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Acoustic cavitation, bubble dynamics and sonoluminescence
Ultrasonics Sonochemistry 14 (2007) 484–491 www.elsevier.com/locate/ultsonch
Acoustic cavitation, bubble dynamics and sonoluminescence W. Lauterborn *, T. Kurz, R. Geisler, D. Schanz, O. Lindau Drittes Physikalisches Institut, Universita¨t Go¨ttingen, Friedrich-Hund-Platz 1, D-37077 Go¨ttingen, Germany Received 5 August 2006; accepted 21 September 2006 Available online 24 January 2007
Abstract Basic facts on the dynamics of bubbles in water are presented. Measurements on the free and forced radial oscillations of single spherical bubbles and their acoustic (shock waves) and optic (luminescence) emissions are given in photographic series and diagrams. Bubble cloud patterns and their dynamics and light emission in standing acoustic fields are discussed. 2006 Elsevier B.V. All rights reserved.
1. Introduction In an acoustic field matter is alternately subjected to pressure and tension. In the tension phase a solid may break when the tension exceeds a limiting value. A liquid also may rupture this time to form cavities or bubbles in the liquid that finally close when the tension is released for longer time. In sound fields the bubbles formed also start to oscillate and give rise to a number of distinct effects generating the research area of acoustic cavitation [1,2]. Bubble dynamics forms its basis and sonoluminescence (light from sound) is one of its more spectacular research topics [3]. Acoustic cavitation has found application in ultrasonic cleaning, forms the physical basis of sonochemistry [4] and is presumably involved in shock wave lithotripsy [5]. 2. Single bubble dynamics Bubbles in liquids are fast moving and small objects not easily investigated. In acoustic fields they normally come in swarms or clouds of different forms and sizes with the individual bubbles strongly interacting. A big step forward was achieved when the single bubble trap was invented by *
Corresponding author. E-mail address: [email protected] (W. Lauterborn). 1350-4177/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultsonch.2006.09.017
Gaitan et al. [6]. Now a single bubble could be held at a fixed position in space for investigation, for instance of its light emitting properties. Fig. 1 shows a simple version of a bubble trap. It consists of a cubical or rectangularly shaped container with just one piezoelectric driving element glued to the bottom. A platinum wire is inserted from the side to produce a bubble by a current pulse. The acoustic radiation force drives the bubble to its stable lift position. This is the position of the sonoluminescing bubble given by the bright spot in the upper part of the figure. The flat faces of the cuvette facilitate photographing the (light emitting) bubble and its shock waves. The possible modes of the resonator are determined by the acoustic impedance of its walls and the attached transducer. The walls act as open ends through the air beyond the walls. The transducer arrangement acts nearly as a closed end. Thus, there is a pressure antinode near the bottom of the vessel. Cavitation does not occur at this location, since the driving amplitude is too low. To achieve SBSL it is necessary to stay below the cavitation threshold. Therefore the bubble is produced artificially and injected. For this vessel, SBSL worked best in the depicted mode. Fig. 2 gives one complete cycle of a radially oscillating single bubble driven at 21.4 kHz at a sound pressure amplitude of 132 kPa photographed at 500 ns intervals. Actually the series was obtained by taking a photograph, shifting the time by 500 ns relatively to the fixed reference phase of the sound field, taking the next photograph and so on.
W. Lauterborn et al. / Ultrasonics Sonochemistry 14 (2007) 484–491
Fig. 1. A simple bubble trap with light emitting bubble.
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Due to the stability of the bubble oscillation (also documented this way) almost arbitrary fine time resolution of the bubble dynamics is possible. The images were recorded using a long distance microscope (Infinity K2). A micro channel plate (PCO IRO) was used as a fast shutter down to 5 ns exposure time. It was attached by a relay optic to a CCD camera (Photometrics Sensys). Illumination was performed by a xenon flash lamp (Hamamatsu L4643). The radial oscillation is highly nonlinear with a fast collapse of the bubble down to a very small radius not resolved in space and time in the photographic series. After several small amplitude oscillations in the compression phase of the sound field the bubble is again expanded largely in the tension phase of the sound field and repeats the cycle. At the end of the fast first collapse of the bubble a shock wave is radiated [7,8]. This shock wave is visualized in Fig. 3 by using a shadowgraph schlieren arrangement and the same camera system as in Fig. 2. The dark spot in the middle of the first frame is not the bubble but the shock wave already deflecting the illuminating light to show up as a dark ring. The bubble does not become visible before about the tenth frame as centre of the shock wave. Thus the shock wave quickly detaches from the bubble surface. The light emitted by the bubble is shown in Fig. 4. It is a spot of the size of the resolution of the photographic
Fig. 2. Oscillation of a single bubble trapped in a standing sound field of frequency 21.4 kHz and a sound pressure amplitude 132 kPa. The time difference between the frames is 500 ns, the size of the frames is 160 lm · 160 lm.
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Fig. 4. Photograph of the light emitted by a trapped bubble. Frame size is 1 mm · 1 mm.
Fig. 3. Shock wave emitted upon first collapse of a bubble trapped in a standing sound field of frequency 21.4 kHz and a sound pressure amplitude 132 kPa. The time difference between consecutive frames is 10 ns, the size of the frames is 1.6 mm · 1.6 mm.
system and of bluish appearance. The real size of the light emitting volume is not known, but estimated to below 0.5 lm in radius. The discussion on this topic is still ongoing [9–11]. The single trapped bubbles can be compared with bubbles that can be generated by focussing laser light into a liquid. Then also a single spherical bubble can be produced.
