Sonoluminescence: How Bubbles Turn Sound into Light

Sonoluminescence, the transduction of sound into light, is a phenomenon that pushes fluid mechanics beyond its limit. An initial state with long wavelength and low Mach number, such as is realized for a gas bubble driven by an audible sound field, spontaneously focuses the energy density so as to generate supersonic motion and a different phase of matter, from which are then emitted picosecond flashes of broad-band UV light. Although the most rational picture of sonoluminescence involves the creation of a ‘‘cold’’ dense plasma by an imploding shock wave, neither the imploding shock nor the plasma has been directly observed. Attempts to attack sonoluminescence from the perspective of continuum mechanics have led to interesting issues related to bubble shape oscillations, shock shape instabilities, and shock propagation through nonideal media, and chemical hydrodynamics. The limits of energy focusing that can be achieved from collapsing bubbles in the far-off equilibrium motion of fluids have yet to be determined either experimentally or theoretically. INTRODUCTION: LIGHT FROM FAR-OFF EQUILIBRIUM FLUID MOTION Sonoluminescence (SL) is a unique phenomenon in fluid mechanics because it evolves out of an initial state within the range of parameters described by the basic equations of Navier Stokes hydrodynamics (Landau & Lifshitz 1987) into a different phase of matter—one with a remarkably high energy density whose characterization requires a completely different set of equations. In particular an imposed sound wave with a Mach number that is small compared with unity and a wavelength that is large compared with the mean free path can, in the presence of a bubble, focus its energy in a runaway fashion so as to generate picosecond flashes of broad-band UV light (Barber & Putterman 1991, Hiller et al 1992, Hiller et al 1994, Barber et al 1997a, Putterman 1998, Crum 1994, Putterman 1995). The energy of a UV photon compared with that of a single atom vibrating A nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. 446 PUTTERMAN n WENINGER Figure 1 A hemispherical bubble trapped on a 500-lm wire in a sound field emits UV flashes of light and damages the metallic surface of the wire. It is not known whether this effect is caused by an imploding (hemispherical) shock, a jet, (Prosperetti 1997) or some other unidentified process. in the imposed sound field represents an energy focusing that spans 12 orders of magnitude. Nature’s tendency to focus energy in the off-equilibrium motion of fluids is spectacularly robust. Figure 1 shows a photo of a single bubble attached to a wire in an acoustically excited fluid (Weninger et al 1997). Owing to the boundary conditions imposed by the wire, the bubble is not spherical but is distorted into an approximation of a hemisphere. Yet this bubble pulsates synchronously with the sound field, expanding during the rarefaction part of the acoustic cycle and collapsing so strongly during the ensuing compression that the input acoustic energy is transduced into UV flashes of light—one flash for each cycle. Figure 2 (see color insert) is an actual photo of the luminescence from a spherical probe A nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. SONOLUMINESCENCE 447 vibrating at about 25 kHz in water. Bubbles spontaneously appear near the probe at the maxima of the dipolar sound field that the probe generates. Despite distortions caused by other bubbles and by the probe itself, these bubbles collapse with sufficient force to generate UV light. The local heating, which is 15 orders of magnitude greater than follows from Kirchoff’s law for the attenuation of sound, is strong enough to lyse cells. In fact this device is regularly used for the surgical procedure called ultrasonically assisted liposuction (Weninger et al 1999a). In that case a small hole up the center of the probe is used to remove the emulsified fatty tissue. This version of SL closely resembles the configuration used in its discovery in 1934 (Frenzel & Schultes 1934, Walton & Reynolds 1984) and in sonochemistry (Suslick & Flint 1987, Long et al 1998). When the pressure drop in flow through a Venturi tube exceeds 1 atm, bubbles spontaneously form and then later emit a flash of light as they collapse downstream (Putterman 1998, Peterson & Anderson 1967, Weninger et al 1999b). In all of these cases the bubbles emit light with the same spectral density as SL. The spectrum is broad band out to photon energies of 6 eV (wavelengths of 200 nm), where it is cut off by the extinction coefficient of water. The case that is most amenable to experimental measurement is that of a single gas bubble trapped at the velocity node of an acoustic resonator (Barber & Putterman 1991, Temple 1970, Gaitan et al 1992) (Figure 3, see color insert). In this case the system can be tuned so that the flashes come out with a clocklike synchronicity—one flash for each cycle of sound with the jitter in the time between flashes ,50 ps (Barber et al 1992). Early explanations of the light-emitting mechanism for SL-invoked frictional electricity (Frenzel & Schultes 1934). This phenomenon is illustrated in Figure 4 (see color insert), where one sees light emitted along the line where the meniscus of mercury meets the wall of a rotating glass cell (Picard 1676). These spectra are not broad band but have lines characteristic of electric discharges. Probably static electrification is not the explanation for SL. But this photo is another example of energy focusing in the off-equilibrium motion of a (non-Newtonian) fluid. For rotational rates of 1 revolution per minute, electrons are continuously separated and accelerated to 1% of the speed of light and discharged in picosecond bursts with energies of $20eV (Budakian et al 1998). The mechanisms underlying triboelectrification are still under investigation (Terris et al 1989). PHENOMENOLOGY OF SONOLUMINESCENCE Key to SL is the radius R as a function of time t for a single bubble pulsating in an imposed sound field. Figure 5 shows a typical R(t). The bubble starts off from an ambient radius of R0 4 5.75 lm, which is the radius at which the bubble is in static mechanical equilibrium with the external ambient pressure (typically 1 atm). As the applied sound field goes negative beyond an atmosphere in the region indicated by tA, the bubble expands. When the total pressure acting on the bubble A nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. 