Ritva Löfstedt

Defining the unknowns of sonoluminescence

Abstract As the intensity of a standing sound wave is increased the pulsations of a bubble of gas trapped at a velocity node attain sufficient amplitude so as to emit picosecond flashes of light with a broadband spectrum that increases into the ultraviolet. The acoustic resonator can be tuned so that the flashes of light occur with a clocklike regularity: one flash for each cycle of sound with a jitter in the time between flashes that is also measured in picoseconds. This phenomenon (sonoluminescence or “SL”) is remarkable because it is the only means of generating picosecond flashes of light that does not use a laser and the input acoustic energy density must be concentrated by twelve orders of magnitude in order to produce light. Light scattering measurements indicate that the bubble wall is collapsing at more than 4 times the ambient speed of sound in the gas just prior to the light emitting moment when the gas has been compressed to a density determined by its van der Waals hard core. Experiments indicate that the collapse is remarkably spherical, water is the best fluid for SL, some noble gas is essential for stable SL, and that the light intensity increases as the ambient temperature is lowered. In the extremely stable experimental configuration consisting of an air bubble in water, measurements indicate that the bubble chooses an ambient radius that is not explained by mass diffusion. Experiments have not yet been able to map out the complete spectrum because above 6 eV it is obscured by the cutoff imposed by water, and furthermore experiments have only determined an upper bound on the flash widths. In addition to the above puzzles, the theory for the light emitting mechanism is still open. The scenario of a supersonic bubble collapse launching an imploding shock wave which ionizes the bubble contents so as to cause it to emit Bremsstrahlung radiation is the best candidate theory but it has not been shown how to extract from it the richness of this phenomenon. Most exciting is the issue of whether SL is a classical effect or whether Plancks constant should be invoked to explain how energy which enters a medium at the macroscopic scale holds together and focuses so as to be emitted at the microscopic scale.

Toward a hydrodynamic theory of sonoluminescence

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Theory of long wavelength acoustic radiation pressure

A general formulation of the radiation force exerted on an object by a long wavelength sound field is developed in terms of an asymptotic multipole expansion. In various limits, the results of King [Proc. R. Soc. London, Ser. A 147, 212 (1934)], Gorkov [Sov. Phys. Dokl. 6, 773 (1962)], and Yosioka and Kawasima [Acustica 5, 167 (1955)] are recovered. In addition, the existence of a spectrum of monopole and dipole radiation force resonances is demonstrated which occur when the bulk modulus of the object is small compared to that of the surrounding medium. Near standing wave resonances, the bulk viscosity is shown to play an essential role in determining the force. For traveling waves, the bulk viscosity can lead to the dominant contribution to the radiation pressure even in the limit of zero frequency. For soap bubbles, the leading‐order contribution to the radiation pressure is shown to be quadrupolar.

Scaling laws for sonoluminescence

The extremely nonlinear dynamics of bubble motion is described by the Navier–Stokes equations of fluid mechanics, as coupled to the laws of heat conduction and mass diffusion. In order to gain insight into the limitations of the hydrodynamic theory of bubble collapse, scaling laws have been derived for the maximum radius, collapse temperature, hot spot lifetime, collapse pressure, and ambient radius in terms of the applied sound field and the assumption that the bubble is a gas‐filled cavity. In order to match the scaling laws to the experimental observations of collapse temperature and flash width requires that the Mach number for bubble motion exceed unity. In conclusion, a description of sonoluminescence must include the properties of imploding shock waves. [Work supported by the US DOE Division of Engineering and Geophysics; R. L. is supported by an A.T.&T. fellowship.]

Sonoluminescence: Skeletons in the closet

Now that the exciting measurements of picosecond flash widths, clocklike emission, broadband ultraviolet light, and the role of noble gas doping have generated substantial interest and theories for sonoluminescence, it is time to take a more sober look at the experimental difficulties that stand in the way of the next round of insights. Parameters which control the steady‐state motion of the bubble have not yet been elucidated. For instance, measurements of the dipole component of the sonoluminescence (SL) indicate that the bubble collapse can choose states with different ellipticity. Hydrogenic bubbles glow for periods ranging from 30 s to 5 min and are very sensitive to as yet unknown impurities. Tiny amounts of organic impurities dramatically alter the light emission. There is also concern that impurities may partly account for the different spectra observed in light and heavy water. Precise temperature control can be essential to prevent the bubble from hopping between different stable states. [Work s...

Theoretical prediction of luminescence from acoustically driven cracks

Under the effect of an intense long wavelength sound field the length of a crack in a solid medium should oscillate. When the crack length is increased the imposed acoustic energy is focused down to regions of atomic dimension so as to break the fundamental bonds which determine the crystal structure. It is suggested that this energy comes out as light whose intensity is periodic with the sound wave. This analysis is based upon the elliptical model of a crack modified to include surface tension. [Work supported by the U.S. DOE Office of Basic Energy Science, Division of Engineering and Geophysics; R.L. is an AT&T Fellow.]

Probing the unknowns of sonoluminescence

The mechanism whereby a bubble transduces sound into a clocklike stream of picosecond flashes of ultraviolet light is robust, complex, and unknown. A theoretical understanding of the key bubble parameter, its ambient radius, is lacking. An explanation as to why this phenomenon has so far only been seen in water is elusive. In addition, we do not understand why cooling the water dramatically increases the light output or why sonoluminescence is so sensitive to doping with a noble gas. Experimentally, the spectrum has been unable to be followed past 7 electron volts and so the limits of energy concentration which can be achieved with sonoluminescence from a single bubble are not yet measured. In addition to yielding clues experiments in progress will most likely serve to deepen the mystery! [Work supported by the US DOE Division of Advanced Energy Projects; RL is an AT&T Fellow.]

Rectified diffusion and single‐bubble sonoluminescence

The remarkably low solubility of air in water may be essential to the observation of stable single‐bubble sonoluminescence (SL) in this system. In other liquids, the mass exchange during a single cycle appears to be sufficient to quench single‐bubble SL. To gain insight into this issue, (1) a theory is developed that unifies mass diffusion and the Rayleigh–Plesset equation, and (2) laser scattering is used as a probe of the time change of bubble parameters due to mass diffusion. [Work supported by the U.S. DOE Division of Advanced Energy Projects and Division of Engineering and Geophysics (Theory); R. L. is an AT&T fellow.]

Limitations of the hydrodynamical theory of cavitation induced sonoluminescence.

The extremely short duration (<50 ps) of the flashes of light emitted by a sound field raises problems for the hydrodynamical description of sonoluminescence. Solutions to the Navier–Stokes equations with such a fast but short‐lived adiabatic compression develop shock fronts. Even in the linear approximation a single 20‐μ bubble that accelerates at this rate would radiate so much sound that its motion would dominate the Q of a 0.1‐liter resonator. The extent to which such a quickly accelerating bubble can be considered to be in local equilibrium is discussed. Nevertheless, fluid mechanics provides valuable scaling laws that can be used to analytically determine the ambient radius, phase of collapse, and maximum and minimum radii of the trapped bubble’s oscillation. [Work supported by the USDOE: Office of Basic Science (theory) and Division of Advanced Energy Projects (experiment) and R. L. is an AT&T fellow.]