Mie Scattering and the Onset of Sonoluminescence

Christopher Spencer
UCLA Physics and Astronomy
Professor Gary Williams
02 June 2014

Time between pulses of SL was found to be \(3.069×10^{−5}±0.01\) seconds, width of an SL pulse was found to be \(1.925∗10^{−6}±0.04\) seconds and Sonoluminescence was observed.

Introduction

Sonoluminescence was first observed in 1934 by H. Frenzel and H. Schulte indirectly by looking at acoustic radar in an ultrasonic water bath [1]. Sonoluminescence is the production of light from sound. Sonoluminescence or SL is the phenomena in which a bubble on the scale of microns is spatially trapped and oscillated by an acoustic field where each compression on the bubble causes a small burst of light [2]. Light emission comes in the form of extrmely short bursts when sonoluminescing. In the case of this experiment a bubble was trapped in a cylinder fileld with liquid where then the acoustic field can be applied. If a laser is but on the trapped bubble then with a photomultiplier the scattering from the bubble can be measured, known as mie scattering. The purpose of this lab is to observe the sonoluminescing phenomena, measure mie scattering,to determine the radius of the bubble in time, and obtain the optical spectrum of SL using diffrent fliters in front of the photomuliplier.

Theory

A discussion about how the bubble gets trapped is necessary here. We have a cylindrical acoustic resonator drive by piezoelectric drivers on both endcaps. Something that is piezoelectric has the property that when there is an applied stress to that material an electric charge accumulates in that material. A bubble is injected by running a current through a heater wire which is inside our resonantor. If the acoustic field is tuned to a resonant mode that has an antinode at the center then the resulting bubble from the heater wire will be attracted to antinode and be trapped there. The pressure needs to be a max in all directions to trap the bubble described by the equation\[\delta p=\delta p_0 J_{mn}(k_rr)cosm\theta \cos\frac{n_z\pi}{L_z}z\] need m=0 modes of J to have a maximum at r=0. The Rayleigh–Plesset equation governs the dynamics of a spherical bubble in an infinite body of liquid and it cab be used here as \[R\ddot{R}+3/2\dot{R}^2=\frac{1}{\rho}(p_0 +2\frac{r}{R})(\frac{R}{R_0})^{3\gamma} -2\sigma-p_{\infty}\] where \(\gamma\) is an adiabatic index and \(\sigma\) is surface tension of water. The light that gets emitted has a max temperature which we will define as \[T_{max}=T_0[(\frac{R_{max}}{R_0})^3]^{\gamma-1}\] where we take \(R_0 \approx 3 \mu m\)
Mie scattering is the scattering of electromagnetic radiation by a sphere. In this lab a laser beam is put on the bubble and a photomultiplier picks up the intensity of the scattered light. The intensity of the light goes as \(I\approx R^2\) and this can allow us to measures how the bubble radious changes in time. If the acoustic drive amplitude can reach a threshold value where the bubble can emit SL. This matches with the collapse point of the bubble on each acoustic cycle and has a pulse on order of \(10^6\) photons emitted in about 100 ps. \(\frac{1}{2}\)

Apparatus and Procedure

A schematic of the cylinder resonator is shown in figure 1. A bubble was created by briefly made by using a trigger to send quick pulses of current in the cylinder. This is not a perfect process and often took a while to get a steady bubble. The PMT has a gain of 50-100 k. It is powered by a 12 V supply and in brief works by the photoelectric effect. A photon comes in and hits a biased photocathode material biased at -2000 V. For every 5 photons an electron comes out of the photocathode and then goes through a “ramping” process and continues to hit biased electrodes. One electron is too small to make enough current for us to actually measure it so it is amplified. The amplified current comes out to be about \(10^{-12}\) for every electron. This current then comes out and can be read by an oscilloscope. Figure 2 shows a photo of what was used in this lab. The laser,cylindrical resonator, PMT, and oscilloscope are shown.

A schematic of the cylindrical acoustical resonator
A photo of the setup used for this experiment.

