SONOLUMINESCENCE in WATER MIXTURES and in LIQUID METALS a Thesis Submitted for the Degree of Doctor of Philosophy in the Univers

SONOLUMINESCENCE IN WATER MIXTURES

AND IN LIQUID METALS

A Thesis submitted for the Degree of

Doctor of Philosophy

in the

University of London

FREDERICK RONALD YOUNG, M.A. (CAMBRIDGE). ABSTRACT

Sonoluminescence from viscous liquid-water mixtures has been measured using a magnetostrictive transducer with a titanium velocity transformer and a photomultiplier tube. The results suggest a correlation between sonoluminescence and viscosity.

The same apparatus has been used to measure the sonoluminescence from water containing dissolved gases. An inverse relationship between the sonoluminescence and thermal conductivity of the gas supports the theory that the light is basically due to an adiabatic compression of the gas during the rapid collapse of the cavitation bubbles.

Sonoluminescence from liquid metals has been measured using a lead zirconate titanate transducer with a glass velocity transformer and the same photomultiplier tube. Thermal diffusivity of the metal appears to have an inverse relationship with sonoluminescence again supporting the thermal origin of the light. 3

ACKNOWLEDGEMENTS

The author wishes to thank Dr. R.W.B.Stephens for his constant guidance and encouragement, Mr. E.A.Neppiras for his advice, and his colleagues in the Acoustics Group for much help and many stimulating discussions. He wishes to thank Mr. T. Shand and Mr. E. Abbott of the workshop of the Physics Department for constructing the mechanical parts of the apparatus, Mr. O.R.Milibank for making the glassware, and Mr. F.Martin for guiding the author's attempts at making the simpler parts of the apparatus. He is grateful to Mr.P.Coppock, Mr. M.Wallace and Mr.M.O.Jackson for the photographic work, and Miss B. Lloyd-Jones and Mr.J.T.Graham for library assistance. He would like to express his appreciation to Mrs.J.D.Harris and Miss E.C.Pope for their patience and good humour in helping the author to produce this thesis. The author is deeply grateful to the Hertfordshire County Council for leave of absence and for financing the research, and to Dr.D.O.Bishop, Dr.J.F.Richardson, Dr.H.Tropper, Mr.GX.Warren and Mr.B.Wood of the Watford College of Technology for their help, advice and encouragement. Finally, he wishes to thank his wife for welcoming his intention to do this research and for constantly supporting him in the vicissitudes which have accompanied the production of this thesis. And the four winds, that had long blown as one, Shone in my ears the light of sound, Called in my eyes the sound of light.

Dylan Thomas. 5

CONTENTS

ABSTRACT 2 ACKNOWLEDGEMENTS 3 CONTENTS 5 SYMBOLS AND UNITS 7 CHAPTER 1 SURVEY OF SONOLUMINESCENCE 1.1. Definitions and Historical Review 10 1.2. Instrumentation for Observing Sonoluminescence 10 1.3. Model Bubble Experiment on Sonoluminescence 11 1.4. Luminescence from Hydrodynamic Cavitation 14 References in Chapter 1 17 CHAPTER 2 SONOLUMINESCENCE FROM VISCOUS LIQUID-WATER MIXTURES 2.1. Introduction 20 2.2. Design of Experimental Arrangement 20 2.3. Calibration Measurements 23 2.3.1. Acoustic Power Output 23 2.3.2. Sound Pressure Amplitude 26 2.3.3. Sensitivity of Photomultiplier Tube 29 2.4. Experiments 33 2.5. Results 33 References in Chapter 2 34- CHAPTER 3 SONOLUMINESCENCE FROM WATER CONTAINING DISSOLVED GASES 3.1. Introduction 37 3.2. Design of Experimental Arrangement 37 3.3. Calibration Measurements- 40 3.4.. Experiments 40 3.5. Results 43 References in Chapter 3 50 6

CILIITER 4. SONOLUMINESCENCE PROM LIQUID METALS 4.1. Introduction 51 4.2. Design of Experimental Arrangement 51 4.3. Calibration Measurements 61 4.3.1. Acoustic Power Output 61 4.3.2. Sound Pressure Amplitude 63 4.3.3. Sensitivity of Photomultiplier Tube 64 4.3.4. Thermocouple 64 4.4. Summary of Liquid Metal Experiments 64 4.5. Results 64. 4.5.1. Correlation of ¶ater and Mercury Experiments 64. 4.5.2. Mercury 65 4.5.3. Gallium 85 4.5.4. Indium 89 4.5.5. Tin 95 4..5.6. Bismuth 98 4.5.7. Collected Results 103 4.5.8. Bismuth in a Magnetic 'Field 103 4..6. Discussion of Results 105 4.6.1. Correlation of Sonoluminescence 105 with other Parameters 4.6.2. Cavitation Threshold Results 114 4.6.3. Mercury Results 114 References in Chapter 4 115 Suggestions for further work 116 Publications 117

SYMBOLS AND UNITS

SI units are used, except where conventional units are much more familiar. Symbol Units Quantity (if used) Attenuation coefficient in Y=Yoe-" a nepers m 1 Density p kg m-3 Energy J Frequency f Hz Magnetic flux density wb m-2 Power W Radiation impedance Z kg s m-2 Resistivity Pi Om Sound displacement amplitude Y m Sound pressure amplitude P Ni 2 Sound velocity c ins" Sound velocity amplitude U ins" Specific heat at constant •.4 _ C, J gm degC degC -. 1 Surface tension a dyn cm Temperature Oc Temperature difference degC -1 -I -4 Thermal conductivity K J cm s degC Thermal diffusivity D OM23 - Ultrasonic attenuation a42 m 1s 2 Vapour pressure atmosphere Viscosity dynamic 77 gm cm-is-1 =Poiser-100cP 2 -1 Viscosity kinematic v cm S =Stoke=100cS Wave number k= an-A m 1 Wavelength X A

Fig.J

Sonoluminescence photographed using an image intensifier camera. 10

Chapter 1 Survey of Sonoluminescence

1.1. Definitions and Historical Review

When a liquid is cavitated by a sound field of a few watts per square centimetre intensity a weak luminescence is emitted. This is called sonoluminescence. Cavitation is the process whereby a gas or vapour filled bubble expands and collapses as the net local pressure in the liquid becomes negative and then increases to above atmospheric. Sonoluminescence in tap water can be seen as a faint bluish glow by a dark-adapted eye, but it is stronger in glycerine. However it is more easily detected by a photomultiplier tube on account of its very low intensity.

Sonoluminescence was first observed in 1933 by Marinesco and Trillat (1) when photographic plates were blackened on exposure for some hours to water cavitated by an oscillating quartz crystal. However, they ascribed this blackening to an.acceleration of the chemical process of oxy-reduction brought about by the ultrasonic waves. Frenzel and Schultes (2) made similar experiments and believed that the effect was actually due to exposure to light. Adequate reviews of the literature on sonoluminescence have been given by Jarman (3), El'piner (4.) and Finch (5).

1.2. Instrumentation for Observing Sonoluminescence

Much of the earlier work was carried out by observing the sonoluminescence with the eye, but all later work has used photomultiplier tubes. This has enabled a quantitative absolute measure of the light to be made and has led to the discovery that sonoluminescence occurs as discrete flashes which are periodic with the sound field but that a sonoluminescence pulse does not occur with every sound cycle. (6). Finch (5) has given a table of the types of photomultiplier tube and of transducer used in studying cavitation by various workers. Quartz crystals working at frequencies up to 2MHz were initially used to produce the cavitation, but more recently magneto - strictive and piezoelectric ceramic transducers working at frequencies from 1 - 30 KHz have been employed.

Flynn (7) photographed the light emitted from a field of cavitation in front of a small 25 KHz ferrite transducer using a Westinghouse Astracon light image intensifier camera. (Fig.1). The exposure was for sec, and the decay time of the output phosphor was of the order of a milli-second. This may be a good way of measuring cavitation activity 11 as the phenomenon maybe measured directly without disturbing the cavitation field. Flynn is making a study to determine the relation between the number and density of bright images and the number and acoustic intensity of cavitation events respectively (8).

1.3. Model Bubble Experiment on Sonoluminescence

Beccaria (1716 - 1781) observed that glass spheres containing air at reduced pressure emitted luminescence when broken in air. Priestley (9) gave the following description of Beccaria's experiments in 1769:

"Signor Beccaria observed that hollow glass vessels, of a certain thickness, exhausted of air, gave a light when they were broken in the dark. By a beautiful train of experiments, he found, at length, that the luminous appearance was not occasioned by the breaking of the glass, but by the dashing of the external air against the inside, when it was broke."

A model bubble experiment on sonoluminescence at GBttingen (10) was designed to study the collapse of a glass sphere of gas under controllable' conditions of purity, of initial gas pressure, of known gas content, and size of sphere. Schmid used a thin-walled glass sphere of 7 cm diameter which was evacuated, filled with various too gases at low pressures, and then CC1 4 immersed in a liquid. On breaking ill r H20 the glass wall by a striking plate, 1.Luft 1 10 the sphere imploded and a flash of ‘ light was emitted. A high speed I cinematograph record of the implosion, which lasted for 4. ms, showed that the walls accelerated t s until the volume of gas was effect- s CO2 ng He lu ively divided into a number of parts h tra each giving rise to strong shock S waves in the liquid and a flash of 01 light near the end of each implosion. Using glycerine as the liquid, a number of experiments were made with (C2H5)20 various filling gases at different CH,, 0 '01 o pressures and the results are shown 10 • 20 30 Torr 60 in Fig. 2. Fiilldruck —0-

Fig.2. Light intensity against filling pressure. Implosion in glycerine (88%) (Schmid) 2

1,0 12 500 5 pWs $.1.Ws 200 2 . . 100 10-1 50 5 / 1

20 . 1 2 I 10 10-2 AilAry a I 5 5 a / . 1

2 ../ 1,0 .

0,5 He

\le 0,2

2 0,1

10-4 0 05 0,5 2 5 10 20 Torr 50 100

0,5 1 2 5 10 20 Torr 50 Pt

Fig.3. Total light output Fig.lf. Total light output against against fillingpressure. filling pressure. Implosion in Implosion in paraffin water

Willer (11) continued this work using smaller spheres of 5 cm diameter as these show less instability in the collapse. He imploded in paraffin spheres containing helium, neon, argon and xenon and Fig. 3 shows the variation with filling pressure0of the emitted radiation energy in the wavelength band 1,.000 A to 6000 A. This shows that the radiation increases with increasing number of gas atoms in the imploding bubbles. However, for greater values of filling pressure, the bubble collapse becomes cushioned, the gas becomes less compressed and therefore less heated so that the radiation energy is reduced. Muller next imploded spheres of neon, argon and xenon in water and obtained curves showing a similar maximum but of much smaller values of total radiated energy, (Fig.4). The difference in the light output in paraffin and water is due to the influence of the liquid molecules and their excitation despite the fact that no allowance was made for light absorption by the liquid. Muller split the emitted light into blue and red components by a special filter and measured the components with blue and red sensitive photomultipliers. 13

2,0 X in P o . . 1,0 \ .

A HeinP 0,5 ...-----1--.-.. V linW 0,2 563 516 474 438 385

01 0,5 2 5 10 20 Tarr 50 432 431 Pi. —0- 589 387

Fig.5. Ratio V of red and blue Fig.6. Spectrum of implosion light light (V = Q red A blue ) for for xenon filled balls in paraffin. nm, xenon and helium in water, and 1nm = 101 for xenon in water

Fig.5 shows V = Q red/Q blue where Q is light energy against filling pressure. It is surprising how little V changes with filling pressure. If the implosion light were from a black body radiator, then the fall in the xenon curve from 24 torr to 8 torr should correspond to a fivefold increase in the relative red fraction of the radiation. Actually, V as a function of filling pressure hardly changes so that we must conclude that the implosion light is not emitted from a black body radiator. Muller obtained further information about the light from a spectrogram of the xenon filled glass sphere (filling pressure 8 torr) in paraffin. Even though this gas gives the greatest light output, it is still necessary to obtain a photograph using the total light of fifteen implosions. Fig. 6 shows a continuum with very distinct sodium D-liRes and the strong Swan band of C2 radicals (5630, 51606 4740, and 4380 A) as well as (weaker) the CH-bands (4320, 4310 and 3870 A). The xenon lines were not seen. All the involved substances (gas, liquid and glass) and especially the sodium in the glass and the paraffin molecules in the liquid influence the nature of the light emitted. Muller concludes that the light from the imploding model bubble- is dependent on the heating of the filling gas during the bubble collapse and also on the excitation of the involved substances produced by thermal processes or chemiluminescence. 14_

Comparison of the results of the model bubble and the sonoluminescence shows a difference in the spectral distribution. Gunther (12) and. Srinivasan (13) both obtained a continuous sonoluminescence spectrum, but Milner points out that this was because of the large slit widths of their photoelectric arrange- ments (up to 130 A and 250 A respectively). Moreover, Heim (14.) produced spectrum photographs of the resonance lines of the alkali and alkaline-earth metals from their salts dissolved in water.

1.4. Luminescence from Hydrodynamic Cavitation

Konstantinov (15) was the first worker to observe light from hydrodynamic cavitation. He noticed bright flashes with a bluish tinge some 0.2 - 0.3 mm long behind a cylindrical obstacle in a water tunnel. Around the junction of the cavitation region flashes with a diffuse yellow tinge occasionally appeared.

