An Investigation into Different Kinds of Resonance Present within a Sonoluminescence System

Mentors: Melia Bonomo, Martin G. Cohen, and John Noé

Laser Teaching Center
Department of Physics and Astronomy
Stony Brook University

Background

My interest in sonoluminescence began at the end of my sophomore year of high school. Deciding that I wanted to work with the process the following year was not difficult due to my interest in the idea of fusion with the high temperatures resulting from the process. However, working with limited materials provided at my high school and working with my own limited understanding of the phenomenon and the hardware used to create sonoluminescence devices provided difficulty.

I contacted Dr. Noe after seeing a paper conducted by one of his students named Christina Huang (link to Christina's page: http://laser.physics.sunysb.edu/~christina/). After a conversation about my device and my interests in the topic, we discussed the possibility of my place with the LTC group over the summer.

My initial ideas with the topic were grandiose (for example, my interest with the topic lied in the debatable, if not debunked theory of possible fusion with the process). Eventually, Dr. Noe convinced me to try investigating the basic physics behind the process to obtain an overviewed understanding and apply what I had learned to other areas. I conducted three basic experiments, the first dealing with into acoustic resonance, the second learning the effect of inductance on an LTC circuit, and the third applying a known inductance to my sonoluminescence set up.

Introduction

Sonoluminescence was first discovered in 1934 when two scientists noticed speckles on their photographic film after attempting to speed up development using ultrasound transducers [2]. Sonoluminescence is the process in which intense high frequency sound waves typically in the range of 23-25 kilohertz are used to induce cavitation in tiny bubbles trapped in a degassed liquid medium. The transition between high and low sound pressure levels traps the bubble and causes it to oscillate (or jiggle) due to the variation between the two extremes [3].

A mode is a vibrational pattern of a given system, and often reflects the symmetry of the system and its boundary conditions. Modes are the natural frequencies at which the particles of a system vibrates in an oscillating pattern, as characteristic of the behavior of a sonoluminescence bubble, with increased amplitude. When an exciting frequency matches the natural frequency, resonance occurs. An example of this is when a drum is hit at a precise location with great force, causing it to emit an exciting frequency belonging to a specific mode. Hitting a drum at different placements can induce the vibrational patterns belonging to individual modes and increase the sound level emitting from the drum.

The increased pressure changes cause volume changes resulting in periodic growth and depletion of the bubble. An induced shock wave converges into a hot spot and causes a process called acoustic cavitation. The shock wave itself influences greater molecular movement within the confined area of the bubble, allowing energy and momentum to transfer between particles and the bubble wall. The outer particles cannot withstand these conditions while holding the boundary of the bubble together, causing the bubble to collapse.

The hot spot is estimated to have a plasmatic core due to the high temperatures found [4]. These temperatures have been noted for reaching over 25,000 Kelvin, however, some estimates state that under the correct conditions, temperatures might reach as high as 3 x 108 Kelvin [5]. Such estimates aroused interest during the early 2000s due to the possibility of nuclear fusion, but this theory is highly debated due to false claims asserting that it had been achieved [5].

Some more recent interest with sonoluminescence primarily resides within medical applications. Acoustic cavitation induced through ultrasound methods in particular has been investigated as a way to help break up blood clots. Bubble growth studies show that growth places stress upon fibrin fibers and cause a jet of sorts that helps to break down the clot. These studies show that bubble cavitations outside of the clot provide more damage than ones within [6].

Sonoluminescence System

The standard setup for sonoluminescence is a spherical flask with piezo-electric transducers (PZTs) attached on opposite sides of the flask. The PZTs are excited by sound waves generated by a function generator and amplified by an audio amplifier. Another smaller PZT on the bottom of the flask acts as a microphone to monitor the response of the flask and the sound of the collapsing trapped bubble that was induced into the system. The response contains many high harmonics of the driving frequency. The signals picked up by the microphone can then be displayed upon an oscilloscope to document the response of the bubble. Resonance is displayed on the oscilloscope when the highest amplitude of peak to peak voltage exists.

Above shows a very basic sonoluminescence device schematic displaying basic placement of wires, instruments and PZTs.

Flask Estimation

To test the acoustic modes of the system, a 125 ml spherical flask with a flat bottom was tested. Spherical flasks filled are known to have three modes, while rectangular shaped containers are known to have four. Due to unique glass shape used within the experiment, the correspondance between shapes and the number of modes within a system could be further investigated.

A basic sweep of the oscilloscope was done in 1 kilohertz intervals giving a nonspecific resonant frequency at 24.5 kilohertz. Assuming that the wavelength was equal to the diameter of the flask, the wave equation was used with these values in addition to the sound of speed in water to determine the diameter values of the flask. This was compared to the actual diameter of the flask to test the validity of this value.