This bubble, however, only lasts for a few of its own oscillation cycles. It is a free instead of a forced oscillation spoken in terms of oscillator theory. It is a strongly nonlinear oscillation as is the acoustically trapped and driven bubble. Fig. 5 shows an example of the free oscillation of a single laser produced bubble. The bubble was induced by a ruby laser with a pulse duration between 30 and 50 ns, a wavelength of 694.3 nm, and an energy per pulse of several 10 mJ. We also work with a Nd:YAG laser with a pulse duration of about 8 ns, a wavelength of 1064 nm and similar energies per pulse. The experiments with laser bubbles are even more demanding than with trapped bubbles as real high speed cinematography has to be applied. In this case a framing rate of 75,000 frames per second has been used to cover the decaying oscillations. The nonlinear free oscillation is strongly damped as seen by the small secondary maximum after rebound from the first collapse. The same is true with the trapped bubbles that, however, repeat
Fig. 5. Free oscillation of a single laser produced bubble in water. The framing rate is 75,000 frames/s, maximum radius is 2 mm.
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Fig. 6. Bubble collapse with shock wave radiated of a single laser produced bubble in water and comparison with theory. The time between frames is about 1 ls.
their cycle over and over again. It is the strong shock wave that carries away most of the energy stored in the bubble [12,13]. Fig. 6 gives an example of the shock wave from a collapsing single laser produced bubble. To catch the shock wave the framing rate has been chosen as about 1 million frames/s. Fig. 6b shows a comparison with a theoretical model of bubble oscillation (Gilmore model, see [2]). A good fit could be achieved except for the exact time of collapse. The strength of the shock waves from the laser bubbles can be measured in absolute pressure terms with a fiber optic hydrophone [14] placed at some distance d from the bubble centre in the liquid (Fig. 7). The fiber optic hydrophone makes use of the alteration of reflection of laser light coming down the fiber when the density in the liquid (and with it the index of refraction) is altered at the tip by a pressure wave in the liquid. Due to the relatively small size of the fiber tip and its high bandwidth it has advantages over conventional (e.g. PVDF) hydrophones for shock pressure
measurements [12,13]. A disadvantage is the lower sensitivity that can be overcome only with high intensity lasers to increase the reflected signal from the fiber tip. Fig. 8 gives the result of a shock wave pressure measurement series with different bubble sizes Rmax. The upper and lower boundaries of the shaded area give the error bounds of the measurements. The pressures obtained at distance d have been extrapolated to the minimum bubble radius by using a 1/r-dependence for the amplitude, where the minimum radius has been obtained by a numerical fit to the bubble collapse similarly as in Fig. 6. About 10 kbar are reached for a bubble collapsing from a radius of 500 lm and about 25 kbar when collapsing from a radius of 3 mm. Unfortunately the collapse pressure from trapped bubbles cannot be measured this way as these bubbles are extremely sensitive to a disturbance nearby and also of lower shock wave strength because of their lower maximum size of less than about a 100 lm and thus less overall energy. But extrapolating the pressure values down to
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Rmax [mm] Fig. 7. Experimental arrangement with a fiberoptic hydrophone for the measurement of bubble collapse shock waves.
Fig. 8. Collapse pressure at minimum bubble radius radiated from a laser bubble versus maximum attained radius.
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smaller radii Rmax gives strong evidence of collapse pressures in the range of a few 1000 bar for standard sonoluminescing bubbles. This estimate is consistent with work for driven bubbles of Holzfuss et al. [7] who have measured the speed of the SBSL shock in the vicinity of the bubble and found a lower limit to the initial shock pressure of about 5.5 kbar, and extrapolated pressures of around 70 kbar. Similar peak pressures of 40–60 kbar were reported by Pecha and Gompf [8]. An investigation of the bubble size dependence has also been made with the light emitted upon bubble collapse. Fig. 9 shows the luminescence pulse widths in dependence on the maximum attained bubble radius for laser bubbles. They range from 9 ns for bubbles starting collapse from a radius of about 1.5 mm down to 4 ns for bubble of maximum radius of about 0.75 mm. These are quite long times when compared to sonoluminescing trapped bubbles which emit light pulses in the 100 ps range [15–17]. The little box near the origin of the graph depicts this range. When comparing the trend of the pulse widths again it seems to be the size of the bubbles that makes the difference: the smaller the bubble the shorter the light pulse width. This is an indication that larger bubbles do not collapse that much stronger as the volume and therefore energy increase would suggest. Also it has been found that the total energy of the emitted light flash from laser bubbles scales linearly with the maximum bubble radius [18], whereas the stored energy in the bubble scales with the volume of the bubble. These facts make upgrading the effects more difficult. Besides the exterior dynamics of the bubble wall and of the liquid there is an interior dynamics of the contents inside the bubble. Chemical reactions initiated by a single trapped bubble have been reported by Lepoint et al. [20] and called single bubble sonochemistry. They observed the release of iodine in Weissler’s reaction by a single oscillating air bubble. More detailed experiments, notably concerning the yield of OH radicals, have been done by Didenko and Suslick [21]. Theoretical studies into the interior dynamics have been done by Storey and Szeri [22] and Yasui et al. [23]. We approached the interior dynamics by
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Fig. 9. Pulse width of the light emission upon collapse of a laser bubble versus maximum attained radius.