Data and Analysis

After first trapping a bubble, mie scattering was used to get an idea of the radius of the bubble. Data was taken using the PMT after scattering laser light off the bubble at voltages from 500 Volts to 590 Volts. Then for the plots, the maximum radius was taken for each voltage and we normalized the radius which is plotted on the y axis in figure 3. Whats interesting to note here is that the oscilloscope has settings thats reads in time negatively which is easily taken care of by taking absolute values for the rest of the data taken but doing that for this plot revereses the direction of the plot and this makes no physical sense.For the sake of the plot I have left it with the time read in negative for this is the correct way to interpret the bubble radius. An interesting property here is that the onset of sonoluminscence occurs here when we see oscillations occur in the radius in time. It can be seen that there is no SL occuring for the first dat point at 500 Volts and as the voltage goes up the onset of SL can be observed.

bubble radius vs time where the radius has been normalized to the maximum radious for each data set
Then when increasing the acoustic drive amplitude, we are interested in the response in the bubble radius. Figure 4 shows the drive amplitude and the response in the PMT. What was observed was the peaks of the drive amplitude coincided with sharp spikes in the PMT and these coincide with the occurence of sonoluminescence. Here it can be seen that there is some noise and background effects taking place but a clear alignment of sharp peaks with the maxs of the drive amplitude.
Graph of the acoustic drive amplitude and its relation to the PMT response voltage

A property of interest is the time between SL pulses. Figure 5 shows how the time between the two pulses were found by identifying two peaks with their corresponding time and subtracting the two values. The value obtained for the time between pulses was \(3.069×10^{-5} \pm 0.01\) seconds, with inherit error in placing the lines at the peak. Also the width of a pulse can be found in the same way and the graph of a zoomed in pulse is shown in figure 6. The value obtained for the width of this pulse was \(1.925*10^{-6} \pm 0.04\) seconds, again with error coming from placing the markers where I believed the start and end of this pulse was.

Graph identifying the peaks in the PMT response to find the time between pulses
Graph identifying the width of a pulse at the onset sonoluminescence

Then to get an idea of the optical range of the light recieved by the PMT, various filters were used and their amplitudes were looked at. Figure 7 shows the amplitudes with a yellow pass, a blue pass, and with no filter. Notice the differences in the amplitudes between the three as this matches what we believed would happen with filtered and unfiltered light. Ratios were then taken of the yellow filter and the blue filter with the light with no filter. The ratio of yellow filtered amplitude to the reference amplitude of the non filtered light was 0.3, ratio for the blue filtered light to the reference was 0.9, the ratio of the former and latter was 0.3 . We want to compare this data to a blackbody with a temperature of 17000 Kelvin with the wavelengths ranging from 250 nm to 800 nm since this is the limit of the PMT’s sensitivity. Figure 8 shows the blackbody theory at 17000 K vs wavelength.Plotted the intesity from blackbody theory and markers where these filters let transmitted light through the filter. The yellow filter transmits light from 310 nm to 440 nm. The blue filter trasnmits wavelengths from 500 nm to 575 nm. What can be understood from the proportions taken from figure 7 is if we can find a wavelength in the transmitted range of the yellow filter then we expect that 30\(\%\) of that value of that wavelength should be found in the transmitted area for the blue filter. It can be seen from from the theoretical curve that intensities are wouldnt be higher than \(2*10^-20 \frac{W}{m^2}\).

Graph of ampltudes of two filters used in comparison with no filter
Blackbody theory curve with markers indicating the ranges of transmitted light.

Conclusion

The lab was succcessful at trapping bubbles in an acoustic field and observing sonoluminescence. The data taken also backs up that we can saw sonoluminescence in these bounces in the radius of the bubble shown in figure 1. From the data the time between SL pulses, width of a SL pulse, and the amplitudes of light with filters through them. This process was done using mie scattering and overall the lab was a success. The oscilloscope did the have the problem that it read in time negatively, so fixing that would be of help to the researcher.

References

\([1]\)-Kordomenos, John. “Sonoluminescence.” Sonoluminescence. N.p., n.d. Web. 02 June 2014.\(<\)http://www.sonoluminescence.com/\(>\)
\([2]\)-Steer, William A. “Sonoluminescence Experiment: Sound into Light.” Sonoluminescence Experiment: Sound into Light. N.p., Sept. 1997. Web. 02 June 2014. \(<\)http://techmind.org/sl/\(>\).

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