Abstract

Introduction

In the beginning, Gaitan said
           "I need a small spot of light to get my Ph.D."
Then...
Gaitan made the light and saw that it was good.
Crum saw the light and quickly signed the thesis ^1a.
Putterman saw the light...
           -it was hot ^1b
           -it was brief ^1c
...and for a while we all believed it was magic^1d.

But most scientist prefer not to believe in magic, even though most everyone else does. Consequently, it was natural for every scientist to explain the phenomenon as a simple example of his/her expertise:
           The Quantum Field Theorists said, "Energy is extracted from the vacuum;"
           The Fluid Dynamicists said, "Colliding liquid jets;"
           The Plasma Physicists said, "Electric discharge from tiny balls of plasma;"
           The Mechanical Engineers said, "Energy from acoustic resonances;
           The Chemists said, "Energy from chemical reactions;"
           and The Shock Physicists said, "Energy from shock waves."

Amidst the controversy, the scientific community showed an unusual amount of respect and tolerance:
           The Experimentalists said "The Theorist are nuts;"
           The Theorists said, "Every other Theorist is nuts."

                                                       -W.C. Moss, D.B. Clarke, and D.A. Young ¹

      Sonoluminescence is the process where a bubble of gas (usually air) is created and forced to be suspended at a specific frequency inside a flask full of a certain liquid (usually water). The bubble experiences vibrations and is forced to rapid continuous contractions that enables the bubble to emit flashes of light. In other words, creating flashes of light from sound waves.

      The flashes of light from the bubble are emitted with precise regularity in the picosecond scale (10^-12 seconds) with basic laboratory equipment. This makes sonoluminescence one of the most inexpensive way to create flashes of light of that size. In addition, the size of the sonoluminescent bubble is so small and the flashes of light are so brief that in order to be measured very precise equipment needs to be used. Even with this precise equipment, only estimates have been obtained.²

History

      During World War I, chemists in Germany working with sonar systems were able to initiate a chemical reaction in a liquid solution. Reinhard Mecke from the University of Heildelberg then suggested that the energy needed to initiate this chemical reaction was the same as the energy needed to excite the emission of light from an atom.³

      In 1934, H. Frenzel and H. Schultes ⁴ from the University of Cologne were the first to observe (multi-bubble) sonoluminescence while conducting research in marine acoustic radars by exposing photographic plates using acoustic sound waves to create cavitation. The process of cavitation is one where bubbles of gas are able to expand and contract due to changes in pressure. Their final explanation of sonoluminescence was that the emission of light was due to frictional energy. Frenzel and Schultes ended their paper commenting that they had other important things to work on.^2,3

      Over the years numerous researchers tried to continue the study of multi-bubble sonoluminescence. Most of the research was inconsistent and stagnant. The majority of the studies that were able to produce sonoluminescence were just able to produce numerous amounts of bubbles that expanded, contracted, collapsed, and emitted light randomly, unpredictably, and chaotic.^2,3

      It wasn't until 1988 that D.F. Gaitan and L.A. Crum at the University of Mississippi were successful in isolating a single sonoluminescent bubble of air at a center of a flask using acoustic resonances.² Single-bubble sonoluminescence was born. After a few years of experiments here and there they eventually abandoned that field of research. Eventually the work was taken up by S.J. Putterman and B.P Barber at UCLA, where Putterman is now one of the most knowledgeable people in sonoluminescence.³

Theory

      The sonoluminescent bubble experiences continuous rapid contractions and expansions with precise regularity, a process that has been extremely studied by physicists. After numerous studies, researchers estimate that a single flash of light lasts about 50 picoseconds, with a time between flashes to be about 35 microseconds, a relation that has not been able to be explained with theories of bubble dynamics.^2,3 As mentioned earlier, very precise equipment has been used to measure pulse durations. Many have used photomultipliers amongst many things with incredibly fast response times, but only to be able to measure the impulse response times of photomultiplier tubes.²

      The size of the bubble can be measured by Mie-scattering, shooting a laser beam and measuring the amount of light scattered from the laser beam. This can be measured by looking at the intensity of the scattered laser beam because it is dependent on the square radius of the sonoluminescent bubble. The square root of the amplitude measured will therefore yield the radius of the bubble.³