Fig. 10. Molecular dynamics simulation of a sonoluminescing bubble. The sound field frequency is 26.5 kHz, the sound pressure amplitude is 1.3 bar and the bubble radius at rest is 4.5 lm. The temperature is plotted colour coded versus the radius and the time near the first collapse of the bubble. The numbers on the colour bar are the temperature in Kelvin.
molecular dynamics calculations [24,25]. This approach naturally includes diffusive processes as heat conduction or species diffusion. A calculation for typical parameters of a sonoluminescing bubble is given in Fig. 10. The temperature in the interior of the bubble has been plotted colour coded for a bubble of radius 4.5 lm, a sound field frequency of 26.5 kHz and a sound pressure amplitude of 1.3 bar. Water vapor and its chemical decomposition have been included in the calculations. The white line separating the liquid in the upper half and the bubble interior marks the bubble wall. The bubble reaches a minimum radius of about 0.8 lm. The temperature in the interior is not quite homogeneously distributed but peaks at the centre of the bubble and reaches about 14,000 K. This is in the range of values derived from experiments via optical spectra of the sonoluminescing pulses and fitting a blackbody curve to the data.
3. Bubble cloud dynamics In acoustic fields the bubbles appearing upon rupture of the liquid by acoustic cavitation are not dispersed homogeneously. Instead they form patterns due to attracting and repelling forces both by interaction with the sound field (radiation forces) and by interaction with other bubbles. A survey of bubble patterns appearing in acoustic cavitation has been given by Mettin [26]. The most common feature of these patterns is the formation of filaments called streamers. In a standing acoustic wave as in a resonator the filaments form a kind of a web with a centre located at the pressure antinode for not too high acoustic pressure amplitudes. A typical web pattern is given in Fig. 11. It resembles erosion patterns of rivers when seen from high altitude. The picture has been taken with backlight illumination at an exposure time giving about the natural impression when looking at the phenomenon by eye. Then
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Fig. 11. Bubble web in a standing acoustic wave called acoustic Lichtenberg figure, single pressure antinode region, long exposure (several periods of the sound field) (Courtesy of A. Billo).
Fig. 12. Bubble web in a standing acoustic wave called acoustic Lichtenberg figure, single pressure antinode region, short exposure (approx. 10 ns) (Courtesy of A. Billo).
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Fig. 13. Multi-bubble sonoluminescence in a standing sound wave. The spatial distribution of the luminescence is correlated with the bubble structure in the sound field (Courtesy of C.-D. Ohl).
the filaments seem densely occupied and the dendritic branched structure is quite pronounced. When short exposure photographs are done that stop the motion of the individual bubbles, both oscillating and translating, the structure gets much more diluted (Fig. 12). Larger and (series of) smaller bubbles alternate in a filament, as if a larger bubble leaves smaller ones on its track towards the centre. Bubble clouds also emit shock waves (see e.g. [27]) and light, then called multi-bubble sonoluminescence (Fig. 13). It is the individual bubbles being of proper size that are doing so. Therefore the pattern of the luminescence is correlated with the bubble filaments where most of the bubbles are situated. The luminescence in pure water saturated with air as in the experiment of Fig. 13 is very faint. It has been captured with an intensified CCD camera and long exposure in otherwise total darkness. The bubble patterns normally oscillate with the sound field frequency, but also may get subharmonic or even chaotic [28,18]. In a standing sound field adjacent pressure antinodes are of opposite phase and thus are the bubble
Fig. 14. Bubble double layer in a standing acoustic wave. Two adjacent pressure antinodes are given the pressure node running horizontally through the middle of each frame. The sound field frequency is 40 kHz. Two periods of the sound field are shown.
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oscillations. This is demonstrated in Fig. 14, where two adjacent pressure antinodes, where the acoustic pressure oscillates between its maximum and minimum, are shown for two periods of the sound field of frequency 40 kHz [19]. The structure breathes with opposite phase between the two pressure antinodes. Long exposure photographs give both structures simultaneously betraying our eye of the real dynamics. Bubble velocities along the filaments have been measured [29,30]. The range covers translation velocities from zero to about 1.6 m/s. They peak, i.e. most bubbles have this velocity, at about 0.1–0.3 m/s with a long tail up to more than 1.6 m/s. Theoretical models have been constructed to describe the pattern formation and the motion of the bubbles within the pattern [31]. Gross features could be covered, notably the depletion of the pressure antinode of bubbles when the sound pressure amplitude is increased. This is due to the nonlinear oscillation of the bubbles that leads to a change in sign of the direction of the acoustic radiation force (first Bjerknes force) at large oscillation amplitudes [32]. 