More concrete evidence for the appearance of luminescence was reported by Schmid (16) who used the Chesterman technique of inducing cavitation by imparting a rapid upward momentum to a vertical tube closed at the bottom and filled with liquid and then rapidly decelerating the tube to produce a low pressure region in the liquid. A large number of cavitation bubbles then appear. By using an electrode to generate a gas bubble nucleus in the low pressure region, Sohmid was able to obtain a single bubble which grew to over a centimetre in diameter, before collapsing rapidly. When the liquid medium was glycerine, luminescence was observed. Jarman and Taylor (17, 18) detected light from the vaporous cavitation induced in flowing tap water by a fall in pressure as it passed through the constriction of a Venturi tube (Fig.7). The light wap emitted as flashes of duration' less than 5 p sec and its spectrum lay between 4-000 /// and 7000 A with a Raximum .1 , intensity at 4700 A. The light --r- emission was two orders of 7/4 magnitude less than for the ion ultrasonically induced sonoluminescence in water, which itself can barely be seen by a dark adapted eye. Only by artificially enhancing the Fig.7. Profile of Venturi tube light emission with the

70 CURVE P COLL ❑ (PSMA) PC ) 60 I x 5.4 a > 4 2 o 5.1 6° 4 ❑ 5O t. 3 0 5.9 4 o 2E13 nave 17% additional Xenon nC T FO 30 :=C- 4_„--4 , ce "C1c'ccf:r' .-

d10 0 •

0.I I 1 , 1 , 190 230 270 310 350 390 430 470 WAVELENGTH (N ANCHAET ERS)

Fig.9. Relative integrated spectral Fig.8. Flow system schematic intensity of xenon light pulses

addition of air or carbon disulphide upstream from the Venturi were they able to obtain an increase of one order of magnitude. None of the remarkably bright "sparks" with blue or yellow fringes as described by Konstantinov were Observed.

Peterson and Anderson (19) produced cavitation in the free stream of water in a location readily accessible for observation using a Venturi in a closed loop system (Fig. 8). The system was filled with vacuum de-aerated water and then either oxygen or xenon gas introduced to raise the gas partial pressure to the desired level. In this study there was no difficulty in observing the light emission in a darkened room. When xenon gas was introduced upstream from the Venturi discrete bluish-white flashes were observed. When gas admission was terminated and the cavitation become self-sustaining, the collapse region took on a bluish-white glow with occasional discrete flashes still discernible, The light emission occurred at the end of the cavity collapse region in a volume approximately 1 cm long and 102 cm in diameter. Peterson and Anderson determined the spectral distribution of the light using a spectrophotometer. Their results (Fig. 9) show that the spectral distribution cannot be associated with a black body radiator. Based on this fact alone, it 16 cannot be stated that the individual light pulse itself has no relation to a black body radiation source. The pulse height spectra show that the intensity of each light pulse is not the same. Theoretical calculations have shown that the size of the cavity before collapse significantly effects the temperature within the cavity during a nonisothernal collapse. If this is the cases then one cannot expect a spectrum determined by many pulses to have a black body distribution. 17

References

1. Marinesco,M., and Trillat,J.J., Comptes Rendus Acad.Sci., 196, 858 (1933). 2. Frenzel,J., and Schultes,H., Zeit. fur Phys. Chem, B27,11.21 (1934). 3. Jarman,P.D., Science Progress, No.184., 632 (1958). 4. EliPiner,I.E., Sov.Phys. (Acoustics), 6,1 (1960). 5. Finch, R.D., Ultrasonics, 1, 87 (1963). 6. Finch, R.D., Nature, 204, 770 (1964). 7. Flynn H.G., Physical Acoustics Vol. 1 Part B (edited by W.P.Mason, Academic Press, New York, 1964). 8. Flynn H.G., Private communication. 9. Harvey, E.N., A History of Luminescence (American Philosophical Society, Philadelphia, 1957). 10. Schmid, J., Acustica, 12, 70 (1962). 11. Muller, H.M., Acustica, 16, 22 (1965/66). 12. Gunther, P., Heim, E., and Borgstedt, H.U. Zeit. fur Elektrodhem, 63, 4.3 (1959). 13. Srinivasan, D., and Holroyd, J.Appl.Phys., 32,446 (1961). 14.. Heim, E., Z.angew. Phys. 12, 423 (1960). 15. Konstantinov, V.A. Dok.Akad.Nank. U.S.S.R. 56, 259 (194.7). 16. Schmid, J., Acustica, 9, 321 (1959). 17. Jarman P.D., and Taylor K.J., Brit. J. Appl.Phys. 15,321 (1964). 18. Jarman P.D., and Taylor K.J., Brit. J. Appl.Phys. 16,675 (1965). 19. Peterson F.B., and Anderson T.P., Phys. Fluids, 10, 874. (1967).

INCORPORATED PHOTOGRAPHER 19 THE GARDENS, WATFORD, HERTS.

TELEPHONE WATFORD 34015 19

Fig.1 0 .

Transducer and velocity transformer 20

Chapter 2 Sonoluminescence from Viscous Liquid-Water Mixtures

2.1. Introduction

The sonoluminescence from glycerine was found by Jarman (1) to be greater than that from any of twenty liquids he examined but he also found that it was not possible to cavitate glycerine at ordinary temperature if it was free of water. It is noteworthy that glycerine is very hygroscopic, ordinary commercial glycerine containing up to 27 water. Negishi (2) found that 50g, glycerine luminesced with considerable brightness. No work could be found on other very viscous liquids.

2.2. Design of Experimental Arrangement

The energising equipment consists of a Mullard Ultrasonic Transducer Type L533 powered by a Mullard Ultrasonic Generator Type L534. These two items comprise part of the Mullard SIM Ultrasonic Drilling Equipment. The transducer (Fig.10) consists of a stack of nickel laminations in the form of a 20KHz half-wave resonant section and is clamped at its nodal point. The drive coil is wound on to a former which surrounds the upper half of the stack. The polarising field is produced by the coils wound on to the U shaped laminated stacks which flank the transducer. The polarising magnetic circuit is completed by the transducer stack. The vibration of the transducer is mechanically amplified by a titanium double quarter- wave velocity transformer having end diameters of 11" and g" and thus amplifying the motion approximately four times. The transducer was monitored by a Solartron CD 1014.3 oscilloscope and an Advance Millivoltmeter Type 77B connected to a crystal accelerometer pick-up fixed to the transducer.

Since much of the sonoluminescence is in the ultra-violet region of the spectrum (3) it is necessary to use a detecting arrangement capable of covering this region. Accordingly, the sonoluminescence was measured by a ihstage E.M6I. photomultiplier tube '6255B' sensitive from 1650 A to 6500 Al and the signal was detected by a Marconi TF1041C high-impedance valve voltmeter. A quartz beaker and supporting quartz plate were used instead of glass to avoid absorption of the ultra-violet light. 21

TRANSDUCER

Figure 11 shells the light tight brass housing containing .the transducer, water-cooled sample COOLING and photomultiplier tube. 44 F WATER Figure 12 is a block diagram .111111101. of the complete apparatus. QUARTZ PLATE PHOTO

PLIED

10 cm ,N=M•1111.1m•

Fig.11. Housing

GENERATOR TRANSDUCER C R 0

VALVE

VOLTISTER

VALVE

VOLTIETER

E H T

Fig. 1 2. Apparatus

4 8 co c t cz 13 A

AAA4VAA vi-ekelew4,\ANN—

R I_ (23 RD RI, R,1 P13

-apoov — 0

E. H.T.

R, Rc RI

V/V

Fig. -13. Dynode chain of Phot °multiplier tube..

Pig.14. Photograph of apparatus for studying viscous liquids

1. Generator 2. Housing 3. BHT unit 4. Valve voltmeter 23

Pigure 13 gives details of the dynode chain of the photomultiplier tube. The manufacturers specify that 0-D1 shall be 200 volts maximum and that there shall be a uniform inter-stage potential thereafter. Accordingly with 2000 volts across the dynode chain, RI was made 1 01Mc2 and R2 to R14 were made 1110. The E.H.T. unit used was an Isotope Developments Limited Type 532D continuously variable in three ranges from 300 to 3000 volts. This proved a highly stable instrument. Figure 14. is a photograph of the complete apparatus. 2.3 Calibration Measurements 2.3.1. Acoustic Power Output

The acoustic power output of the transducer was measured thermally by noting the rise in temperature of a given volume of liquid in a 250 ml.lagged quartz beaker in which the horn of the transducer is partially immersed. Three runs under different conditions were made as below: (a) Cavitated 100 ml of Water for 10 minutes Mass of quartz beaker = 57.5 gm. Specific heat of quartz = 0.18 (Hanovia lamp catalogue). Initial temperature of water = 20.0°C. Final temperature of water = 43-0°C. Temperature rise = 23.0 dee. Heat developed = (100 57'5 x 0.18)23 = 2600 cal. Energy developed = 2600 x 4.18 joules = 10870 joules 10870 Wattage 600 _ 18.1 watts 21

(b) Cavitated 200 ml of Water for 10 minutes Initial temperature of water = 21.0°C. Final temperature of water = 33'6°C. Temperature rise 12.6 degC. Heat developed (200 + 57.5 x 0.18)12.6 2684 cal. Energy developed 2684. x 4.'18 joules = 11200 = 11200 Wattage --gbr = 122,..2vatta

(c) Cavitated 100 ml of Glycerine for 10 minutes Initial temperature of glycerine = 21.5C. Final temperature of glycerine = 57'0°C. Temperature rise = 35.5 degC. Average specific heat of glycerine over this range = 0.586. (Handbook of Chemistry and Physics. Chemical Rubber Publishing Co.) Heat developed = (100 x 0.586 + 57.5 x 0.18)35.5 = 2445 cal. Energy developed = 2445 x 4.18 joules = 10200 0200 Wattage = 1—or = 17.0 watts We can consider the average power output as 18 watts. Power Intensity Diameter of stub = = 0.375" = 0.95 cm. Area of stub = 0.705 mil- Power Intensity = 0.705 = 25.27 25 watts cm

(d) The transducer had a piezo-electric crystal mounted on it to provide feedback control of the generator. This control was not found to be necessary and instead this crystal was connected to a valve voltmeter and used to monitor the power output of the transducer. The power output was varied by off-tuning the generator. At a frequency of 21.5 KHz, the power output was measured thermally at four different values of voltage developed across the piezo-electric crystal. In each case 100 cc of water was cavitated in a lagged quartz beaker for 10 minutes. 25

ACOLtSrfC ocoer OtAqt-3" Walfts

12 -

5. 6 '7 Ct 9 s/-a/ Vohs

Fig.].5. Acoustic Power Output against Crystal Voltage. 26

Temp Energy Voltage developed Initial Final° Wattage. crystal. Rise developed. across Temp.°C. Temp. C. degC. joules. watts.

0.9 19.5 20.5 1.0 460 0.77 1.1 20.0 22.6 2.6 1197 2.0 2.7 18.2 30.8 12.6 5810 9.7 6.3 19.5 44.0 24'5 11290 18.8

Fig.15 is a plot of acoustic power output against crystal volts. It was decided to carry out all subsequent work at a voltage indicated by the crysal of 2.7 volts corresponding to 9.7 watts, say 10 watts. 2.3.2. Sound Pressure Amplitude

Let P = sound pressure amplitude and Y = sound displacement amplitude then WY = U where U = sound velocity amplitude and w = 27rf where f = frequency. P = UZ, where Z is the radiation impedance of a circular piston operating in a liquid. This problem is dealt with in "Sonics" by Heuter and Bolt (Wiley) p.55; where it is shown that Z = 417777 where R and X are the resistive and reactive components of the impedance. At a frequency of 21.5KHz, the sound wavelength A in water = 1.4 x 103 = 0.065 m. 2°15 x 104 Hence the wave number k = -x- = 72-675 . = 9645 m".

Effective radius of transducer stub a = 0.4 cm = 0.004 m (since end of end surface is not scored). = 0.386. From Fig.3.1. in Heuter & Bolt, = 0.07 R= 0.07 x 10 x 1.4 x10 kg s m Po 3 3 = 0.98 x 105 -2 X = 0.37 X= 0.37 x105 x x 105 = 5.24x 105kg s P0 IS PM Sig.4..) 27 V/v VoL.T.5

120 too PM- - - - _ _ VP/ votss

i Li 014 V-1-'0:7- ct. I-4o, rani t.v."; h.

10 BO 40

I00 ZOO Soo 400 SOO c.00 700 FILoi art., latif t.oxi rs •

PM .S;ci.at v/v VOLTS

200

4 !Go

• its 100 000 CtAsti • 20 o0o 4c)000 69000 8430o0 , Ct ro

F,ig.16. Calibration of Photomultiplier tube. PM Sicl,c.-k 28 V/v vot-Ts.

I a go o so voLT--;

PI,JC)cttitoAC

40 gZ+ Ito )001/ IV 40o 800 1por) !goo ADoo ;4•00 x to pho(- c pc..h,e_a-„,k.,

100 600 Z.0c, 000 3rso 000 40(:),0D° x-10

Fig. 17. Calibration of Photomultiplier tube; 29

Impedance Z = IPETTF =19.82 + 51.82 x 104 = 496 + 2680 x104 =4277 x104 = 5.26 x105 kg s 11.1 Now P = 0YZ. Using a graticule microscope, the displacement amplitude at 2.7 crystal volts is Y = 9 x 10-6 m. and hence P = 6.4. x105 newtons m-2 or 6.4. atmospheres. 2.3.3. Sensitivity of Photomultiplier Tube From the manufacturer's catalogue, the overall sensitivity of all stages of EMI tube 6255B = -1-- lumen per Ampere 5000 - 5000 x11 x10.b lumen per volt = 1:8 x10-11 lumen volt-1, since impedance of valve voltmeter used = 11 Megohms. This refers to luminous flux received at the photocathode (visible light) which has an area of 15.4. cm2. Hence overall sensitivity of photomultiplier tube = 1'8 x 10'14I 154+ lumens om 2volt . Since i lumen cm 2 = 1 phot ...12 Overall sensitivity of photomultiplier tube = 1.2 x 10 phot volt . Over the wide range of luminous flux measured the sensitivity of the photomultiplier tube was found to be non-linear. Hence the photomultiplier tube was calibrated for non-linearity with a torch bulb using constant current at different distances. To cover the wide range a log 3 neutral density filter was used. The results of this calibration are shown in Fig.16, using arbitary units of light flux. The overall sensitivity of the photomultiplier tube previously calculated will apply for small values of photomultiplier tube signal, say 0 to 100 volts, i.e. 0 to 33 arbitary units of light flux. Hence 1 arbitary unit of light flux corresponds to 3 volts. i.e. 3 x 1.2 x 10-12= 3'6 x 10-12phot. Hence the calibration curve can now be redrawn in terms of luminous intensity at the photocathode, in phots. (Fig.17) 30

1800 S01101001\ eSceAkce Luxint5.0 LAn PiNDIS c4:,.14..tzte . Pkors x 16.

1400

• ZO 40 6o 100 -7c416-zu-1,-;,e (1:),j votowe).

