcation set has also been found for other nonlinear oscilla...