4. Summary and discussion An introduction into the dynamics of bubbles in liquids has been given mainly from an experimental viewpoint. Single spherical bubbles and bubble clouds are considered. Free oscillations of a single bubble can be initiated by focussed laser light, forced oscillations by trapping a bubble in the pressure antinode of a standing sound field. Free oscillations of large amplitude are strongly damped by radiation of shock waves upon bubble collapse [12,13,18]. The same is true with trapped bubbles and their forced oscillations, however, in this case the energy lost is resupplied by the driving sound field to lead to a perpetual nonlinear oscillation. Upon collapse a short light flash is radiated in both cases. Both the width and the total energy of the flash scale with the maximum bubble radius and not with its volume that is proportional to the total energy stored in the bubble. This behaviour cannot yet be explained as a detailed knowledge of the mechanism of light production is still lacking. Presumably the light emitted is a mixture of blackbody radiation by the finally adiabatic increase in temperature and of bremsstrahlung from the interaction of charged particles in the hot plasma inside the bubble. Molecular dynamics calculations of the interior dynamics of a spherical bubble are reported. The temperature inside the bubble has been calculated this way. When chemical reactions are included the temperature drops to values as derived from experimentally determined optical spectra. The filamentary cloud patterns in standing acoustic waves have been shown in long and short exposure. Long exposures integrate over several cycles of the sound field and bubble oscillations as well as partly over the transla-
tional motion of the bubbles. Therefore they enforce the impression of a filamentary structure. Short exposures stop the bubbles in their momentary location and oscillation phase. Then the bubbles may appear large or small according to their state in their oscillation cycle. Bubble clouds also emit light. The spatial light pattern is correlated with the filamentary pattern and surely is radiated from the individual bubbles that make up the filaments in the clouds. Acknowledgements The authors thank all their coworkers of the Go¨ttingen cavitation group who have contributed over the years to increase our understanding of cavitation bubbles, in particular Robert Mettin, Dagmar Krefting, Ju¨rgen Appel, Stefan Luther, Philipp Koch, Claus-Dieter Ohl, and Ulrich Parlitz. Financial support by the German Federal Ministry of Education and Research (BMBF) and by the German Research Foundation (DFG) is gratefully acknowledged. References [1] C.E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press, Oxford, 1995. [2] T.G. Leighton, The Acoustic Bubble, Academic Press, London, 1994. [3] F.R. Young, Sonoluminescence, CRC Press, Boca Raton, 2005. [4] T.J. Mason, J.P. Lorimer, Applied Sonochemistry, Wiley-VCH, Weinheim, 2002. [5] R.C. Srivastava, D. Leutloff, K. Takayama, Shock Focussing Effect in Medical Science and Sonoluminescence, Springer, Berlin, 2002. [6] D.F. Gaitan, L.A. Crum, C.C. Church, R.A. Roy, J. Acoust. Soc. Am. 91 (1992) 3166–3183. [7] J. Holzfuss, M. Ru¨ggeberg, A. Billo, Phys. Rev. Lett. 81 (1998) 5434– 5437. [8] R. Pecha, B. Gompf, Phys. Rev. Lett. 84 (2000) 1328–1331. [9] M.P. Brenner, S. Hilgenfeldt, D. Lohse, Rev. Mod. Phys. 74 (2002) 425–483. [10] D. Hammer, L. Frommhold, J. Mod. Opt. 48 (2001) 239. [11] K. Yasui, T. Tuziuti, M. Sivakumar, Y. Iida, Appl. Spectrosc. Rev. 39 (2004) 399. [12] W. Hentschel, W. Lauterborn, Appl. Sci. Res. 38 (1982) 225. [13] A. Vogel, W. Lauterborn, J. Acoust. Soc. Am. 84 (1988) 719. [14] J. Staudenraus, W. Eisenmenger, Ultrasonics 31 (1993) 267. [15] B.P. Barber, S. Putterman, Nature 352 (1991) 318. [16] B. Gompf, R. Gu¨nther, G. Nick, R. Pecha, W. Eisenmenger, Phys. Rev. Lett. 79 (1997) 1405. [17] R. Pecha, B. Gompf, G. Nick, Z.Q. Wang, W. Eisenmenger, Phys. Rev. Lett. 81 (1998) 717. [18] W. Lauterborn, T. Kurz, R. Mettin, C.-D. Ohl, Adv. Chem. Phys. 110 (1999) 295–380. [19] R. Mettin, P. Koch, D. Krefting, W. Lauterborn, in: O.V. Rudenko, O.A. Sapozhnikov (Eds.), Nonlinear Acoustics at the Beginning of the 21st Century, Faculty of Physics, MSU, Moscow, 2002, pp. 1003– 1006. [20] T. Lepoint, F. Lepoint-Mullie, A. Henglein, in: L.A. Crum, T.J. Mason, J.L. Reisse, K.S. Suslick (Eds.), Sonochemistry and Sonoluminescence, Kluwer, Dordrecht, 1999, pp. 285–290. [21] Y.T. Didenko, K.S. Suslick, Nature 418 (2002) 394. [22] B.D. Storey, A.J. Szeri, Proc. R. Soc. 456 (2000) 1685–1709. [23] K. Yasui, T. Tuziuti, M. Sivakumar, Y. Iida, J. Chem. Phys. 122 (2005) 224706. [24] B. Metten, Molekulardynamik-Simulationen zur Sonolumineszenz, Der Andere Verlag, Osnabru¨ck, Germany, 2001.
W. Lauterborn et al. / Ultrasonics Sonochemistry 14 (2007) 484–491 [25] B. Metten, W. Lauterborn, in: W. Lauterborn, T. Kurz (Eds.), Nonlinear Acoustics at the Turn of the Millenium, AIP Conf. Proc. 524, Melville, New York, 2000, pp. 429–432. [26] R. Mettin, in: A.A. Doinikov (Ed.), Bubble and Particle Dynamics in Acoustic Fields: Modern Trends and Applications, Research Signpost, Kerala, India, 2005, pp. 1–36. [27] W. Lauterborn, in: W. Lauterborn (Ed.), Cavitation and Inhomogeneities in Underwater Acoustics, Springer, Berlin, 1980, pp. 3–12. [28] W. Lauterborn, A. Koch, Phys. Rev. A 35 (1987) 1974–1976.