SOnoluminescence of Glycerine-Water Mixtures at 10 watts.

SpKolurnivteSce:Ace. otAA Tv`" 4.11 12oo al. Ph 01.0 COA-k Cie • Pkort 1000 • 3- 6kloroto‘pcv,,e. 1-R alot. go> • E ehe qtticA.

• C9cloke_yav,,01.

600

400

200

AO 40 60 $0 100 % wickbcf VotUrAe) 4 Fig. 19. Sonoluminescence of Liquid-Water Mixtures at 10 watts. 32

3-chloro- Ethylene Glycerine propane Cyclohexanol glycol 1-2 diol CHOH CH2OH CH2OH V 1 1 CH2 CH2 CH2OH Structural Formula CHOH CHOH 1 I CH 1 i 2OH CH2OH CH2 Cl CH2 CH2 CH2 --... Sonoluminescence. Phots -io at Photocathode x 10 . 1750 1250 100 450 Viscosity at 20°C. Cp. 14.90 73 68 . 20 r-- . -- '-'3 Density. g.cm . 1.26 1.32 0.94 1.12 Thermal conduCtivity. -.4 ! 4 cal.cm-is-i deg0-1 . 6-8x10 62x10- -1 - 1 : t Specific heat. cal g s . 0.565 0.42 0.54

Fig.20. Sonoluminescence and various parameters of the pure liquid 33

2.4.. Experiments

A specially distilled supply of glycerine of 99.9% purity was obtained from Unliver. Fresh tap water was used for dilution, as tests showed that this gave the same results as distilled water. Pure glycerine was generally successively diluted with water, the same volume being cavitated each time. In other runs, water was successively diluted with glycerine or a series of mixtures kept in stoppered bottles was used. All gave the same results. The sample was contained in a 250 ml quartz beaker to transmit the ultra- violet content of the emitted light.

The sonoluminescence was found to be time-dependent, relaxation and hysteresis effects being observed. Therefore the procedure was adopted of measuring the signal after 15 sec of continuous cavitation when the signal was reasonably steady. For all samples between 0 and 9C glycerine, the temperature did not rise above 25°C from 19°C initially. For 100 glycerine the rise was from 19°C to 37°C despite a fast flow of cooling water. This is due to the appreciable heat generated through viscosity especially in the immediate neighbourhood of the cavitation bubbles (4); also the thermal conductivity of glycerine is only about half that of water. Using a 250 ml sample of glycerine, it was difficult to keep the cavitated glycerine cool as the outer cylinder of liquid acted as an insulator. Hence for the 15 ml glycerine water mixtures the experiment was conductedo using a beaker and the temperature did not rise about 28 C from 19 C For 3-chloropropane 1-2 diol, cychexanol,ando ethylene glycol, the temperature did not rise above 30°C from 19 C and so a 250 ml sample was cavitated.

2.5. Results

Fig. 18 shaws the sonoluminescence from glycerine-water mixtures(S). The possible correlation of viscosity with sonoluminescence` is also shown in the figure by the curve for glycerine-water mixtures (V)(5). It is to be expected that the heating of the bubbles through viscous energy dissipation will produce a higher temperature for bubbles' formed in glycerine than in water. With glycerine it was noticed that there were many more bubbles than with water and thus the increase in light output could be attributed to this and not to an increase in the brightness of each bubble. Fig.19 shows the sonoluminescenoe from water mixtures of 3-chloropropane 1-2 diol, cyclohexanol and ethylene glycol. The cyclohexanol-water mixtures had a tendency to separate out and car had to be taken to agitate the mixture thoroughly. Fig.20 gives the various properties of the four liquids. No obvious correlation exists between the sonoluminescence and these properties, except perhaps viscosity. 34+

References

1. Jarman, P.D., Proc.Phys.Soc., 73, 628 (1959). 2. Negishi, K., J.Phys. Soc. Japan, 16, 1430 (1961). 3. Finch, R.D., Ultrasonics, 1, 87 (1963). 4. Kuttruff, H., Acustica, 12, 230 (Akustiche Beihefte) (1962). 5. Thorpe, J,F., Dictionary of 4plied Chemistry, .6, 54. (Longmans, Green and Co., London, 1943). 35

Relative intensity of sonoluminescence

Gas A B C D

Xenon 540 6700 Krypton i80 2000

Argon. 54. 95 290 Nitrogen 4.5 20 35 Oxygen 1 35 35 35 35 Air 20 77 Neon 18

Helium 1

A Prudhomme and Guilmart C Gunther et al. B Srinivasan and Holroyd D Parke and Taylor

Fig.21. Effect of dissolved gas on the intensity of sonoluminescence from water 36

0 RING GAS INLET TUBE

VACUUM CONNECTION

a C

;: N

0 RING 0 RING. 1 I COOLING WATER

Fig. 22. Detail of sample holder. 37

Chapter 3 Sonoluminescence from Water containing Dissolved Gases

3.1. Introduction

Harvey (1) made the first qualitative observations of the effect of dissolved gas on the sonoluminescence from water. He found that the phenomenon appeared with air, oxygen, neon, weakly with nitrogen, but did not show with hydrogen or carbon dioxide. Srinivasan and Holroyd (2), Parke and Taylor (3), Gunther et al (ii.) and Prudhomme and Guilmart (5) measured the relative intensities using photomultiplier tubes. Fig. 21 is a table given by Finch (6) of their results with oxygen as a standard. Prudhomme and Guilmart actually measured their intensitiesig the ultra-violet using a photocell operating in the range 1900 A to 2800 A with a sharp maximum sensitivity at 2300 The experiment here was designed to provide a comprehensive study of seventeen different gases dissolved in water, including all the rare gases and the first four saprated hydrocarbons, using a photomultiplier sensitive from 1650 A to 6500 A. 3 . 2. Design of Experimental Arrangement

The apparatus used in the study of the sonoluminescence from viscous liquids was modified in three ways:- (a) The ring holding the quartz beaker was replaced by a thick brass ring A, brazed on to the inside of the brass housing and a i" thick brass ring B, which could be bolted down on to the ring A and sealed by an 0-ring. The section of the brass housing between the quartz beaker Q and the transducer could then be made vacuum tight. (b) A ;5 " brass tube C, was brazed into the side of the brass housing„ above the quartz beaker to permit a vacuum connection. ( A. g stainless steel tube D, was fixed in the brass housing with araldite and led down to the bottom of the quartz beaker to permit the gas under test to be bubbled through the water. Fig. 22 shows these amendments to the housing which otherwise is exactly the same as shown previously in Fig.11. 38

Transducer chamber

. Ti Vacuum X pump Vacuum chamber T2

Photo— multiplier tube Gas mercury chamber Cylinder manometer

Fig. 23. Arrangement for engassing water with gas .39

Transducer chamber

Vacuum chamber

Photo— multiplier tube chamber

Fig. 24. Arrangement for admitting gases at atmospheric pressure. 4-0

3.3. Calibration Measurements

The calibration for acoustic power output, sound pressure amplitude, and for the sensitivity of the photomultiplier tube determined in section 2.3. also apply for this study of dissolved gases in water. 3.4.. Experiments

The quartz beaker was filled with tap water up to a point 25 mm. above the base of the beaker and placed in the apparatus. It was first necessary to remove the dissolved air from the sample. This was done by evacuating the apparatus to a pressure of 3. cm. of mercury by a vacuum pump for one minute. On cavitating, no sonoluminescence could be detected showing that all the dissolved air had been expelled, The gas under test was then bubbled through the water for five minutes. The water was then cavitated and the sonoluminescence signal recorded after 15 seconds. The gas was then bubbled through the water for another five minutes and the sonoluminescence again noted. If these two readings were the same we assumed that the water was saturated with gas.

Fig. 23 is a schematic diagram showing the piping and valves to the vacuum pump and cylinder of compressed gas. The sequence of operations was as follows:-

1. Close T3 and T/4.° Open T1 and T2. Evacuate. 2. Close Tl. Open T3. Switch off vacuum pump. 3. Open T4. slightly. (T4. is a needle valve). 4. Open Tl. Close T2. Pass gas for 5 minutes.

In order to check whether in fact gas was being bubbled through the water a microphone was fixed to the outside of the housing H, and connected to a loudspeaker via an amplifier. This proved to be a very good way of monitoring the gas flow through the water.

In the case of xenon and krypton, glass bulbs of gas at atmospheric pressure had to be used and the following procedure was then employed: The glass bulb 1/1 containing a rare gas is welded on to a smaller bulb V2 with two taps T1 and T2 in series and a side tube containing a steel ball B, and this is connected into the system as shown in Fig.21i-. 41

Gas Luminous Intensity at -10 Photocathode. Phots x 10 .

Air 2.40 Nitrogen 1.22 Oxygen 2.40

Helium 1.16 Neon 3.20 Argon 30 Krypton 50 Xenon 125

Methane 0.80 Ethane 0.85 Propane 1.00 n-Butane 1.00

Carbon Monoxide 2.40 Carbon Dioxide 0.86 Nitrous Oxide 2.20 Freon 3.60 Hydrogen. 0.86

Fig. 25. Sonoluminescenoe from different gases dissolved in degassed water. 1 2

Luminous Intensity Sonoluminesoence Total Radiation Gas at Photooathode.Young. Prudhomme & GuiImart. Energy. Muller. Phots x 10 1c. Relative results. Ws.

Helium 1.16 1 Neon 3.20 18 0.002 Argon 30 54• 0.014 Krypton 50 180 Xenon 125 54.0 1.3

Fig. 26. Sonolumineseence from the rare gases dissolved in degassed water. 43

Initially the vacuum pump is connected directly to the two glass bulbs and switched on with T1 and T2 open. t;After five minutes Ti is then closed and the steel ball lifted by a magnet to smash the glass seal S. T2 is closed and we now have a volume of gas V2 available for experiment. With 19./.1 T5 and T6 open the apparatus is evacuated. T4., T5 and T6 are then closed and air allowed to seep into the housing until the pressure was about 30 cm. of mercury. T1 was opened to fill the space between it and taps T5 and T6 with gas. T6 was then opened slightly and the rare gas bubbled through the water. Three more gas fillings of V2 were bubbled through the water. T6 was closed and T4. was opened to ensure thepressure above the sample was atmospheric (T3 already having been opened) and the water was cavitated for 15 seconds and the sonoluminescence recorded. Another gas filling of V2 was made to check if the signal was the same. If not, another gas filling of V 2 was passed. Usually the signal was constant to 3% after six bulbs of gas. 3.5. Results All the samples were cavitated at an acoustic power of 9.7 watts corresponding to a sound pressure amplitude of 6..4 atmospheres in water. For each gas, the result given is the average of between five and ten determinations, these usually agreeing to about 4%. In some cases the reading had to be discarded as it was found on removing the beaker that some of the water had been displaced by the pressure changes. Also, occasionally a bubble of gas would become trapped under the stub of the velocity transformer and would cause a very unsteady sonoluminescence signal on the valve voltmeter. The true sonoluminescence signal was remarkably. steady.

Fig. 25 is a table of results of seventeen different gases dissolved in degassed water. These can be divided into four classes: air and its constituents, the rare gases, the first four saturated by hydrocarbons, and miscellaneous gases. In the last class, the very low values for carbon dioxide and hydrogen are of interest since Gritting and Sette (7) found that the sonoluminescence was non-existent for these gases.

Fig. 26 compares the results for the rare gases dissolved in water with those obtained by Prudhommenand Guilm§rt (5) using a photocell operating in the range 1900 A. to 2800 4; and obttined by Muller (8) in which the light in the range 4000 A to 6000 A was measured from glass bulbs of gas imploded in water.

If the sonolminescence is basically due to an adiabatic compression of the gas during the rapid collapse of the cavitation bubbles, then any loss of energy of the gas molecules due to thermal conduction will modify this simple theory and cause lower final Luminous Iiitensity at Sonoluminescence. Thermal Conductivity. Photocathode. Young. Prudhomme & Guilmart. 1 — Gas Phots Relative results cal cm s de o 1650 it. — 6500 A 1900 A — 2800 A ---

4 Helium 1.16 x 10w 1 3.41 x 10 Neon 3•20 18 1.11 Argon 30 54. 0.39 Krypton 50 180 0.208 Xenon 125 54.0 0.123

Fig. 27. Sonoluminescence from the rare gases dissolved in degassed water and thermal conductivity. 15

S011olUmiykesceiAce , .- kuhAthovs.: Thic%NcALJ P V%oVocc,k not 140 ' X 10

1 ao

loo

a 3 xio

Thermal CoiNctuctwtty. ca. ,!,TA s ciesc

Fig.28. Sonoluminesoenee against thermal conductivity for the rare gases. 16

Luminous Intensity Thermal Gas at Photocathode. ConductiVity 74 -1 -1 Phots cal cm a dee ...