V =λ f

1497 m/s = λ (24.5 x 103cycles/s)

6.1 centimeter = λ

6.1/2 = 3.05 centimeters

When the diameter was actually measured for the system, the diameter was calculated to be exactly 6 centimeters for the spherical flask of with a flat bottom.

Flask Estimation Problem with Possible Explanation

Sonoluminescence is often depicted as taking place within the first mode out of four modes of a pressure system. The first mode of the system shown on the diagram below would contain pressure nodes (where no pressure is influenced) on either side by the transducers with an antinode (with great pressure) produced in the center trapping the bubble by the high pressure fluctuations. The pressure nodes of the system are influenced by the pressure release conditions of a spherical system within fluid influenced by the particularly rigid characteristics of the spherical glass walls.

This statement contradicts the method used in the previous section that used one wavelength as the diameter of the sphere. Within the first mode, the diameter of the sphere would be equal to half of the wavelength. If this is true, why was the estimate close to the actual 6 centimeter diameter of the sphere? This question can be answered by further research into acoustic modes within a liquid. The first or fundamental mode represents the pressure fluctuations produced by the introduction of sound into the system. However, a second vibrational pattern is created by the pressure introduction. This mode has been classified as the second mode of the system, depicting the vibrational patterns belonging to the specific particles. This pattern is referred to as sound pressure gradient caused by the Bjerknes force (or buoyancy) that exists within a liquid system [8]. The estimation uses the second mode belonging to the particle adjustments due to the sound in its calculations. Both the first mode belonging to the pressure variations and the second mode belonging to the particle motion coexist within the liquid environment.

Acoustic Results

Upon completion of a more in-depth sweep of the oscilloscope ranging from 0 to 50 kilohertz, the specific resonance frequency of the first acoustic mode was determined to be 24480 hertz, around the 24500 estimate when a more general sweep was completed. This number can be displayed on the graph below showing the more in depth acoustic sweep.

This data indicated many more than the three resonant frequencies, indicating that there are more than three acoustic modes belonging to the experimental setup of the circular flask with a flat bottom. In contrast, this flask seemed to have over eleven peaks within the 0 to 50 kilohertz range alone.

Sonoluminescence System Circuit Results

The 100 mh inductor was placed into circuit with the sonoluminescence device in order to help calculate the correct inductance value to reduce the impedance of the circuit. To get the smallest impedance values within the circuit, the voltage values for the capacitance and the inductance must be out of phase but have the same value in magnitude in order to cancel out.

C = 1/ Angular Frequency2L

C = 1/(23620 hertz x 2 x Angular Frequency)2 x .1 Henry

C = .454 nanoFarads

When the capacitance values for the two PZTs are determined, these values were used to find the inductance required to minimize the impedance of the circuit and maximize circuit flow by altering the circuit frequency.

L = 1/Angular Frequency2Cvalue

L = 1/(24.5 kilohertz x 2 x Angular Frequency)2 .454 nanoFarads

L = 93 millihenrys

The buzzing noise that occured created by the bubble response was influenced by the inductance of 100 millihenries being close to the correct value for the circuit of 93 millihenries. This can also explain the similarities between the two resonant frequencies. In order to make a 93 millihenry inductor, a coil with a specific wire will have to be created.

Furture Work

Future work with this process includes the creation of the coil to achieve a 93 millihenry inductor. In addiion, more work could be done testing the effect that shape has on resonance within an acoustic system. This could be tested by possibly altering water levels so that there are different amount of area belonging to the surface of the water.

Refrences

[2] McCluney, S. (2010). Sonoluminescence: Sound into light. Informally published manuscript, Physics, University of California, Santa Cruz.

[3] Suslick, K. S., & Flannigan, D. J. (2012, August 16). Inside a collapsing cavity: Sonoluminescence as a spectroscopic probe.

[4] Flannigan, D., & Suslick, K. (2005). Plasma Formation and Temperature Measurement During Single-bubble Cavitation. Nature, 434, 52-55.

[5] Wrbanek, J. D., Wrbanek, S. Y., & Fralick, G. C. (2007). Development of techniques to investigate sonoluminescence as a source of energy harvesting. NASA, 2007(October), 1-17.

[6] Weiss, H., Selvaraj, P., Okita, K., Matsumoto, Y., Voie, A., Hoelscher, T., & Szeri, A. (2013). Mechanical clot damage from cavitation during sonothrombolysis. The Journal of the Acoustical Society of America, 133(5), 3159-75.

[7] Brenner, M., Hilgenfeldt, S., Lohse, D., & Rosales, R. (1996). Acoustic Energy Storage in Single Bubble Sonoluminescence. Physical Review Letters, 77(16), 3467-3470.

[8] Solway, M., & Kojima, H. (2007). The Dependence of Single Bubble Sonoluminesence on Mixtures Mixtures of Noble Gases. Retrieved from http://www.physics.rutgers.edu/~mikesol/Presentations/mikesolPresentationSonoluminescence.pdf