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[29] S. Luther, R. Mettin, P. Koch, W. Lauterborn, Ultrason. Sonochem. 8 (2001) 159–162. [30] J. Appel, P. Koch, R. Mettin, D. Krefting, W. Lauterborn, Ultrason. Sonochem. 11 (2004) 39–42. [31] R. Mettin, S. Luther, C.-D. Ohl, W. Lauterborn, Ultrason. Sonochem. 6 (1999) 25–29. [32] I. Akhatov, R. Mettin, C.D. Ohl, U. Parlitz, W. Lauterborn, Phys. Rev. E 55 (1997) 3747–3750.
Acoustic cavitation, bubble dynamics and sonoluminescence W. Lauterborn *, T. Kurz, R. Geisler, D. Schanz, O. Lindau Drittes Physikalisches Institut, Universita¨t Go¨ttingen, Friedrich-Hund-Platz 1, D-37077 Go¨ttingen, Germany Received 5 August 2006; accepted 21 September 2006 Available online 24 January 2007
Abstract Basic facts on the dynamics of bubbles in water are presented. Measurements on the free and forced radial oscillations of single spherical bubbles and their acoustic (shock waves) and optic (luminescence) emissions are given in photographic series and diagrams. Bubble cloud patterns and their dynamics and light emission in standing acoustic fields are discussed. 2006 Elsevier B.V. All rights reserved.
1. Introduction In an acoustic field matter is alternately subjected to pressure and tension. In the tension phase a solid may break when the tension exceeds a limiting value. A liquid also may rupture this time to form cavities or bubbles in the liquid that finally close when the tension is released for longer time. In sound fields the bubbles formed also start to oscillate and give rise to a number of distinct effects generating the research area of acoustic cavitation [1,2]. Bubble dynamics forms its basis and sonoluminescence (light from sound) is one of its more spectacular research topics [3]. Acoustic cavitation has found application in ultrasonic cleaning, forms the physical basis of sonochemistry [4] and is presumably involved in shock wave lithotripsy [5]. 2. Single bubble dynamics Bubbles in liquids are fast moving and small objects not easily investigated. In acoustic fields they normally come in swarms or clouds of different forms and sizes with the individual bubbles strongly interacting. A big step forward was achieved when the single bubble trap was invented by *
Corresponding author. E-mail address: [email protected] (W. Lauterborn). 1350-4177/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultsonch.2006.09.017
Gaitan et al. [6]. Now a single bubble could be held at a fixed position in space for investigation, for instance of its light emitting properties. Fig. 1 shows a simple version of a bubble trap. It consists of a cubical or rectangularly shaped container with just one piezoelectric driving element glued to the bottom. A platinum wire is inserted from the side to produce a bubble by a current pulse. The acoustic radiation force drives the bubble to its stable lift position. This is the position of the sonoluminescing bubble given by the bright spot in the upper part of the figure. The flat faces of the cuvette facilitate photographing the (light emitting) bubble and its shock waves. The possible modes of the resonator are determined by the acoustic impedance of its walls and the attached transducer. The walls act as open ends through the air beyond the walls. The transducer arrangement acts nearly as a closed end. Thus, there is a pressure antinode near the bottom of the vessel. Cavitation does not occur at this location, since the driving amplitude is too low. To achieve SBSL it is necessary to stay below the cavitation threshold. Therefore the bubble is produced artificially and injected. For this vessel, SBSL worked best in the depicted mode. Fig. 2 gives one complete cycle of a radially oscillating single bubble driven at 21.4 kHz at a sound pressure amplitude of 132 kPa photographed at 500 ns intervals. Actually the series was obtained by taking a photograph, shifting the time by 500 ns relatively to the fixed reference phase of the sound field, taking the next photograph and so on.
W. Lauterborn et al. / Ultrasonics Sonochemistry 14 (2007) 484–491
Fig. 1. A simple bubble trap with light emitting bubble.
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Due to the stability of the bubble oscillation (also documented this way) almost arbitrary fine time resolution of the bubble dynamics is possible. The images were recorded using a long distance microscope (Infinity K2). A micro channel plate (PCO IRO) was used as a fast shutter down to 5 ns exposure time. It was attached by a relay optic to a CCD camera (Photometrics Sensys). Illumination was performed by a xenon flash lamp (Hamamatsu L4643). The radial oscillation is highly nonlinear with a fast collapse of the bubble down to a very small radius not resolved in space and time in the photographic series. After several small amplitude oscillations in the compression phase of the sound field the bubble is again expanded largely in the tension phase of the sound field and repeats the cycle. At the end of the fast first collapse of the bubble a shock wave is radiated [7,8]. This shock wave is visualized in Fig. 3 by using a shadowgraph schlieren arrangement and the same camera system as in Fig. 2. The dark spot in the middle of the first frame is not the bubble but the shock wave already deflecting the illuminating light to show up as a dark ring. The bubble does not become visible before about the tenth frame as centre of the shock wave. Thus the shock wave quickly detaches from the bubble surface. The light emitted by the bubble is shown in Fig. 4. It is a spot of the size of the resolution of the photographic
Fig. 2. Oscillation of a single bubble trapped in a standing sound field of frequency 21.4 kHz and a sound pressure amplitude 132 kPa. The time difference between the frames is 500 ns, the size of the frames is 160 lm · 160 lm.