Methane 0.80 x 101° 0.800 x10-4 Ethane * 0.85 0.495 Propane 1.00 0.4.11 n-Butane 1.00 0.368

Pig, 29. Sonoluminescence from saturated hydrocarbons dissolved in degassed water and thermal conductivity. 17

Soholuminescekce

_Lurw,AockS -i ii ~lljil~t JJ at Kot-occti,,A,,. I.0 -to P 1.1 rs X10

o-e Methane

0.6

0.4

O- 2

I 0.1 o• a 0.•3 0.4 0.5 0.6 0.8 _ 4 Thermoi Con,Avc-Yi 1Cy. r •S Jej es -00

Fig. 30. Sonoluminescence against thermal conductivity for the saturated hydrocarbons. Luminous Intensity at Total Radiation Energy Gas Photocathode. Young. Muller. Phots Ws

- 10 Neon in water 3.2 x 10 0.002 Argon in water 30 0.014. Neon in paraffin 4.4 30 Argon in paraffin 600 50

Fig. 31. Sonoluminesoence from neon and argon dissolved in water and in paraffin. 4.9 temperatures. Thus the luminous intensity will be dependent on the thermal conductivity of the gas if there is time for heat conduction to occur. Hickling (9) shows that there is a clear inverse relation between the thermal conductivities and the luminous intensities obtaiRed by Prughomme and Guilmart in the ultra-violet region of 1900 A to 2800 A for the rare gases. Fig. 27 shows their results together with ple luminoRs intensities obtained here in the wider range of 1650 A to 6500 A, and values of thermal conductivity (10). Fig. 28 is a graph of the luminous intensity against thermal conductivity of the gas, the acoustic power in all cases being 9.7 watts. The smooth curve shows a clear inverse correlation. The first four saturated hydrocarbons are_ another group of gases whose thermal conductivities vary in a fairly uniform manner. Fig. 29 shows the values of luminous intensity and thermal conductivity (11) for these gases and Fig. 30 is a plot of the results. An inverse correlation is again seen. There is some doubt as to the effect of the solubility of the gas on the sonoluminesoence. Hickling (9) concludes that, provided there is sufficient gas present, it is not certain that the luminous intensity should be strongly dependent on the solubility. A few runs were made with argon and neon dissolved in paraffin to compare with results with MUller's results (8) on glass bulbs imploded in paraffin. He obtained much higher intensities with paraffin and he attributed this to an excitation mechanism. Fig. 31 gives these results showing that argon dissolved in paraffin gives a particularly high result. Mailer obtained a spectrogram (Fig.6) of the light from the xenon-filled sphere in paraffin. This showed the strong Swan band of C2 radicals as well as (weaker) the CH bands. The xenon lines were not seen. For the excitation and emission of the C band Muller put forward the following possible processes:- 1. The breakdown of the paraffin molecules forms an excited C 2 molecule which reverts to the lower state with the emission. 2. Carbon atoms resulting from the breakdown, recombine to form C2 molecules.

3. Higher energy states arise with the Ca molecules because of the strong heating of the gases which then emit light on return to the lower energy states. 50

References

1. Harvey, E.N. J.Amer. Chem. Soc. , 61, 2392 (1939) . 2. Srinivasan, D. and Holroyd, L.V., J.App. Phys., 32, 446 (1961). 3. Parke A.V.M. and Taylor, D., J.Chem.Soc., 4., )111 )12 (1956). Gunther P., et al., Zeit Fur Eleoktrochem, 61, 188 (1957). 5. Prudhomme, R..00, and Guilmart T., J.Chem.Phys., 54•, 336 (1957)• 6. Finch, R.D., Ultrasonics, 1. 87, (1963). 7• Griffing, V and. Sette, D., J.Chem.Phys., 23, 503 (1955). 8. Muller, H.M. Acustica, 16, 22 (1956/66). 9. Hickling, R. 0 J.Acoust.Soc.Am. 35, 967 (1963). 10. Kannaluick, W.G. and Carman, E.H., ProcoPhys.Soc. B,65,701 (1952). 11. Handbook of Chemistry & Physics (Chemical Rubber Company, Cleveland, Ohio, 1965) . 4.1 st ed. 51

Chapter 4.. Sonolumir' iescence from Liquid Metals

4.1. Introduction

Jarman (1) investigated the sonoluminescence from 15 pure liquids of widely different properties. He found that the light intensity increased with increasing values of a2/pv where a is the surface tension and pv is the vapour pressure of the liquid. This relationship drew the attention of Kuttruff (2) to the case of mercury for which the value of a2/Pv is 75,000 times greater than that of water.

There is another reason for studying mercury. If sonoluminescence occurs, as suggested by Frenkel (3), through the existence of electric charges at the surface of a cavity and giving rise to a discharge on its collapse, then it should appear very weak in mercury on account of its high electrical conductivity. If on the other hand, sonoluminescence is due to the adiabatic heating of the gases inside the cavitation bubble consequent upon the rapid compression during the bubble implosion then appreciable luminescence in mercury is to be expected.

Kuttruff overcame the difficulty of the opacity of mercury by producing cavitation adjacent to a transparent surface. He used a glass velocity transformer which was driven at one end by a tubular barium titanate transducer working at 25 KHz and whose other end dipped into the mercury. The mercury cavitated at the end of the glass rod and the light travelled up the glass rod and through the hollow transducer to the photomultiplier tube. He found that the intensity of the luminescence from mercury was much greater than that from ethylene glycol under the same excitation conditions. Kuttruff found that the spectrum of this emitted light was continuous and was thus similar to the emission from cavitation in water. As a further check he allowed a small pool of mercury to roll along the glass surface of an evacuated tube. He noted that a faint electrical discharge took place at the moving interface between the mercury and the glass, but in this case the spectrum was a typical line spectrum of mercury. The above considerations would seem to rule out Frenkel's theory that the luminescence arises from discharges between surface electric charges.

4.2. Design of Experimental Arrangement

The basic design followed Kuttruff's arrangement, and an operating frequency of 30 KHz was chosen on account of availability of transducers and nearness to the author's previous operating frequency of 20 KHz, while at the same time it was near to that employed by Kuttruff. The length of. a 20 KHz PZT tubular transducer would be 8 cm. and this length with an . 1.9 cm,1 1 1.9 cm 1.9 cm 1 0.6 cm

Pyrex Pyrex Stainle ti Steel 0a

I I a co co E

.4.

0 Pyrex--r k 11.0 1.0 cm cm (a) (b)

Fig.32. VELOCITY TRANSFORMERS. 53 outside diameter of 1,9 cm. presents insurmountable manufacturing difficulties. Accordingly a 30 KHz PZT4. tubular transducer was obtained from Brush Clevite Co.Ltd. with the following dimensions: Outside diameter 1.5 cm. Inside diameter 1•2 cm. Length 5.2 cm. This had a fundamental longitudinal frequency of 30 KHz since JE(1 - f - 121 where E = Young9 s modulus perpendicular to the polarising axis, k = km= Coupling coefficient for long bars with length perpendicular to the polarising axis, and f = 30 KHz.

Brush Handbook ( E = 8.15 x 10" dyn cm-20 for PZT4, p = 7.6 gm cm-3. k3,= 0.300 Using the above relation 1= 5.2 cm.

The glass double quarter-wave velocity transformer must have a longitudinal fundamental frequency (f0) of 30 KHz.

Hence its half-length = Trf 1= /N. cm. since E(glass)= 6.1 x io" • -2 dyn om . Various shapes of velocity transformer were tried and bonded to the transducer with araldite (Fig. 32). Design (a) of solid glass proved weak at the mid-point which is a pressure anti-node, and two such transformers snapped at the middle when energised. Design (b) was an attempt to overcome this weakness by making the velocity transformer of stainless steel, having an anial hole and a trasparent pyrex disc cemented on to the narrow end. In this case the half-length = 4.2 cm. assuming E = 20.0 x 1099dyn cm-2 and p= 7.75 gm om-3.(4) This design however suffered from the weakness of the bond between the stainless steel and the pyrex disc which kept breaking under stress. As a result design (c) was then used which consisted of a straight tapered pyrex rod and it proved very successful and was used in all subsequent experiments. The only bond is between the pyrex rod and the transducer and this point is a pressure node.

511-

VALVE 1 OSCILLATOR ;AMPLIFIER 'VOLTMETER.

- TRANSDUCER

VELOCITY TRANSFORMER

Fig. 33 EXCITATION OF TRANSDUCER 55

STAINLESS STEEL

THERMOCOUPLE

TWIN BORE CAPILLARY TUBING

J L

Fig. 34 FURNACE POT

-I „ I

56 trA

PHOTOMULTIPLIER

-- TRANSDUCER

VELOCITY TRANSFORMER

We FURNACE C C LIQUID METAL

THERMOCOUPLE

Fig.35 LIQUID METAL APPARATUS.

57 58

Fig. 36.

Photograph of transducer, velocity transformer, and housing for photomultiplier tube for studying' liquid metals.

1. Furnace 3. Transducer 1..1 Velocity transformer 5. Housing for photomultiplier tube

V-% 6o

Fig. 37. Photograph of complete apparatus for studying liquid metals.

1. Furnace 2. Variac control for furnace 3. Transducer 4.. Velocity transformer 5. Housing for photomultiplier tube 6. Amplifier 7. Valve voltmeter monitoring acoustic input 8. Valve voltmeter registering light output 9. Oscilloscope monitoring acoustic input 10. E.H.T. unit for photomultiplier tube 11. Ice junction of thermocouple 12. Scalamp galvanometer for registering thermo -electric current 13. Light-tight shield

The edge of the oscillator can just be seen to the left of the oscilloscope. The glass apparatus in the background is for producing degassed water. 61

The insulation at the upper end of the transducer was carefully scraped off and two fine wires carefully soldered on to the silver electrodes. The transducer was energised by an Advance 81A oscillator and Solartron AWS53 power amplifier giving an overall gain of 15. A Heathkit Model V.74/UK valve voltmeter was used to monitor the voltage across the transducer (Fig.33).

A furnace pot (Fig.34) was designed so that the liquid metal under test could be heated and the sonoluminescence measured at temperatures up to 300 C. This pot was made of stainless steel and held 4.5 ml of liquid metal this being the available volume of gallium. The sides of the pot extended downwards to provide a clamping surface below the upper surface of the pot, around which was wound the heater coil WW. The base of the furnace was fitted with a screw plug made of pyrophyllite and carrying a piece of twin bore capillary tubing carrying the thermocouple wires. These were T1 and T2 Alloy of British Driver- Harris Co. Ltd., size .0076in and were fused together just beyond the end of the capillary tubing, to form a hot junction which was protected by a glass cap.

Anickel/chrome heating element insulated with braided glass fibre and made by Electrothermal Engineering Ltd., was coiled round the furnace. This heater with a capacity of 3W covered the range adequately. The fine adjustment of a Variac transformer permitted the furnace temperature to be kept steady to within 1 degC.

Fig. 35 is a block diagram of the arrangement. Fig.36 is a photograph of the arrangement with the furnace (1) and light-tight shield (13) removed.

Fig. 37 is a photograph of the complete apparatus. The same photomultiplier tube was used as previously described in Chapter 2 and the signal was detected by another Heathkit Model V.74/UK valve voltmeter.

4.3. Calibration Measurements

Acoustic Power Output

The acoustic power output of the PZT4. 30 KHz transducer was measured thermally by noting the rise in temperature of 9 cc. of water in a lagged pyrex beaker in which the end of the velocity transformer was immersed. Three five-minute runs were made with different voltages across the transducer. Thermal capacity of beaker = 2.14 cal degC1. 62

WATTAGE 4. DEVELOPED

120 1.0

VOLTAGE ACROSS TRANSDUCER . Fig• 38. Acoustic Power Output against Transducer Voltage• 63

Voltage Energy across Temperature developed Wattage Transducer Rise de&. joules watts

50 12.8 595 2.0 100 21.2 985 3.3 150 24.0 1110 3.7

Fig. 38 is a plot of acoustic power output against voltage-across the transducer. Most of the experiments were carried out at a voltage across the transducer of 120 V thus corresponding to an acoustic power output of 3.6 W. 4.3.2. Sound Pressure Amplitude Let P = sound pressure amplitude, and Y = displacement amplitude, then wY = U where U = velocity amplitude and w = 2lTf where f = frequency. The case here is that of a moving piston driving a liquid and Z (=P/U) will be the radiation impedance of the circular piston in water. From (5), Z = dlR2 + X2 where R and X are the resistive and reactive components of the impedance. At a frequency of 33 KHz, the acoustic wavelength X in water = 0 042 m, whence -1 k = 2v = 761472 = 149m .

Effective radius of transducer stub a = 0.45 cm. = 0.0045 m. (since edge of end surface is not scored), so ka = 0.67.

From Fig.3.1. in (5), = 0.22 R = 0.22 x 103 x x 103 = 310,000 kg 71.213." POt„ X = 0.6 X = 0.6 x 103 x 1.4 x 103 = 840,000 kg m-28-I Poo Impedance Z = R2 + X2 = 3-12 + 8.4.2 x 105 9.6 + 70.7 x 105 80.3 x 105 Z = 9 x 105 kg . 64.

Using a graticule microscope, the displacement amplitude at 150 volts across the transducer is Y = 0.0035 cm. = 3.5 x 10 6m. Now P = wYZ = 6.5 x 105 newtons 111".2 = 6.5 atmospheres. 4.3.3. Sensitivity of Photomultiplier Tube The calibration for the sensitivity of the photomultiplier tube determined in section 2.3.3 also applies for this study of liquid metals. 4.3.4. Thermocouple The thermocouple was directly connected across a high resistance Pye Scalamp galvanometer and calibrated with the junctions in melting ire and looping water and the temperature could be measured to 1 C at 300 C.