448 PUTTERMAN n WENINGER Figure 5 Radius versus time for a typical sonoluminescing bubble. Shown is a 3-torr argon bubble with R0 4 5.75 lm and Pa 4 1.58 atm. The ambient temperature is 108C and, for the purpose of modeling the damping, the viscosity has been set to 0.05 cm/s. (A) A full cycle of sound. (B) The afterbounces. becomes positive again, the bubble continues to expand for a time tB, owing to its inertia, and then finds itself perched at a maximum radius Rm ' 10 R0, when the total pressure has once again become equal to 1 atm. At this point the volume of this bubble has increased a factor of 1000 from its ambient value, and so its internal pressure has gone down about a factor of 1000. The near vacuum in the bubble cannot withstand the 1 atm from outside, and so the bubble catastrophically collapses in a manner first calculated by Rayleigh in 1917. The collapse is arrested as the bubble approaches its van der Waals hard core (roughly R0/9), as shown in Figure 6, which is an enlargement by a factor of 1000 of the time scale in Figure 5A. At this moment of extreme stress and heating, the bubble’s contents have approached solid densities, and the flash of light is emitted. Also shown in Figure 6 is the fact that the collapse velocity of the bubble reaches over four times the ambient speed of sound in the gas. And, as shown in Figure 7, which is a A nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. SONOLUMINESCENCE 449 Figure 6 Radius versus time as the bubble collapses supersonically toward its van der Waals hard core. The data are taken for a 150-torr 1% xenon-in-oxygen bubble with R0 4 4.1 lm and Pa 4 1.45 atm. The temporal resolution of 500 ps is achieved with pulsed Mie scattering (Barber et al 1997a). To apply Mie theory, the index of refraction of the gas in the bubble has been reckoned to unity. sixfold enlargement of the Figure 6 time scale, the acceleration at the turnaround exceeds 3 2 10 g. After the light emission, the bubble pulsates freely (Figure 5B) and then sits dead in the water waiting for the next cycle, when this all repeats with remarkable synchronicity. The spectrum of SL from a helium bubble in water is shown in Figure 8. These data display the strongly UV spectrum as well as the sensitivity to temperature. Colder water makes for a much stronger light emission (Hiller et al 1992). Typically as the water is cooled from 308C to 08C, the intensity of SL increases by a factor of ;100 with emissions at 08C ranging up to 10 photons per flash. So far it has been determined that SL in water is sensitive to the particular gas used, the ambient temperature and pressure, the partial pressure at which the gas has been dissolved into the water, and the acoustic amplitude. So far the effects of changing the acoustic frequency (typically 12–45 kHz) appear to be comparatively small. The flash widths for various parameters are shown in Figure 9. They range from 30 ps for well-degassed air in water to .200 ps for xenon bubbles in cold water (Gompf et al 1997, Hiller et al 1998). An important aspect of the flash is that its width is independent of color (as measured so far for air and helium bubbles). The flash width at 200 nm is within a few percent of the flash width at 800 nm. This measurement challenges any adiabatic theory of light A nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. 450 PUTTERMAN n WENINGER Figure 7 Radius versus time near the minimum radius with an overlay of the sonoluminescence flash for 150-torr 1% xenon in oxygen at 40 kHz. The 25-ps resolution in A is achieved with time-correlated single-photon counting (O’Connor & Phillips 1984) applied to pulsed Mie scattering. For comparison R(t) from Figure 6 is overlaid. Application of time-correlated single-photon counting to the SL flash (Gompf et al 1997) determines a width of 150 ps (Hiller et al 1998) for this system. Also shown is a solution of Rayleigh’s equation of bubble motion. In B the uniform adiabatic heating implied by the Rayleigh-Plesset equation (taking Cp/Cv 4 5/3 and using the van der Waals equation of state) is compared with the SL flash. The afterpulsing is an artifact of the tube. For the RP simulation, R0 4 4.1 lm and Pa 4 1.45 atm. Light for the Mie scattering measurements was collected from a large solid angle, and small diffractive corrections were not made to these data. emission, because smooth heating and cooling would lead to longer emissions of low-energy photons. If the argon that constitutes 1% of air is removed, the light emission becomes very weak and unstable (Hiller et al 1994). In general SL from oxygen and nitrogen is very difficult to achieve, unless they are mixed with some noble gas. Hydrogenic gases also pose challenges, but in well-controlled resonators these bubbles can glow for about a minute or longer (Barber et al 1995, Löfstedt et al 1995). Hydrogenic bubbles are significantly more stable than oxygen and nitrogen. Also, whereas 1% argon added to oxygen or nitrogen dramatically improves the light emission and stability, such a small dosing has no observable effect on a hydrogen bubble (Barber et al 1997a). Finally xenon plays a special role. In SL from a single bubble, xenon yields the brightest emission, ;fivefold brighter than helium bubbles. In alcohols (WenA nn u. R ev . F lu id M ec h. 2 00 0. 32 :4 45 -4 76 . D ow nl oa de d fr om a rj ou rn al s. an nu al re vi ew s. or g by N O R T H C A R O L IN A S T A T E U N IV E R SI T Y o n 08 /1 4/ 09 . F or p er so na l u se o nl y. SONOLUMINESCENCE 451