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Fig. 4. Photograph of the light emitted by a trapped bubble. Frame size is 1 mm · 1 mm.
Fig. 3. Shock wave emitted upon first collapse of a bubble trapped in a standing sound field of frequency 21.4 kHz and a sound pressure amplitude 132 kPa. The time difference between consecutive frames is 10 ns, the size of the frames is 1.6 mm · 1.6 mm.
system and of bluish appearance. The real size of the light emitting volume is not known, but estimated to below 0.5 lm in radius. The discussion on this topic is still ongoing [9–11]. The single trapped bubbles can be compared with bubbles that can be generated by focussing laser light into a liquid. Then also a single spherical bubble can be produced.
This bubble, however, only lasts for a few of its own oscillation cycles. It is a free instead of a forced oscillation spoken in terms of oscillator theory. It is a strongly nonlinear oscillation as is the acoustically trapped and driven bubble. Fig. 5 shows an example of the free oscillation of a single laser produced bubble. The bubble was induced by a ruby laser with a pulse duration between 30 and 50 ns, a wavelength of 694.3 nm, and an energy per pulse of several 10 mJ. We also work with a Nd:YAG laser with a pulse duration of about 8 ns, a wavelength of 1064 nm and similar energies per pulse. The experiments with laser bubbles are even more demanding than with trapped bubbles as real high speed cinematography has to be applied. In this case a framing rate of 75,000 frames per second has been used to cover the decaying oscillations. The nonlinear free oscillation is strongly damped as seen by the small secondary maximum after rebound from the first collapse. The same is true with the trapped bubbles that, however, repeat
Fig. 5. Free oscillation of a single laser produced bubble in water. The framing rate is 75,000 frames/s, maximum radius is 2 mm.
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Fig. 6. Bubble collapse with shock wave radiated of a single laser produced bubble in water and comparison with theory. The time between frames is about 1 ls.
their cycle over and over again. It is the strong shock wave that carries away most of the energy stored in the bubble [12,13]. Fig. 6 gives an example of the shock wave from a collapsing single laser produced bubble. To catch the shock wave the framing rate has been chosen as about 1 million frames/s. Fig. 6b shows a comparison with a theoretical model of bubble oscillation (Gilmore model, see [2]). A good fit could be achieved except for the exact time of collapse. The strength of the shock waves from the laser bubbles can be measured in absolute pressure terms with a fiber optic hydrophone [14] placed at some distance d from the bubble centre in the liquid (Fig. 7). The fiber optic hydrophone makes use of the alteration of reflection of laser light coming down the fiber when the density in the liquid (and with it the index of refraction) is altered at the tip by a pressure wave in the liquid. Due to the relatively small size of the fiber tip and its high bandwidth it has advantages over conventional (e.g. PVDF) hydrophones for shock pressure
measurements [12,13]. A disadvantage is the lower sensitivity that can be overcome only with high intensity lasers to increase the reflected signal from the fiber tip. Fig. 8 gives the result of a shock wave pressure measurement series with different bubble sizes Rmax. The upper and lower boundaries of the shaded area give the error bounds of the measurements. The pressures obtained at distance d have been extrapolated to the minimum bubble radius by using a 1/r-dependence for the amplitude, where the minimum radius has been obtained by a numerical fit to the bubble collapse similarly as in Fig. 6. About 10 kbar are reached for a bubble collapsing from a radius of 500 lm and about 25 kbar when collapsing from a radius of 3 mm. Unfortunately the collapse pressure from trapped bubbles cannot be measured this way as these bubbles are extremely sensitive to a disturbance nearby and also of lower shock wave strength because of their lower maximum size of less than about a 100 lm and thus less overall energy. But extrapolating the pressure values down to
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Rmax [mm] Fig. 7. Experimental arrangement with a fiberoptic hydrophone for the measurement of bubble collapse shock waves.
Fig. 8. Collapse pressure at minimum bubble radius radiated from a laser bubble versus maximum attained radius.
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smaller radii Rmax gives strong evidence of collapse pressures in the range of a few 1000 bar for standard sonoluminescing bubbles. This estimate is consistent with work for driven bubbles of Holzfuss et al. [7] who have measured the speed of the SBSL shock in the vicinity of the bubble and found a lower limit to the initial shock pressure of about 5.5 kbar, and extrapolated pressures of around 70 kbar. Similar peak pressures of 40–60 kbar were reported by Pecha and Gompf [8]. An investigation of the bubble size dependence has also been made with the light emitted upon bubble collapse. Fig. 9 shows the luminescence pulse widths in dependence on the maximum attained bubble radius for laser bubbles. They range from 9 ns for bubbles starting collapse from a radius of about 1.5 mm down to 4 ns for bubble of maximum radius of about 0.75 mm. These are quite long times when compared to sonoluminescing trapped bubbles which emit light pulses in the 100 ps range [15–17]. The little box near the origin of the graph depicts this range. When comparing the trend of the pulse widths again it seems to be the size of the bubbles that makes the difference: the smaller the bubble the shorter the light pulse width. This is an indication that larger bubbles do not collapse that much stronger as the volume and therefore energy increase would suggest. Also it has been found that the total energy of the emitted light flash from laser bubbles scales linearly with the maximum bubble radius [18], whereas the stored energy in the bubble scales with the volume of the bubble. These facts make upgrading the effects more difficult. Besides the exterior dynamics of the bubble wall and of the liquid there is an interior dynamics of the contents inside the bubble. Chemical reactions initiated by a single trapped bubble have been reported by Lepoint et al. [20] and called single bubble sonochemistry. They observed the release of iodine in Weissler’s reaction by a single oscillating air bubble. More detailed experiments, notably concerning the yield of OH radicals, have been done by Didenko and Suslick [21]. Theoretical studies into the interior dynamics have been done by Storey and Szeri [22] and Yasui et al. [23]. We approached the interior dynamics by
10
Pulse width (ns)
8
6
4
2 0 0.0
0.5 1.0 Maximum bubble radius (mm)
1.5
Fig. 9. Pulse width of the light emission upon collapse of a laser bubble versus maximum attained radius.