Summary of Liquid Metal Experiments

The object of the experiment was first to measure the sonoluminescence from mercury and then to cavitate other liquid metals to see if they would give any sonoluminescence8 The other liquid metals chosen, having melting points below 300 C, were gallium, indium, tin and bismuth. The variation of the sonoluminescence with temperature of these lignin metals was investigated from the melting point to 300°C. In the case of bismuth which is strongly diamagnetic an attempt was made to see if the sonoluminescence signal and the onset of audible cavitation was affected by a magnetic field. The volume of liquid metal placed in the furnace was 4.5 ml. In the case of those liquid metals which are solid at room temperature, the calculated mass was weighed out and then placed in the furnace. 4.5. Results 4.5.1. Correlation of Water and Mercury Experiments

In order to provide a quantitative link between the results for viscous liquid-water mixtures and for water containing dissolved gases on the one hand, and the results for liquid metals on the other hand, equal volumes of water and mercury were cavitated in turn, in the furnace pot, under the same conditions of: Frequency 336000 Hz Temperature 21 C Volts across Transducer 120 V Acoustic Power 3.6 W The sonoluminescence measured by the photomultiplier tube was Fresh Tap Water 0.5 x10-la phots New Triple Distilled Mercury 260 x 10-12phots Thus under these conditions mercury gave a sonoluminescence about five hundred times than that from water. 65

1..5.2. Mercury Tests were first made with mercury at room tsmperature6 During the following runs the temperature rose from 19-5 C to 21.0 C. The valve voltmeter connected to the photomultiplier tube gave the values below, in volts, for various exciting voltages across the transducer. The dark current was equivalent to 0•35 V.

Exciting. Voltage across Photomultiplier Voltage and Transducer Number of Run 1 1 2 3 4 5 1- 6 30 0 0 o - o 0 0 60 0 0 38 30 60 - 70 1 90 0 0 50 50 80 80 120 0 0 63 70 85 90 150 0 0 70 80 90 105 Mummer In order to obtain more information about the threshold voltage extra runs were done with values of 40V and 50V across the transducer: ....----;—...... ftru— Exciting Voltage across Photomultiplier Voltage and Transducer Number of Run 7 8 9 - 10

30 0 0 0 0 40 0 0 0 0 30 0 0 ' =80 0 60 0 0 100 0 90 100 100 110 110 120 110 110 115 116 150 - - 110 110 115 110 Thus mercury needs considerable initial cavitation to get it into a condition giving the maximum reproducible sonoluminescance for a given input acoustic power. Hence the mercury was allowed to cool down to 19.50C and then ten more runs done when the temperature again rose to 21•00C: 66

Exciting Photomultiplier Voltage and Number of Run Voltage taorOse 11 12 13 14 15 ' 16 . 17 18 19 20 Transducer , A l / .°,,,

30. , ' '. . 0 0 0 3o 3o 42 50 64 66 4o 0 0 0 0 55 5o 72 80 95 100 5o 0 0 0 0 7o 90 100 106 102 112 6o 0 0 0 0 90 100 108 106 106 118 90 .0 0 0 0 1114. 110 114 118 118 119 120 0 0 0 0 114. 106 115 118 11 8 119 150 0 0 0 100 114 104 115 118 118 119

This table of values again emphasises that mercury needs considerable initial cavitation to get it into a condition giving the maximum reproducible sonoluminescence for a given output acoustic power. Runs were then done at higher temperatures, and for each value of temperature, the runs were repeated until the values were reproducible:

Temperature: 49.5°G rising to 50.0°C.

Exciting Voltage across Photomultiplier Voltage and Transducer Number of Run 1 2 3 - 30 60 4.5 60 4.0 100 100 110 50 112 110 116 60 116 114. 118 90 116 112 118 120 116 111 116 150 116 110 114. 67

Temperature: 101 °C falling to 100°C.

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 4•

3o 40 40 4.3 44 40 70 94- 105 100 5o 88 103 112 112 60 90 106 113 114 90 94. 106 113 114- 120 94. 105 108 112 15o 95 104 108 111

Temperature: 151°C.

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 10 12 40 40 36 50 66 52 6o 7o 62 90 80 80 120 82 86 150 83 84. SonolurAivte„:ce.r, ,ce nrtOr-orvo.4ti VOitcle

Yoh

100

-eDzso 0c 40

0 0 0 40 0 8o 100 I20 1¢p Vo fts Ex cit".3 Voivae across ItaAASJLtce r

Fig. 39. Sonoluminescence from Mercury against Voltage across Transducer for various Temperatures. 69

Sorvolurninesceh.ce Voltaj c 120 Volirs E voltage across Ti ctw atize r MO Volts

50 1010 IS0 100 4Go 0C. Teretetaftme

Fig.40. Sonoluminescence from Mercury at 120 Volts across Transducer against Temperature. 70

Temperature: 200°C.

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3

30 6 8 7 40 22 20 20 50 32 30 30 6o 42 40 40 90 62 62 66 120 76 70 74. 150 76 7o 72

Temperature: 250°C.

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3

30 10 10 Removed stopper 8 4.0 20 20 from light- 20 50 30 31 tight shield 30 60 36 40 to release any 40 90 52 54 excess pressure 56 120 62 62 due to greater 64- 150 64. 64 mercury vapour 64 pressure.Replaced stopper.

These results are shown graphically in Figs. 39 and 40. The fact that the mercury needed considerable initial cavitation to get into a condition giving the maximum reproducible sonoluminescence could be explained by a layer of air being trapped below the glass velocity transformer and preventing coupling with the mercury until it was agitatedo away. To test whether this was so, the apparatus was tilted by 10 to the vertical and the experiment repeated. 71

Temperature: 194,0°C. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 4 5 3o 0 56 66 20 10 40 30 94 90 80 70 50 97 106 106 100 90 60 108 112 110 108 100 90 116 116 116 113 110 120 118 118 117 115 112

Temperature: 50.0°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 ii- 30 10 0 0 0 40 20 0 0 10 50 52 75 98 108 60 78 100 110 114 90 100 110 116 118 120 108 114 116 118 72

Temperature: 101°C. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 0 0 40 50 50 50 100 100 6o 110 110 90 113 114. 120 113 113

Temperature: 151°C .

Exciting Voltage across hotvultiplier Voltage and Number of Run Transducer 1 2

30 0 0 4.0 30 34. 50 70 66 6o 80 74 90 84. 86 120 80 86

Temperature: 200°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 . 0 4 40 12 12 50 22 20 60 30 25 90 116 42 120 50 50 73

4 Sonclrvkit.ecewce,

FhOtOrAiAlhilel \toPet3e lao 509C V011-5 ooC. (1°C..

100

1509C

$30

AO 40 60 go too lad VDUs

Exciring vJ'root aetocf.; rrahscLACer

Fig. 4.1. Sonoluminescence from mercury against exciting voltage across transducer for various temperatures, with tilted transducer. 74-

Temperature: 250°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 6 5 40 12 14. 50 20 20 60 24 26 . 90 40 42 120 46 52 Threshold for Audible Cavitation 20 24. Threshold for Sonoluminescence Signal of 10 Volts 36 36

Temperature: 300°C. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 10 10 40 18 19 50 24- 60 3o 28 90 40 36 120 4-7 42 Threshold for Audible Cavitation 24. 22 Threshold for Sonoluminescence Signal of 10 Volts 30 30

Fig. 41 corresponds to Fig. 39, i.e. sonoluminescence against exciting Voltage across the transducer for various temperatures. It will be seen that the curves for 19°C, 50°C and 100°C are in the reverse order to the general pattern. This probably due to two opposing factors. As we increase the temperature the sonoluminescence decreases. At the same time, as more

Sono\uh,-,,e5cevx.e. 1 F10\- -orv,v_th[le r VoVrcQ e Exciriv,5 A 4 I o Volts Volv-c ge across 11-cts..-s.oLA..ce.r

io volts

4-0

50 ioo 'so /co aSo 3oc °C: Temerat'vre

Fig. 42. Sonoluminescence from mercury at 120 volts • transducer exciting voltage against temperature, with tilted transducer.

readings are taken, more air is agitated away from the lower face of the transducer producing better coupling with the mercury. The crossing over of the curves for 200 degC. and 250 degC. with the curve for 300 degC. could be connected with the very rapid increase in the saturation vapour pressure of mercury from 18mm. of mercury at 200 degC. and 76 mm. of mercury at 250 degC. to 248 mm. at 300 degC. When the sonoluminescence is plotted against temperature for a fixed voltage of 120 V across the transducer, as in Fig. 42 where every reading is shown, the irregularities in Fig. 44 are seen to be of a small order, and good agreement with the previous corresponding graph in Fig. 40 is seen. Runs were then done at lower temperatures using a freezing mixture of ice and salt. The first set of runs was at room temperature. Then the furnace was surrounded by a polythene bag containing the freezing mixture. This took the temperature down to - degC and a set of runs was done. Other sets of runs were done at + 6.2 degC and then again at room temperature.

Temperature: + 22.00C Exciting Voltage across Photomultiplier Voltage and Number of Run t Transducer 1 2 3 4 5 30 60 110 0 60 1 0 22 60 127 90, 128 120 128 Threshold for Audible Cavitation Threshold for Sonoluminescence Signal of 10 Volts

Temperature: - 4.30C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 .4 30 116 20 20 20 60 124 121 119 119 90 125 123 123 123 120 124. 123 123 123 Threshold for Audible Cavitation 8 8 8 8 Threshold for Sonoluminescence Signal of 10 Volts 8 8 8 8 77

Temperature: 6.200 Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 'I 2 3 4

30 18 30 10 8 6o 120 118 116 113 90 123 122 121 120 120 123 122 121 120 Threshold for Audible Cavitation 30 30 30 30 Threshold for Sonoluminescence 30 30 30 30 Signal of 10 Volts

Temperature: 4. 22.0°G. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 4. 3o 6 24. 14. 20 60 110 115 112 114. 90 120 120 119 119 120 120 120 119 119 Threshold for Audible Cavitation 30 30 30 30 Threshold for Sonoluminescence Signal of 10 Volts 6 6 6 6

Examination of the signal results for 120 V across the transducer for these four sets of runs shows a steady decrease from 129 volts to 119 volts. The mercury had a thick scum on it at the end. This was removed. A long set of runs was then done taking the temperature down as low as possible to the freezing point of mercury and allowing it to rise slowly to room temperature. 78

Temperature: + 23.0°C. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 4- 5 6 30 2 13 14 22 25 20 60 128 128 128 126 125 125 90 128 128 128 126 126 126 . - 120 128 128 128 126 126 126

7 8 9 10 11 12 13 14 15 16

16 15 20 16 20 20 20 20 20 20 121i. 124. 123 123 123 122 122 122 122 122 125 125 124. 124. 124. 124. 124. 124. 124- 124 125 125 124 124. 124 124. 124. 124. 124 124.

After each of these 16 runs the temperature was allowed to fall to +23.0 degC. The scatter of the 30V Transducer Voltage readings was due to the fact that we were on the threshold voltage. Once again there was thick scum on the mercury at the end. This was removed.

Temperature: — 36.0°C. Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 30 0 2 5 60 0 120 120 90 124 123 124. 120 124. 123 124 79

Temperature: — 27.0°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 30 6 2 60 123 126 90 125 126 120 126 126

Temperature: — 17.0°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 30 0 2 60 126 126 90 126 126 120 126 126

Temperature: — 8.0°C Exciting Voltage across Photomultiplier Voltage and Number of Rum Transducer 1 2

30 4- 4 60 124 121. 90 125 125 120 125 125

Temperature: + 2.0°C ti ' Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 30 6 12 60 124 123 90 125 124 120 125 124 400 xlo SoholotyCvA"ef:cttAza 80 Pilots LumiriotAs ivtrehs.it i l'hol-occainocie -ec - 8°C

aot.) -36°C, 4-2°C.1.1k

1°C

LD +10o.0

4 isoC +200:2 100 mamat -Faso * 430 0'G

Cia 90 lac) Volts E,,cihyt3 Vo110.Qe ro S Tra'AS

Fig. 43. Sonoluminescence from mercury against exciting voltage across transducer, for full range of temperatures.

81 SonolutylivNes cet,ce 4ociz to 1,litntrotAs IvArthS11-4 cAV Pholocaltocle, Phors

Soo

2oo

VOO

►

i I 1 0 .1_ t 1 I 1 -50 0 +So +too +160 .1--oo +2So +3ooC , TerYtt)trorure Fig. 44. Sonoluminescence from mercury at 120 volts transducer exciting voltage against full range of temperature. 82

Temperature: 11.0°C

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 30 20 32 60 122 122 90 124 12!♦. 120 121. 121.

Temperature: 21.0°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

30 50 30 60 120 119 90 122 121 120 122 121

The mercury again had a thick scum on it at the end. This was probably due to oxidation caused by the very high local temperatures produced in the bubbles' collapse. All these sonoluminescence signals which were recorded as voltages registered on a valve voltmeter connected across the photomultiplier tube were converted to luminous intensity in phots at the photocathode, and the complete series are plotted in Figs. 43 and 44. Measurements of the threshold exciting voltage across the' transducer, for audible cavitation, and for a sonoluminescence signal of 10 volts across the photomultiplier tube, were also made:

Temperature 20.8°C 49.8°C 100.5°C Number of Run 4. 7 8 9 lo 17 18 19 20 1 2 3 1 2 3 i.i. Threshold for Audible Cavitation 30 90 90 50 90 20 30 20 20 20 20 20 20 25 25 25 83

Temperature 151°C 200°C 250°C Number of Run 1 2 1 2 3 1 2 3 Threshold for 25 25 25 20 18 20 20 20 Audible Cavitation . •

Then repeated with the tilted transducer:

Temperature 19.0°0 50.0°C. 10'..0°C 150°C Number of Run 1 2 3 4. 5 1 2 3 4 1 2 1 2 Threshold for Audible Cavitation 30 4.0 30 40 40 40 4.5 44 40 40 40 36 34 Threshold for Sonoluminescence Signal of 10 Volts 10 20 20 30 4.5 40 40 40 40 36 34.