      The bubble is first the size of a few microns (micrometers, 10^-6 meters). The resonant sound waves then allow the flask to experience pressure changes. These pressure changes put the liquid used inside the flask under tension and the size of the bubble increases to about 50 microns. The volume of the bubble increases and the amount of atoms and molecules inside will remain the same. With this reasoning, the bubble will reach its maximum size and the inside of the bubble will be close to being a vacuum. The inside and the outside of the bubble at this point differ in pressure, the outside of the bubble being subjected to atmospheric pressure at all times. This difference in pressures will lead to a collapse of the bubble. The size will then decrease to about 0.5 micron. This size will be the smallest that it can get due to repulsion of atoms and molecules. Therefore, one can say that the size of the bubble is dependent on the gas that is trapped inside of it.³

      In addition, the size of the bubble is also dependent on the gas dissolved at the surface of the water. Some of this gas that has been dissolved at the surface will eventually get into the bubble. This gas will diffuse into the bubble when the bubble is greater in size due to the low pressure inside. The gas will diffuse out of the bubble when the bubble is smaller in size due to the high pressure inside. This average of the two flows will ultimately determine the size of the bubble.^2,3

      Unfortunately, there is a discontinuity with high resonant sound waves. As the amplitude of the resonant frequency is increased, the average size should increase along with it. Experimentally this does not occur at higher amplitudes. There is a change before the flashes of light and the size of the bubble becomes smaller for a little while. After the emission of light, the bubble then continues increasing as the amplitude of the resonant sound waves is increased.³

      Another feature of sonoluminescence is the amplitude in which the resonant frequency is located. The sonoluminescent bubble must be driven in an acoustic field where the bubble will be able to expand and contract. If the field is too low, the bubble will be unable be sustained in the flask and undergoes radial pulsations. As the field increases, the sonoluminescent bubble will then relocate itself between the nodal and anti-nodal regions of the flask. If the field is too high, the bubble will be unstable and will dissipate.²

      The collapse of the bubble is where the luminescence comes in. This occurs as the bubble slows the contraction process right before it gets to its smallest size. The theory that has been mostly agreed upon says that up to this point most of what it is going on is due to adiabatic heating (heating process where no heat is transfered from and to the system). The compression of gas then allows the internal energy to increase due to the work done during the process, which leads to an increase in temperature. Therefore, for a sonoluminescent bubble, where there is no heat transfer, the volume decreases, the temperature rises, and the bubble is able to sustain higher pressures. In addition, the amplification of this phenomenon is made by the spherical shock wave that it is created within the bubble as it changes. Light is emitted. The emission of light then causes the bubble to increase in size just a little bit. The process is then repeated again and again.³

      Others believe that the light created by sonoluminescence is solely created by the shock wave. The sonoluminescent bubble is symmetric, forced to remain spherical due to small amounts of surface tension until its explosion. Using this theory, temperatures inside the sonoluminescent bubble can be expected to reach 10⁸ Kelvin.²

      A sonoluminescent bubble gives off light that is for the most part ultraviolet. By theory, these rapid contractions and expansions allow the bubble to sustain temperatures much higher than the surface of the sun. In 1991, a measurement by R.A. Hiller under the supervision of Putterman was able to measure photon energies of 6 eV, which corresponds to a temperature of inside the bubble of about 72,000 K. These temperatures are achieved due to the rapid collapse, which in where a spherical shock wave just mentioned is produced. One conclusion about the temperatures is that the surface of the bubble does not evaporate due to the rapid changes in heating and pressure.³

      Sonoluminescence is also a highly sensitive phenomenon. It has been recorded that sonoluminescence is also dependent on temperature of the water inside the flask. Putterman even states that the amount of light that a sonoluminescent bubble gives off increases 200 times when the temperature decreases from 35 degrees Celsius to 0 degrees Celsius. ³