Fig. 10. Molecular dynamics simulation of a sonoluminescing bubble. The sound field frequency is 26.5 kHz, the sound pressure amplitude is 1.3 bar and the bubble radius at rest is 4.5 lm. The temperature is plotted colour coded versus the radius and the time near the first collapse of the bubble. The numbers on the colour bar are the temperature in Kelvin.
molecular dynamics calculations [24,25]. This approach naturally includes diffusive processes as heat conduction or species diffusion. A calculation for typical parameters of a sonoluminescing bubble is given in Fig. 10. The temperature in the interior of the bubble has been plotted colour coded for a bubble of radius 4.5 lm, a sound field frequency of 26.5 kHz and a sound pressure amplitude of 1.3 bar. Water vapor and its chemical decomposition have been included in the calculations. The white line separating the liquid in the upper half and the bubble interior marks the bubble wall. The bubble reaches a minimum radius of about 0.8 lm. The temperature in the interior is not quite homogeneously distributed but peaks at the centre of the bubble and reaches about 14,000 K. This is in the range of values derived from experiments via optical spectra of the sonoluminescing pulses and fitting a blackbody curve to the data.
3. Bubble cloud dynamics In acoustic fields the bubbles appearing upon rupture of the liquid by acoustic cavitation are not dispersed homogeneously. Instead they form patterns due to attracting and repelling forces both by interaction with the sound field (radiation forces) and by interaction with other bubbles. A survey of bubble patterns appearing in acoustic cavitation has been given by Mettin [26]. The most common feature of these patterns is the formation of filaments called streamers. In a standing acoustic wave as in a resonator the filaments form a kind of a web with a centre located at the pressure antinode for not too high acoustic pressure amplitudes. A typical web pattern is given in Fig. 11. It resembles erosion patterns of rivers when seen from high altitude. The picture has been taken with backlight illumination at an exposure time giving about the natural impression when looking at the phenomenon by eye. Then
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Fig. 11. Bubble web in a standing acoustic wave called acoustic Lichtenberg figure, single pressure antinode region, long exposure (several periods of the sound field) (Courtesy of A. Billo).
Fig. 12. Bubble web in a standing acoustic wave called acoustic Lichtenberg figure, single pressure antinode region, short exposure (approx. 10 ns) (Courtesy of A. Billo).
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Fig. 13. Multi-bubble sonoluminescence in a standing sound wave. The spatial distribution of the luminescence is correlated with the bubble structure in the sound field (Courtesy of C.-D. Ohl).
the filaments seem densely occupied and the dendritic branched structure is quite pronounced. When short exposure photographs are done that stop the motion of the individual bubbles, both oscillating and translating, the structure gets much more diluted (Fig. 12). Larger and (series of) smaller bubbles alternate in a filament, as if a larger bubble leaves smaller ones on its track towards the centre. Bubble clouds also emit shock waves (see e.g. [27]) and light, then called multi-bubble sonoluminescence (Fig. 13). It is the individual bubbles being of proper size that are doing so. Therefore the pattern of the luminescence is correlated with the bubble filaments where most of the bubbles are situated. The luminescence in pure water saturated with air as in the experiment of Fig. 13 is very faint. It has been captured with an intensified CCD camera and long exposure in otherwise total darkness. The bubble patterns normally oscillate with the sound field frequency, but also may get subharmonic or even chaotic [28,18]. In a standing sound field adjacent pressure antinodes are of opposite phase and thus are the bubble
Fig. 14. Bubble double layer in a standing acoustic wave. Two adjacent pressure antinodes are given the pressure node running horizontally through the middle of each frame. The sound field frequency is 40 kHz. Two periods of the sound field are shown.