Temperature 200°C 250°C 300°C Number of Run 1 2 1 2 1 2 Threshold for Audible Cavitation 30 25 20 24. 24.22 Threshold for Sonoluminescence Signal of 10 Volts 36 36 36 36 30 30

A preliminary set of low temperature runs was taken:

Temperature +22.0°C ..4.•3°C 1.6.2°C Number of RUn 1 2 3 4 5 6 1 2 3 4 1 2 3 4 Threshold for Audible Cavitation 20 30 30 30 30 20 8 8 8 8 30 30 30 30 Threshold for Sonoluminescence Signal of 10 Volts 20 20 - 8 - 20 8 8 8 8 30 30 30 30

Temperature +22.0°C Number of Run 1 2 3 4. Threshold for Audible Cavitation 50 30 30 30 Threshold for Sonoluminescence Signal of 10 Volts 30 6 6 6 Tray.sclucer Itreshold of Exaly1 AtA,c1",ble Wir,ge C) error 50. Volts

4o F ce 0

1 /

SO 100 IS6 ZOO Z.S0 300 'C Tem ercjOr4

Ira t-. c.e T/Areaold of 0 error Exettl,As 10 NJ $Cno.OPA'w.eSCe4At-e VOito se.

V6ir

ao 0

o ► 19 so 100 ISO Aoo aSso 3ooe'c Te-rni)er Aire

1 cliFtetmce 6e11.3.en 1 Average 14. 2 ihrestsolds 5 • o o ao 30 .°10 10.

Fig. 45. Thresholds of audible cavitation and sonoluminescence for mercury against temperature. 85

A final long set of low temperature runs was taken:

Temperature -36.0°C -27.0°C -17.0°C -8.0°C +2.0°C +11.0°C +21.0°C Number of Run 1 2 3 12 12 1 i 2 1 2 i 2 r Threshold for Audible Cavitation 30 30 30 30 30 30 30 30 30 30 30 30 30 Threshold for Sonoluminescence Signal of 10 Vblts 30 30 30 10 10 30 30 30 20 10 10 10 6 10

Fig. 43 shows the two threshold curves for onset of audible cavitation and onset of a 10 Volt sonoluminesoence signal against temperature. These two curves have the same general shape and agree to 15% on average.

4.5.3. Gallium (mp 30°C) The initial objective here was to find out whether it was possible to cavitate gallium and produce sonoluminescence. The exciting voltage across the transducer was increased to the threshold of the sonoluminescence signal, and is recorded below. The sonoluminescenoe signal was measured in terms of the voltage developed across the photomultiplier tube as in section 4..5.2 for mercury.

Temperature 39.0°C rising to 40.0°C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2

10 Threshold Threshold 30 120 3 60 120 30 90 120 60 120 120 80 4 86

Temperature: 70.0°C 11 Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 25 Threshold Threshold Threshold 30 60 40 50 60 80 80 80 90 80 80 80 120 90 80 80

It was noticed that the sonoluminescence signal fell quite rapidly with time.

Temperature: 101.0°C

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 20 Threshold Threshold Threshold 30 80 30 30 60 80 100 90 90 120 110 100' 120 120 110 100 1

Temperature: 152°C

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 25 Threshold Threshold Threshold 30 10 10 8 60 25 20 12 90 25 20 18 120 25 22 22 87

Sonolun\-vilescehc e Boo I \‘'ei,A611,1 Pl‘ccoi -11 urvv.A,:mAs I 'x0 PhOVS

-0 40°C

100

A loleG

100

3o Co qo

Exeihn3 Vol.ra/e Ck GrO5TralASchtcer

Fig. Sonoluminescence from gallium against exciting voltage across transducer, for six temperatures. SOVNOILM.11,%eSCO,Ce.

tA S TOT?, v4:4 0.1". P1•01-oc0.Vtode,

0 error

a00

100

0 oG —SO +SO 4400 +ISO 4-2o0 + 2.50 Te et cliati,

Fig._47. Sonoluminescence from gallium at 120 volts transducer exciting voltage against temperature. 89

Temperature: 200°C Exciting Voltage across Photomultiplier Voltage and. Number of Run Transducer 1 2 3 25 Threshold Threshold Threshold 30 10 10 8 6o 25 20 12 90 25 20 18 120 25 22 22

0 Temperature: 252 C Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 28 Threshold Threshold Threshold 30 11 11 11 60 16 16 16 90 20 20 20 120 22 24. 28

On removal from the furnace, the lower flat face of the pyrex velocity transformer was found to be coated with gallium. This had to be scraped off. The sonoluminessence signals recorded above as voltages across the photomultiplier tube were converted into luminous intensities in phots at the photocathode. These values are plotted in Fig. 46 against the exoiting voltage across the transducer, for various temperatures. In Fig. 4.7 the sonoluminescence at 120 Volts transducer exciting voltage is plotted against temperature. 4..5.4. Indium (mp 156°C)

Temperature: 170°C

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 15 Threshold Threshold Threshold 30 30 20 13 6o, 6o 50 3o 90 7o 5o 4o 120 70 50 40 s otiolorAlv‘e2celAce

IlipAiwous 71 4en-5.111 PLa7code

100 XIO rkotS

ri 30 bo t zo Volts E yelti„j across TraKs',..1Licer

Fig. 48. SonoluminesCence from indium against exciting voltage across transducer, for four temperatures. 91

SOYNOlurtimeSten•Ce t,A-.ccA-L„ck, 9 ISG C

10o -12 x10 ?LOS ►

O +150 4-2oo -So O 4-50 -110o 4 2SO C Tem-1)er

Fig. 4.9. Sonoluminescence from indium at 120 volts transducer ereiting voltage against temperature.

Temperature: 200°C

'Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 25 Threshold Threshold Threshold 30 5 3 2 60 11 10 7 90 16 14 . i 14 120 20 17 15

Temperature: 231°C xciting Voltage across Photomultiplier Voltage and Number of Run

Transducer 1 2 3 40 Threshold Threshold Threshold 3o 0 0 6o 0 6 6 90 10 10 10 120 11. 13 13

Temperature: 260°C

Exciting Voltage across Photomultiplier Voltage and Number of Run Transducer 1 2 3 60 Threshold Threshold Threshold 30 0 0 0 60 8 8 8 90 11 11 11 120 13 13 13

Fig. 48 gives the corresponding absolute sonoluminescence intensities in phots at the photocathode as a function of the exciting voltage across the transducer, for the four temperatures. Fig. 49 shows the sono — luminescence at 120 volts transducer exciting voltage as a function of temperature.

Sonoiumivlesce,Ace C 0 X10 TvreAss:tii Gh PLoti.c..c,tkode 255 C • • 1. p1,10IrS 40 7c5C RUN 3

:0 .A.4-o•C

3o VoN Excithl ac_ross TrituAs. cit.,cer

Fig. 50. Sonoluminascence from tin against exciting voltages across transducer, for three temperatures.

911.

SOnolt)rAiheStetAce A rn17 3 1,3m1,%:.0tAs, 1nlehsX c4Y. ?L A-0 cati,ode (.0.11 xto phots • 0 4.0 0 ao

0 -So 450 +100 4iSo 4-00 -Faso 4300*c. Te,m1-)erah,r e.

Fig. 51. Sonoluminescence from tin at 120 volts transducer exciting voltage against temperature. 95

4..5.5. Tin (mp 232°C)

The table below gives the corrected sonoluminescence signals after allowing for the dark current, which varied with temperature, and was equivalent to the following photomultiplier voltages: Temperature Dark Current 240°C 1 270°C 3 255°C 5 i Temperature 240°C 270°C 255°C Exciting Voltage Photomultiplier Voltage and Number of Run across Transducer 1 2 3 1 2 3 1 2 3 ----1 30 0 0 0 0 0 0 0 0 0 60 1 1 '1 1 i 1 0 1 90. 2 1 11 21 3 3 31 4 5 120 2 21 21 6 6 6 8 9 io i

The lower flat face of the pyrex velocity transformer was found to be coated with tin on removal from the furnace. This was removed partially by filing, and then soaking in dilute nitric acid.

Fig. 50 shows the corresponding absolute sonoluminescence intensities in phots at the photocathode as a function of the exciting voltage across the transducer, for the three temperatures. Fig. 51 shows the absolute sonoluminescence at 120 Volts transducer exciting voltage against temperature.

The irregular sequel-18e of the results was probably due to making the measurements at first 240 C, then 270 C and then allowing to fall to 255 C and not allowing sufficient time between these sets of runs for the temperature of the furnace, tin and tip of velocity transformer to stabilise. 58 another set of readings was takenwith the temperatures in the order 240 C, 270 C and extended to 300°C; and for each temperature the apparatus was allowed to stand for five minutes before cavitating. 96

(20-1cIctrAiv.esceiNce

LI. 01th C> P 0 C.49,Ve` `)

30 6o q0 VoltS

E ac.co ss r

Fig. 52. Sonoluminescence from tin against exciting voltage across transducer, for 240°C, 270°C, 300°C.

SOnOlUmineSCence, k vari 'hocks ?Lotoce-2t-Lock

100 X10

0 +SO 4100 4-150 +200 +2S0 Tenoerai-vre

Fig. 53. Sonolminescence from tin at 120 Volts transducer exciting voltage against temperature. 98

Temperature 240°C Exciting Voltage Photomultiplier Voltage and Number of Run across Transducer ' 1 2 3 4 5 6 7 30 4. 0 0 0 0 2 4. 60 10 0 0 0 0 30 28 90 16 26 34. 0 38 42 46 120 20 38 48 2 52 52 58 Threshold for Sonoluminescence Signal of 10 Volts 20 90 70 30 120 90 30

Temperature 270°C 300°C Exciting Voltage Photomultiplier Voltage and Number of Run across Transducer 1 2 3 4. 1 2 3 4. 30 6 0 0 0 6 6 5 6 60 26 28 30 28 28 32 32 30 90 46 46 46 44 46 46 46 45 120 58 58 56 56 59 56 54 54. Threshold for Sonoluminescence Signal of 10 Volts 20 30 30 30 12 ' 30 30 30

Fig. 52 shows the corresponding absolute sonoluminescence intensities as a function of the exciting voltage across the transducer, for the three temperatures. Fig. 53 shows the absolute sonoluminescence at 120 Volts transducer exciting voltage against temperature. 4.5.6. Bismuth (mp 269°C) Measurements were made at 285°C and 300°C which was the highest temperature which could be reached by the furnace. The table below gives the sonoluminescence as a voltage developed across the photomultiplier after correction for dark current. 99

c'lOhOtUrv,1%AeSCeA-Ce

1-.CArrstinsA-A-P. 1.1"-rCINS;t1i air ITNA'ac-eteocie

•loo -12 - xto

i:o

EXcii-in5 Vo165,1c. 1"s cluce

Fig. 54. Sonolumine scenes from bismuth against exciting voltage across transducer, for 285°C and 300°C. leo

SovlolOmike s cei"ce o NchcatLocte

100 -12. X10

-50 0 (00 n,C,o 3 00eC TemiDer at-vre

Fig. 55. Sonoluminescence from, bismuth at 120. volts transducer exciting voltage against temperature. 101 400-itA- Sor1010m'aleScev,Ce x10 0,011.5 turw:inolks It4I,Aa k_PLA,catt,Dcle

0 H3

o a In

£ Sh

C=3 Bi

100

0 1,10- 450 +100 4150 +200 +250 +3ooi5 Teml)ercz.V'w-e

Fig. 56. Sonoluminescence at 120 volts transducer exciting voltage against temperature. 102

s s_

POSITION A. POSITION B.

Fig. 57. Cavitating bismuth in a magnetic field. 103

Temperature 285°C 300°C Exciting Voltage Photomultiplier Voltage and Number of Run across Transducer 1 2 3 4 5 1 2 3

30 0 2 2 2 0 0 0 0 40 1 8 14 16 18 24 22 22 50 8 22 33 38 40 46 42 42 6o 52 36 14.6 54 56 60 56 56 90 48 74 78 84 82 81 78 78 120 74 84 88 90 go 86 84 84

Fig. 54 shows the corresponding absolute sonoluminescence intensities as a function of the exciting voltage across the transducer, for the two temperatures. Fig. 55 shows the absolute sonoluminescence at 120 Volts transducer exciting voltage against temperature.

4.5.7. Collected Results Fig. 56 shows the absolute soncluminescence intensity at 120 Volts transducer exciting voltage against temperature for the five liquid metals.

4.5.8. Bismuth in a Magnetic Field

The mass susceptibility of bismuth is high, -1°27 x 10-8kg-1 at 260°C W. The bismuth sample was heated to 300°C and then cavitated first in a magnetic flux density of 0•40 Ta M-2(4000 oersteds) produced between the pole pieces of a powerful permanent magnet and then outside the magnetic field, In order to make sure that the magnetic field did not affect the photomultiplier tube, the latter was surrounded by a mumetal shield and placed in the upper end of a cardboard tube two feet long as shown in Fig. 57. Position A shows the bismuth in the magnetic field and position B outside the magnetic field. To check that the photomultiplier tube was not affected by the magnetic field, a weakly glowing torch bulb was fixed to the glass velocity transformer and the current through it adjusted to give the same photomultiplier tube signal as from the cavitating bismuth. This signal was then noted with the glass velocity transformer in and then out of the magnetic field. The table gives the results of this experiment for 120 V transducer exciting voltage. 104.

Photomultiplier Voltage Source of Light and. Number of Run 3 Cavitating Bismuth in Magnetic Field 4.0 71.•1 4.0 Cavitating Bismuth out of Magnetic Field 4'0 4.0 Torch Bulb on Glass Stub in Magnetic Field 4.1 4.•1 4.0 Torch Bulb on Glass Stub out of Magnetic Field 4.1 4.0 4-1

Dark Current as Threshold of Source of Light Photomultiplier Voltage Audible Cavitation and Number of Run and Number of Run 1 2 3 1 2 3 Cavitating Bismuth in Magnetic Field 0.6 o•6 0 • 6 30 30 30 Cavitating Bismuth out of Magnetic Field 0.6 0.6 0.6 30 30 30 Torch Bulb on Glass Stub in Magnetic Field o•6 •6 •6 Torch Bulb on Glass Stub out of Magnetic Field 0.6 •6

Thus we can say that the magnetic field has no measurable effect to within g/1 either on the sonoluminescence or on the onset of audible cavitation. 105

4.6 Discussion of Results 4.6.1. Correlation of Sonoluminescence with other Parameters.

The tablesbelow give various parameters that might correlate with sonoluminescence. All values and that of the sonoluminescence are at 20 degC above the mp. Numbers in brackets are the sources and are given in the list of references at the end of the chapter.