      Many people have also tried to find sonoluminescence using different liquids. For the most part these type of experiments have been unsuccessful, even though there is no explanation on why other liquids should not work. The other mixture besides water that has also been used where people actually were able to produce sonoluminescence is a mixture of water and glycerene. In addition, other gases besides air (78% nitrogen, 21% oxygen, and traces of Argon, water, and carbon dioxide amongst many others) has been used to create a bubble of air. Surprisingly, using a mixture of liquid air (80% nitrogen and 20% oxygen) yields a low intensity of sonoluminescence. The addition of 1% argon increases the intensity almost back to normal. The addition of any other noble gas (helium, xenon) also brings about sonoluminescence, each one with a unique spectrum. But overall, the role of these inert gases is still unknown.³

      Another area where there has been intensive research is the study of sonoluminescence spectra. The spectrum for single-bubble sonoluminescence does not appear to have any peaks that stand out, it does not have any emission lines or spectral bands that would yield evidence of any atomic/molecular transitions, and can easily be fit under a blackbody curve. Under these measurements, the temperature could be measured out to be around 16,000 Kelvin when the temperature of the water in the experiment is at room temperature. The temperature measured will increase to about 30,000 Kelvin when the temperature of the water is lowered.²

      Due to the nonlinear nature of the sonoluminescent bubble, there are many theoretical research put into it by using an analytical approach. This is due to the difficulty of experimental research that can be put in due to conditions of the bubble and its size. In order to accomplish an analytical approach, one must look into an equation of motion for the surface, an equation for the energy of the liquid used, an equation for the energy of the gas used, and a calculation on the conservation of momentum.²

      Adiabatic heating and the theory of shock waves are not the only ideas that have been used to explain this phenomenon include chemical reactions, plasma, Bremsstrahlung radiation, and so on, most of which will not be mentioned in this paper.

      One must say that there are many different paths that the study of sonoluminescence yields. Nonetheless, the main attraction that researchers have towards sonoluminescence is the incredible concentration of energy that occurs from the collapse of the sonoluminecent bubble. This research has brought many ideas, from studies of acoustic cavitation to influencing chemical reactions,

Experiment

      The apparatus used to perform single-bubble sonoluminescence consisted of the setup that has been used almost universally, written by R.A. Hiller and B.P. Barber.⁵ Please refer to that article for a more specific instructions.

      The setup consists of two piezo-electric transducers glued with epoxy on opposite sides of a standard 100 mL flask and a third smaller piezo-electric transducer picks up the interaction of the sound waves and the bubble for display on the oscilloscope.

      The main procedure to create single-bubble sonoluminescence is done by trapping a bubble in the center of a spherical flask filled with . This area is the location where the buoyancy force that allows the bubble to rise to the surface of the flask is equal to the force created by the resonant sound waves.³ In order to cancel out these forces, the bubble be driven at an acoustic standing wave.²

      Equally important is the volume of the flask that is being used. The resonant frequency used is highly dependent on the volume. The reason the 100 mL flask was used in this experiment was because at this volume the resonant frequency needed was about 25 kHz, a frequency somewhat higher than human hearing. Other sized flasks could have been easily used, but the main problem lies with people being subjected to high-pitched hums.

      In order to produce sonoluminescence, one must make the flask vibrate at a resonant frequency. This frequency, as mentioned earlier, is highly dependent on the size of the flask. The resonant frequency can be theoretically be found by using the speed of sound in water (1482 m/s at 20 degrees Celsius) and dividing it by the diameter of the spherical flask. In addition, the use of a glass flask will make the actual frequency to be ten percent higher. Using the same setup as everyone else, the resonant frequency comes out to be somewhere about 25,000 Hz.⁵

      In addition, one must first take some of the air out of the water. This process is commonly know as degassing. There are two methods that can be used to degas water, by boiling the water for about fifteen minutes and the other way is by using a pump.⁵ The process that was mostly used for this experiment was by using the latter.

      To create a bubble inside the flask, a simple dropper was used. First one must extract some of the water with the dropper and then just let a drop fall into the water in the flask. When the drop comes in contact with the surface of the water, a couple of bubbles of air are produced. With the function generator on around the right frequency, the bubble of air will automatically drift towards the middle of the flask. Now that the bubble is in place, the experimentation can begin.