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oscillations. This is demonstrated in Fig. 14, where two adjacent pressure antinodes, where the acoustic pressure oscillates between its maximum and minimum, are shown for two periods of the sound field of frequency 40 kHz [19]. The structure breathes with opposite phase between the two pressure antinodes. Long exposure photographs give both structures simultaneously betraying our eye of the real dynamics. Bubble velocities along the filaments have been measured [29,30]. The range covers translation velocities from zero to about 1.6 m/s. They peak, i.e. most bubbles have this velocity, at about 0.1–0.3 m/s with a long tail up to more than 1.6 m/s. Theoretical models have been constructed to describe the pattern formation and the motion of the bubbles within the pattern [31]. Gross features could be covered, notably the depletion of the pressure antinode of bubbles when the sound pressure amplitude is increased. This is due to the nonlinear oscillation of the bubbles that leads to a change in sign of the direction of the acoustic radiation force (first Bjerknes force) at large oscillation amplitudes [32]. 4. Summary and discussion An introduction into the dynamics of bubbles in liquids has been given mainly from an experimental viewpoint. Single spherical bubbles and bubble clouds are considered. Free oscillations of a single bubble can be initiated by focussed laser light, forced oscillations by trapping a bubble in the pressure antinode of a standing sound field. Free oscillations of large amplitude are strongly damped by radiation of shock waves upon bubble collapse [12,13,18]. The same is true with trapped bubbles and their forced oscillations, however, in this case the energy lost is resupplied by the driving sound field to lead to a perpetual nonlinear oscillation. Upon collapse a short light flash is radiated in both cases. Both the width and the total energy of the flash scale with the maximum bubble radius and not with its volume that is proportional to the total energy stored in the bubble. This behaviour cannot yet be explained as a detailed knowledge of the mechanism of light production is still lacking. Presumably the light emitted is a mixture of blackbody radiation by the finally adiabatic increase in temperature and of bremsstrahlung from the interaction of charged particles in the hot plasma inside the bubble. Molecular dynamics calculations of the interior dynamics of a spherical bubble are reported. The temperature inside the bubble has been calculated this way. When chemical reactions are included the temperature drops to values as derived from experimentally determined optical spectra. The filamentary cloud patterns in standing acoustic waves have been shown in long and short exposure. Long exposures integrate over several cycles of the sound field and bubble oscillations as well as partly over the transla-
tional motion of the bubbles. Therefore they enforce the impression of a filamentary structure. Short exposures stop the bubbles in their momentary location and oscillation phase. Then the bubbles may appear large or small according to their state in their oscillation cycle. Bubble clouds also emit light. The spatial light pattern is correlated with the filamentary pattern and surely is radiated from the individual bubbles that make up the filaments in the clouds. Acknowledgements The authors thank all their coworkers of the Go¨ttingen cavitation group who have contributed over the years to increase our understanding of cavitation bubbles, in particular Robert Mettin, Dagmar Krefting, Ju¨rgen Appel, Stefan Luther, Philipp Koch, Claus-Dieter Ohl, and Ulrich Parlitz. Financial support by the German Federal Ministry of Education and Research (BMBF) and by the German Research Foundation (DFG) is gratefully acknowledged. References [1] C.E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press, Oxford, 1995. [2] T.G. Leighton, The Acoustic Bubble, Academic Press, London, 1994. [3] F.R. Young, Sonoluminescence, CRC Press, Boca Raton, 2005. [4] T.J. Mason, J.P. Lorimer, Applied Sonochemistry, Wiley-VCH, Weinheim, 2002. [5] R.C. Srivastava, D. Leutloff, K. Takayama, Shock Focussing Effect in Medical Science and Sonoluminescence, Springer, Berlin, 2002. [6] D.F. Gaitan, L.A. Crum, C.C. Church, R.A. Roy, J. Acoust. Soc. Am. 91 (1992) 3166–3183. [7] J. Holzfuss, M. Ru¨ggeberg, A. Billo, Phys. Rev. Lett. 81 (1998) 5434– 5437. [8] R. Pecha, B. Gompf, Phys. Rev. Lett. 84 (2000) 1328–1331. [9] M.P. Brenner, S. Hilgenfeldt, D. Lohse, Rev. Mod. Phys. 74 (2002) 425–483. [10] D. Hammer, L. Frommhold, J. Mod. Opt. 48 (2001) 239. [11] K. Yasui, T. Tuziuti, M. Sivakumar, Y. Iida, Appl. Spectrosc. Rev. 39 (2004) 399. [12] W. Hentschel, W. Lauterborn, Appl. Sci. Res. 38 (1982) 225. [13] A. Vogel, W. Lauterborn, J. Acoust. Soc. Am. 84 (1988) 719. [14] J. Staudenraus, W. Eisenmenger, Ultrasonics 31 (1993) 267. [15] B.P. Barber, S. Putterman, Nature 352 (1991) 318. [16] B. Gompf, R. Gu¨nther, G. Nick, R. Pecha, W. Eisenmenger, Phys. Rev. Lett. 79 (1997) 1405. [17] R. Pecha, B. Gompf, G. Nick, Z.Q. Wang, W. Eisenmenger, Phys. Rev. Lett. 81 (1998) 717. [18] W. Lauterborn, T. Kurz, R. Mettin, C.-D. Ohl, Adv. Chem. Phys. 110 (1999) 295–380. [19] R. Mettin, P. Koch, D. Krefting, W. Lauterborn, in: O.V. Rudenko, O.A. Sapozhnikov (Eds.), Nonlinear Acoustics at the Beginning of the 21st Century, Faculty of Physics, MSU, Moscow, 2002, pp. 1003– 1006. [20] T. Lepoint, F. Lepoint-Mullie, A. Henglein, in: L.A. Crum, T.J. Mason, J.L. Reisse, K.S. Suslick (Eds.), Sonochemistry and Sonoluminescence, Kluwer, Dordrecht, 1999, pp. 285–290. [21] Y.T. Didenko, K.S. Suslick, Nature 418 (2002) 394. [22] B.D. Storey, A.J. Szeri, Proc. R. Soc. 456 (2000) 1685–1709. [23] K. Yasui, T. Tuziuti, M. Sivakumar, Y. Iida, J. Chem. Phys. 122 (2005) 224706. [24] B. Metten, Molekulardynamik-Simulationen zur Sonolumineszenz, Der Andere Verlag, Osnabru¨ck, Germany, 2001.
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