Ltomic rtomic m.p. b.p. Liquid Valency o, o Number Weight 0 C Range

Hg 2 80 201 -39 357 395 Ga 3 31 70 30 224.7 2217 In 3 49 115 156 2070 1914. Sn 4. 50 119 232 2623 2391 Bi 5 83 209 269 1663 1391

Sonolumill-'Vapour Surface Jarman Thermal Density Specific Heat escence phots at Pressure Tension 2ara- Conduct- at Constant photo- atmos- cm....4 meter_ ivity icathode pheres dyn dyne cm1Jcm-1 s-1 g cm-3 Pressure -1 ....1 at 120 Atmos- °C-1 J g 00 Volts pheres A Transducer pv a atiloir K Cp Exciting Voltage (6) (1) (7) - . Hg 368 x 10" 1210" 488(7) 1013 .086(7) 13.6 -142 ....36 (8)(9) Ga 204. 10 706(10) 1042 .34(7) 5.9 *398 In 96 10...22 558(7) 1027 -25*(11) 7.3 .256 ..o24 Sn 96 10 574(7) 1029 '31(7) 7.3 •259 -14 Bi 116 10 387(7) 1019 '11(7) 9.8 .153 (8 *0°C 100°C 106

SOhltn;',.?-SCeA"-ce LUDNtv

-36 -32 -2.9 . -.2o -t2 —18 feyq 1,4A4vre .10

Fig.58. Sonoluminesoence against Vapour Pressure.

107

SonOtUrniheSceA•kce- 400 LUmihous I4einsitj 01- Pkotocal-iNocke- xlo-11 plgtot$ 300

boo

100

So . 3 7 lo 0 30 c,.;2s

Thermal intusivtht

Fig. 59. Sonoluminescence against 1/Thermal Diffusivity 108

Thermal Dynamic Kinematic Ultrasonic Ultrasonic Resistivity . Diffusivity Viscosity Viscosity Velocity Attenuations -1 -1 1 2 OM S cP cS MS m s Dm IDK/ /f2 v . 776 0 « PI Cp n

(12) (12) (7) (7)

...'S Hg .045 1.61 117 1478 5.71 x 10 '91 Ga •115 1.70 288 2873 1.58 x 10-15 .26

In .133 1.65 226 2318 Not done *33 Sn •169 1.75 240 2464. 5.63 x 10-is .48 ..015 Bi .074 1.58 161 1655 8.05 x10 1.28

With the exception of gallium, vapour pressure appears to correlate with sonoluminescence (Fig. 58), and thermal diffusivity appears to give an inverse relationship with sonoluminescence (Fig. 59). The latter would support the theory that sonoluminescence is basically due to an adiabatic compression of the bubble content during the rapid collapse of the cavitation bubble, as any loss of energy due to thermal diffusivity would modify this theory and cause lower final temperatures. The table below gives the characteristic impedances, pc, of the five liquid metals and of the glass velocity transformer. The transmission coefficients at, for sound from the velocity transformer to the liquid metal, can then be calculated from the formula: R1R2 a where R1 and R2 are the characteristic t (R1 + R2) impedances of the two media.

Characteristic Transmission Impedance Coefficient pa at 2 -1 kg m 8 Hg 2.05 x107 0.93 Ga 1.69 0.97 In 1.71 0.97 Sn 1.82 0.95 Bi 1.62 0.97 Glass 1'17 .., The transmission coefficients are remarkably similar and so good matching is achieved for all the liquid metals.

109 V011-01e, GCroSS TO4Asckycel"

ski" So,/ko\Ur:ivesce►.ce S431.al pc %DV 6,0 Volts

4. 4

60 4 rl 4-• O O sn

0—e Bi

1 0 100 el 00 era -,re

Pig. 60. Cavitation threshold against temperature.

110

3o0C -r le exciI"vre

300

3o0 Tn

Sr 300

• 300

0 -47 -40 -32 - -14 lo 10 to to gat-m0515Letes to° Vqour Ivressvre Fig. 61. Temperature against vapour pressure

111 Co ItesS,old Volts TtatSGLAcer tet S011‘01tArp,:vv.eceisce toV

Co Sn

0 -48 -az -IL -c 0 Io to k) 10 arvAmiLex4 10

_Va'pout 1)fessure

Fig. 62. Cavitation threshold against vapour pressure Svt-Face 112 500 .400

VatpuLt o-.11) g-e-'44— —`10

—50 +100 +15o +10e. 4 250 TerrterahAte Fig.63. Sonoluminescence, surface tension, and reciprocal of vapour pressure against temperature for mercury 113

S 011.7111tre SCONC e LU111.1110u,S T1AehS Alf . oto (A lm) k

300 —1 x10 ?Lot's

loo

10 12

Fig. 64.. Sonoluminescence against (surface tension) for mercury. vapour pressure 114

4.6.2. Cavitation Threshold Results

Fig. 60 is a set of graphs of cavitation thresholds against temperature for five liquid metals. Fig. 61 is a set of graphs of temperature against vapour pressure (6). From these two figures a set of graphs of cavitation threshold against vapour pressure is plotted (Fig. 62). These do not show any similarity.

4.6.3. Mercury Results Fig. 63 shows the sonoluminesoence, surface tension, and reciprocal of the vapour pressure for mercury against temperature (9)(6). There is good correlation and the peaks at -20 C for sonoluminescence and at -35 C for surface tension are very interesting. Fig. 64. is a plot of the sonoluminescence against the Jarman parameter (surface tension)2,0), for mercury at different teaperatures, and again vapour pressure shows good correlation. The content of the cavitation bubbles is interesting. Mercury will not dissolve air (13), but air will certainly be trapped in the pores of the flat face of the glass velocity transformer when it is lowered into the mercury. It is this air which will be oavitated. The continual cavitation will cause a steady erosion of the velocity transformer, producing particles of glass which will act as cavitation nuclei, and gradually shortening the velocity transformer causing its resonant frequency to change. Although this off-tuning was not noticeable through the series of experiments, the eroding away of the glass means that a liquid metal contaminated with glass particles is being studied, despite the use of a high purity sample. 116

Suggestions for Further Work

Future work should have the exciting voltage across the transducer, the transducer displacement, the temperature, and the sonoluminescence continuously monitored on a four channel recorder (1). For work on liquid metals a hollow cylindrical transducer should be used in a radial mode. The liquid metal would be contained in a polythene cell inside the cylinder and the light brought out by a light guide. This would avoid the transducer being in contact with the liquid metal and one could try to induce vaporous cavitation from a pure air free liquid metal. The spectrum of sonoluminescence could be recorded by a. spectrograph (2)(3). This would give information about the nature of the light, i.e. whether it is thermal, or due to excitation or both (3)(4)(5).

Gab rielli, I., Iernetti, G. and Lavenia, A., Acustica, 18, 171 (1967). Srinivasan, D., and Holroyd, J.App.Phys., 32, 446 (1961). Kuttruff, H., Acustica, 12, 230 (Akustiche Beihefte)(1962). Muller, H.M., Acustica, 16, 22 (1965/66). Dybwad, G.L, and Mandeville, C.E., Phys.Rev., 161,527 (1967). 117

Publications

Young, F.R., Sonoluminescence from Glycerine-Water Mixtures, Nature, 206, 706 (1965). Young, P.R., Sonoluminescence from Viscous Liquids, Paper C 37, 5th International Congress on Acoustics. Liege (1965). Smith, R.T., Webber, G.M.B., Young, F.R. and Stephens, R.W.B. Sound Propagation in Liquid Metals, Advances in Physics, 16, 515 (1967). (Reprinted from Nature, Vol. 206, No. 4985, p. 706 only, May 15, 1965)

Sonoluminescence from Glycerine-Water Mixtures THE -sonolumineseence from glycerine-water mixtures extending over the full range of 0-100 per cent glycerine has been investigated. A specially distilled supply of glycerine of 99.9 per cent purity was obtained and the sample of volume 5 ml. was contained in a 15-m1. quartz beaker cooled by circulating cold water. Fresh tap water was used, as tests showed that this gavelhe same results as distilled water. Cavitation was produced by a magneto. strictive window-type transducer coupled to a titanium double quarter-wave velocity transformer, the system being adjusted to deliver a constant acoustic power of 10 W at a frequency of 21.5 kc,'s over an area of 0.7 cm2. The transducer was monitored by an oscilloscope and valve voltmeter connected to a crystal accelerometer pick-up fixed to the transducer. The sonoluminescence was measured by a 13-stage E.M,I. photomultiplier tube '6255B' sensitive from 1650 A to 6500 A, and the signal was detected by a high-impedance valve voltmeter.

190 1,400

180 1,200

0 . 170 1,000 q

160 800 0 ir.3

1- 150 600

0 .Ca 140 400

130 200

120 0 0 20 40 60 80 100 Percentage of glycerine (by vol.) Fig. 1. Sonoluminescence from glycerine—water mixtures The sonoluminescence from glycerine was found by Jarmanl to be greater than that from any of 20 liquids he examined; but he also found that it was not possible to cavitate glycerine if it was free of water. It is note-, worthy that glycerine is very hygroscopic, ordinary commercial glycerine containing up to 2 per cent water. Negishi° found that 50 per cent glycerine luminesced with considerable brightness. In the work recorded here sonoluminosconce was found to be time-dependent, relaxation and hysteresis effects being observed. Therefore the procedure was adopted of measuring the signal after 15 sec of cavitation when it was reasonably steady and reproducible. For all samples between 0 and 90 per cent glycerine, the temperature did not rise above 23° C from 19° C initially. For 100 per cent glycerine the rise was from 19° C to 28° C despite a fast flow of cooling water. This is duo to the appreciable heat generated through viscosity, especially in tho immediate neighbourhood of the cavitation bubbles3 ; also the thermal conductivity of glycerine is only about half that of water. It is to be expected that this heating of the bubbles through viscous energy dissipation will produce a higher temperature of the bubbles' contents and hence greater sonoluminescence for glycerine than water. The possible correlation of viscosity with sonoluminesconco is indicated by the results shown in Fig. 1, which also records the viscosity of glycerine-water mixtures4. F. RONALD YOUNG Watford College of Technology, Hertfordshire.

Jarman, P., Proc. Phys. Soc., 73, 628 (1050). NegIsitl, K., J. Phys. Soc. Japan, 18, 1450 (1961). ' Kuttruff, H., Acustica,12, 230 (Alcustlehe Ilelhefte) (1962). 4 Thorpe, J. R, Dictionary of Applied Chemistry, 6, 54 (T,ongtnans, Green and Co., London, 1943),

Printed In Great Britain by Fisher, Knight & co., [Ad., St. Albans. 5t CONGR[S INTERNATIONAL D'ACOUSTIQUE LIEGE 7-14 SEPTEMBRE 1965 C37 Sonoluminescence from Viscous Liquid-Water Mixtures

F. Ronald Young Watford College of Technology (now at Physics Dept., Imperial College of Science and Technology, London.)

The sonoluminescence from mixturesof water and glycerine, 3-chloropropane 1-2 diol, cyclohexanol, and ethylene glycol over the full range of 0 - 100% water has been investigated. Cavitation was produced by a transducer adjusted to deliver a constant acoustic power of 10W. The sonoluminescence increased by about 60% from 0 to 100% glycerine, by 40% from 0 to 100% 3-chloropropane 1-2 diol, by about 30% from 0 to 100% cyclohexanol, and by about 20% from 0 to 100% ethylene glycol. The determining parameter seems to be viscosity.