      When looking at the flask for the bubble, it is convenient to be in a dark place with a light source behind the flask. This makes the finding of the bubble easier. Once the bubble is found, it can easily be found at other times

      In the dark, one can look at the bubble of air without looking directly at the flask, a process that is easier to do. When the bubble is not present, the oscilloscope will pick up the resonance of the flask. As the bubble is introduced to the flask, the signal in the oscilloscope shows some ripples. These shows the presence of the bubble, showing the collapses of each cycle. Once everything is set in order, one can then look at the flask to see the sonoluminescent bubble.

Results

      The first experiments that were performed were done in order to get more information about the degassing procedure. Studies were then made by studying the behavior of the bubble. After several measurements, an idea was developed to see how much the water needs to be degased.

      During this period sonoluminescence was sought. After a few days it was achieved, but it was unstable (lasting about 3-5 seconds every 5-10 seconds) and the output of the light seemed to be less than it had been reported by others.

      The efforts were then directed into the improvement and the fine tuning of the setup to increase the light intensity. Different frequencies were measured to study the behavior of the bubble. The graph below shows a scan of frequencies with the same degassed water during different days.

      Other measurements were made to study the shape and frequency of the acoustical resonance as a function of volume inside of the flask and degree of degassing. The graphs below show scans of frequencies with the same degassed water using different volumes. The procedure was repeated for three days.

After most of the measurements at volumes were made, our efforts were then guided towards understanding of a more detailed approach. Instead of making broad measurements, we concentrated on studying the peaks.

Conclusion

      Sonoluminescence is still a recent development in the wonderful world of physics. There are yet many things to be studied and measured. Only with time will one tell where sonoluminescence will lead. Only then will there by faster and more acurate apparatus to study this tiny bubble.

      As part of the National Science Foundation program, Research Experience for Undergraduates, the author personally feels that a lot was learned from this experience. Due to the amount of time of the duration of the program other experiments were not performed. Overall, a basic understanding of sonoluminescence was achieved.

The addition of a new multimeter will defenately make some of the measurements much easier to do. Some of the problems that were encountered before were due to the difficulty to read measurements using a multimeter due to the high frequencies that it is being subjected to.

Work is also under way to observe the sonoluminescence light with a sensitive photomultiplier tube.

Acknowledgments

      The author would like to thank John Noé, Harold Metcalf, and members of the Laser Teaching Center at State University of New York at Stony Brook for their help, time, and patience in this experiment. I would also like to thank Dominik Hammer and Lothar Frommhold from the University of Texas at Austin for introducing me to sonoluminescence when they invited Lawrence A. Crum to speak at the school. This experiment was funded by NSF Grant No. PHY 99-12312.

References and Notes

1. W.C. Moss, D.B. Clarke, and D.A. Young
           "Star In A Jar"
           Sonochemistry and Sonoluminescence 159-164 (1999)
           Edited by L.A. Crum, T.J. Mason, J.L. Reisee, and K.S. Suslick

a. D.F. Gaitan
           "An Experimental Investigation of Acoustic Cavitation is Gaseous Liquids"
           Ph.D. thesis, University of Mississippi.
     D.F. Gaitan, L.A. Crum, C.C. Church, and R.A. Roy
           "Sonoluminescence and bubble dynamics for a single, stable, cavitation bubble"
           Journal of the Acoustical Society of America 91, 3166-3183 (1992).

b. R. Hiller, S.J. Putterman, and B.P. Barber
           "Spectrum of synchronous picosecond sonoluminescence",
           Physical Review Letters 69, 1182-1184 (1992).
           The emission spectrum is consistent with that of a 2 eV black body radiator.

c. B.P. Barber and S. Putterman. "Observation of Synchronous Picosecond Sonoluminescence",
           Nature 352, 318-320 (25 July 1991).
          The measured pulse width is less than 50 ps.

d. No existing model of sonoluminescence could explain the 50 ps. pulse width.

3. S.J. Putterman
           "Sonoluminescence: Sound Into Light"
           Scientific American, 46-51 (February 1995).

4. H. Frenzel and H. Schultes
           Z. Phys. Chem. 27B (421), (1394)

5. R.A. Hiller and B.P. Barber
           "Producing Light From A Bubble Of Air"
           The Amateur Scientist, Scientific American, 96-98 (February 1995).