1. Introduction . The sonoluminescence from glycerine was found by Jarmanl to be greater than that from any of 20 liquids he examined; but he also found that it was not possible to cavitate glycerine if it was free of TRANSDUCER water. It is noteworthy that glycerine is very hygroscopic, ordinary commercial glycerine containing up to 2% water. Negishi2 found that 50% glycerine VAPOUR SHIELD luminesced with considerable brightness. No work could be found on other very 5tOLING viscous liquids. SAMPLE WATER 2. Apparatus. Pig. 1 shows the light-tight housing QUARTZ PLATE, which contains a 250 ml quartz beaker for the sample; nickelmagnetostrictive iTOTO 1ULTI transducer; titanium double quarter- FLIER wave velocity transformer; quartz plate; circulating cooling- water; 13 stage E.M.I. photomultipIer tube 2g 55B sensitive from 1650A to 6500A. Fig. 2 is a block diagram of the complete apparatus. The transducer was monitored by an oscilloscope and valve voltmeter PIG. 1 HOUSING connected to a crystal accelerometer Sonoluminescence from Viscous Liquid—ater fixtures 2

GENERATOR TRANSDUCER C R 0

VALVE

VOLTMETER

VALVE PD VOLTMETER

E H T

FIG. 2 APPARATUS

pick—up fixed to the transducer. The signal was detected by a high impedance valve voltmeter. 3. Experiments. A specially distilled supply of glycerine of 99.9;. purity was obtained. Fresh tap water was used, as teats ahowod that thin gave the same results as distilled water. Pure glycerine was generally successively diluted with.water, the same volume being cavitntod each time. In other runs, water wan ouccesaively diluted with glycerine or a series of mixtures kept in atoppored bottles wan used. All gavo the sumo results. Tho nyntom was adjusted to deliver a constant acoustic powor (moasurod calorimotrically) of 10:1 over an area of 0.7 cm2. Tho peak diaplacomont amplitude of the velocity transformer wan measured by a travelling microscope and found to bo 0.0009 cm. If the stub were considered to bo a circular piston in an infinite flat bafflo3 radiating into an infinite medium the sound pressure amplitude can bo calculated to be approximately 7 atmospheres. Tho nonoluminenconce was found to be timo—dependent, relaxation and hystorsis effects being obsorvod. Therefore tho procedure was adopted of moaouring tho signal after 15 soc. of cavitation when it was reasonably steady. For all samplon between 0 and 90; glyporino, tho tomporaturo did not rise above 25 despite afastflowofcoolingwater.Thisisduetotheappreciableheat fact thatwiththe250mlitwasdifficulttokeepstrongerconcentrations 4. Results. half thatofwater. generated throughviscosityespeciallyintheimmediateneighbourhoodof With glycerineitwasnoticedthatthereweremanymorebubblesthanwithwater and thustheincreaseinlightoutputcanbeattributedtothisnotan of glycerinecool,theouterannularcylinderliquidactingasaninsulator. obvious correlationexistsbetweenthesonoluminescenceandtheseproperties, against %liquidinFig.5isnotlinearshowingthatthecurve3 increase inthebrightnessofeachbubble. in Fig.4arenotstraightlinesshowingthatthecurves3 cavitation bubbles not exponential.Fig.6givesthevariouspropertiesof4liquids.No to dependonthesizeofsample,assomeexperimentsundertakenusinga15ml except perhapsviscosity.Forglycerine-watermixturesthevariationseems EN CEIICE beaker gaveacurveslightlydifferentfromFig.3 power curves.Aplotoflog SONOLLR ES 0 C from19 Fig. 3showstheresults.Logplotsofsonoluminescenceagainat%liquid 190 180 170 160 140 150 130 120 . FROM LIQUID-WATER MIXTURES FIG. Sonoluminescence fromViscousLiquid-WaterMixtures 0 20406080100 ° C initially.For100%glycerinetherisewasfrom19 3 % LIQUIDBYVOLUME SONOLUMINESCENCE 4 ; alsothethermalconductivityofglycerineisonlyabout ▪ • • X GLYCERINE e sonoluminescenceof3-chloropropane1-2diol ETHYLENE GLYCOL CYCDOHEXANOL 3-CHLOROPROPANE 1-2DIOL - LOG .9 2.16 8 crl 2 U) FIG. 10 2.28 2.24 2.26 2.22 2.18 2.20 2.14 2.12 2.10 (% LIQUIDINLIQUID-WATERMIXTURE) 4 5 . ThisMaybeduetothe 1:0 1.21.41.61.82.0 FROM LIQUID-WATER MIXTURES LOG OFSONOLUMINESCENCE

° C to37 0 C 3 Sonoluminescence from Viscous Liquid `Hater Mixtures 4

5.2

4.9

4.8 0 20 40 60 80 100 LIQUID BY VOLUME FIG. 5 LOG SONOLUMINESCENCE 3-CHLOROPROPANE 1-2 DIOL/% LIQUID WITH WATER e

Glycerine 3-chloropropane Cyclohexanol Ethylene 1-2 diol glycol

CH2OH CH2OH CHOH CH OH 2 2 1 / N 1 CHOH CHOH CH CH CHCH2OH2OH Structural Formula 1:z d/e1 2 CH 1 I CH OH CH C1 .•CH2 2 2

Sonoluminescence 190 185 152 170

% Increase of Sonoluminescence 60 40 30 20 of water

Viscosity at 20°C. Cp 1490 73 68 20

Density e. cm-3 1.26 1.32 0.94 1.12 4 Thermal conductivity 6.8 x 104 6.2 x 10 -1 -1 -1 cal. cm s dog.0

Specific hoat cal g a 0.565 0.42 0.54 ---- FIG. 6 SONOLUMINESCENCE OF THE PURE LIQUID AND VARIOUS PARAMETERS

1 Jarman, P., Proc.Phyo.Soc., 73, 628 (1959) 2 0 Negi hi, K., J.Phyo.Soc.Japan, 16, 1450 (1961) 3Heuter and Bolt, Sonico, 56 (John Wiley, Now York) 4Kuttruff, H., Acuatica, 12, 230 (Akuoticho Beihefte) (1962) 5Young, F. R., Nnturo 206, 706 (1965) Reprinted from ADVANCES IN PHYSICS (PHILOSOPHICAL MAGAZINE SUPPLEMENT) Vol. 16, No. 63, p. 515, July 1967

Sound Propagation in Liquid Metals

By R. T. SMITH, G. M. B. WEBBER, F. R. YOUNGt and R. W. B. STEPHENS

Department of Physics, Imperial College, London ACOUSTIC measurements in liquid metals have been primarily concerned with the direct measurement of velocity and attenuation. The work in progress at Imperial College is concerned mainly with ultrasonic velocity measurements in various molten metals and alloys, large amplitude propagation in mercury and the temperature variation of sonoluminescence in various molten metals. Attenuation measurements provide means of distinguishing the monatomic behaviour or otherwise of simple liquid metals which are notably different from non-metallic liquids in that the major contribution to the sound absorption is due to the thermal conductivity loss. Attention is directed to the discussion of attenuation given in earlier reviews, e.g. Stephens (1963) and Webber (1965). Fig. 1

270 300 35D 400 TEMPERATURE °C Temperature variation of the sound velocity in liquid bismuth. + Present measurements. 0 Due to Hill and Ruoff (1965). The sound velocities determined by several authors, using a variety of techniques, are not always consistent in absolute magnitude or rate of change with temperature. A pulse interferometer technique, which is described in detail in Webber (1965), has been used to determine the sound ¶ Now at Watford College of Technology, Hertfordshire. 516 Conference on the Properties of .liquid Metals velocity in liquid bismuth. Previous measurements obtained in mercury and indium with this technique agree to within a few m sec-1 with those obtained by Hill and Ruoff (1965) and Beyer and Coppens (1965), who used pulse-echo comparison and pulse repetition rate techniques respectively. In fig. 1 it is seen that the sound velocity in liquid bismuth varies non-linearly with temperature above 29000 and the present measurements agree closely with those due to Hill and Ruoff (1965). However, the latter observed that the sound velocity remained constant in the temperature range from the melting point to about 290°c whilst Gitis and Mikhailov (1966) reported a constant value of 1674 m sec-1 to about 320°c and then decreasing with rise in temperature. In the present measurements the sound velocity was observed to decrease in the temperature range from the melting point to 290°c and did not indicate significant structural changes in liquid bismuth close to the melting point. An attempt has been made to explain the systematic behaviour of the sound velocities within each valency group, reported by Webber (1965). Assuming that the ions interact by a screened Coulomb interaction, Ziman (1964) shows that the longitudinal acoustic velocity c' in a metal is given by : [2ZEF1112 ✓ (1) 3.M j

Table I . Sound velocity at the melting point of various liquid metals. The experimental values are taken from Webber and Stephens (1966)

Theoretical Experimental Metal Valency Z c' c c m sec-1 m sec-1 m sec-1

Na 1 2940 2940 2526 K 1 1810 1810 1890 Rb 1 1140 1140 1260 Cs 1 880 880 967 Cu 1 2580 2580 3460 Ag 1 1740 1740 2710 Zn 2 4180 2960 2712 01 2 2850 2020 2166 Hg 2 2100 1490 1478 Al 3 8750 5050 4670 Ga 3 5430 3140 2873 In 3 3760 2170 2318 T1 3 2750 1590 1625 Sn 4 4630 2310 2464 Pb 4 3350 1680 1776 Sb 5 5340 2390 1893 Bi 5 3940 1760 1649

Conference on the Properties of Liquid Metals 517

where Z is the valency, EF the free electron value of the Fermi energy and M is the mass of the ion. The values of c' at the melting points of various liquid metals are shown in table 1 and are in close agreement with experimental values for the alkali metals. The presence of strong core repulsion in copper and in silver is indicated by their larger experimental velocities. The theoretical velocities c' become progressively larger than the experimental values for the polyvalent metals ; however, the systematic trends are reproduced within each valency group. Webber has found that an excellent correlation appears to exist between the experimental velocity and velocity c defined by : 2EF 112 (2) c= 3.mi This correlation is examined more closely in Webber and Stephens (1966). The presence in the metals of attractive Van der Waals forces and direct repulsive forces between ion cores, and the effect of lattice structure will modify the values of c' and when these factors are included it will be of interest to see whether the factor Z-112 is physically significant or is a fortuitous numerical factor. The propagation of high amplitude sound in liquids is characterized by an absorption coefficient in excess of that for waves of small amplitude. The increased absorption is related to the corresponding distortion (i.e. increased harmonic content) of the wave shape by variation of both (a) local sound velocity and (b) local particle velocity at different points of the wave. The magnitude of the distortion expressed as the velocity of a point of the wave relative to a point of zero pressure is computed by Rudnick (1958) in terms of the thermodynamic variables : co + =1 (acc)p(71,1 1/2 (ap)r pocou = Ku, T) + (3) where c is local sound velocity, co the velocity at point zero pressure, u the particle velocity, (aciaT)p, (ac/aP)/, are temperature and pressure gradients of sound velocity, y is ratio of specific heats, CI, the specific heat at constant pressure, T the temperature and po the value of undisturbed density. The three factors contributing to change in local phase velocity (eqn. (3) ) are particle velocity, excess temperature and pressure in the sound wave. In liquids of low dissipation the pressure term is the dominant cause of distortion. In mercury the relative magnitude of the three terms are (1, — 0.23, + 4.1). The excess temperature is seen to oppose distortion as is the case for most liquids. The propagation of even very intense sounds in liquids (excess pressures up to 1000 atmospheres) can be regarded as isentropic. The non-linear equation for compressibility is then written as :

p po A P Po) B (19 — Pole ( (4) Po 2 ` Po 518 Conference on the Properties of Liquid Metals where P is total pressure and Po the internal pressure, ap A =Po () =Po-o2 B= 1-0 a p 2 Po UP s 2 Ha2P) C-11 is wave condensation, suffix s indicates derivatives evaluated at constant entropy. In eqn. (3) K= (14- B12A). The distortion of high amplitude waves is eventually limited by the dissipative processes occurring at the front of the wave (i.e. viscosity and heat conduction). However, in most liquids provided the value of acoustic Reynolds' number

" >1, Re=bw (5) where P ex is excess pressure, ng, 7/13 the shear and bulk viscosities, k the thermal conductivity, and C, the specific heats at constant pressure and volume, respectively, and 1 1 b=trie -i-nB+k

The balance between non-linear distortion and absorption at the leading edge of the wave can give rise to a wave which has a stable shape (saw-tooth) over a certain propagation distance. When Ro> 1 the saw-tooth is characterized by a pressure jump which can extend over very small distances. Fig. 2

CATHODE TEC TROTIlt FOLLOWER OSCILLOSCOPE

STEEL - SHOCK TUBE

DP T5 CRYST

SHOEK COA

TUT NOL

CHARGING CIRCUIT

SPANK GAP Apparatus for generation and detection of high amplitude pulses in liquids.

Single high amplitude pulses (fundamental frequency 100 kc), initial pressures up to 200 atmospheres, are propagated in a mercury column using the arrangement in fig. 2. Measurements of attenuation of peak pressure arc made using a mm thick x 3 mm diameter PZT5 disc as a broadband receiver mounted on a stainless-steel holder and attached to a vernier height gauge. A plot of the absorption coefficient a (from the Conference on the Properties of Liquid Metals 519

Fig. 3

•09 15 K V MERCURY

•05

-04 1,7t PROPAGATION -02 DISTANCE = 50 CM

I 5 10 15 20 25 30 PEAK CRYSTAL VOLTAGE VOLTS Variation of absorption coefficient with peak crystal voltage. measured slope of the peak pressure versus distance curve) against the peak crystal voltage (which is proportional to peak pressure) shows a characteristic peak in the absorption (fig. 3). The transition to saw-tooth region which by simple theory is characterized by an oc proportional to peak pressure is not clearly indicated over the propagation distance covered which was about 55 cm. The pressure at the face of the tungsten disc was about 100 atmospheres. Measurements are being extended over greater distances. For a weak pressure step the thickness over which the discontinuity extends is computed from hydrodynamics (Landau and Lifshitz 1959), as : 8b V3 L— (6) a217)' cs(P—P0)(—ap2 s where V is specific volume, b (see page 518), P —Po the pressure step and ( a2V_ ) = ( 1+ B ) 2 V3 ap2 2A co which assumes linear dissipative processes in the layer of discontinuity and the viscosity and thermal conductivity to be constants. If we insert values for mercury into eqn. (6) with (B/A) = 7.8 obtained from Beyer and Coppens (1965) we find a value of L= 2.5 x 10-3 cm for a pressure step of 10 atmospheres. Zarembo (1960) with the same assumption of linear dissipative processes relates the width of a saw-tooth wave to the absorption coefficient as :

= A a10 L T (7) where al, is the small amplitude absorption coefficient of wave with fundamental frequency, a the absorption coefficient for saw-tooth waves and A the wavelength at fundamental frequency. The assumption is L' < A. 520 Conference on the Properties of Liquid Metals Measurement of a for saw-tooth waves will enable the values of shock front thickness to be estimated and compared with the hydrodynamic results (eqn. (6)). Thus, information on the dissipative processes occurring in the front can be obtained e.g. bulk viscosity over wide frequency band. The assumption of linear dissipative processes in the shock front and application of the hydrodynamic concepts to very thin layers will need to be examined in relation to the magnitude of the pressure step.

Fig. 4

PROIOMULTIPLIER

TRANSDUCER

VELOCITY TRANSFORMER

2- FURNACE 0 LIQUID METAL J L I HER MO C CU rLC Apparatus for generation and detection of sonoluminesconee in liquid metals.

The phenomenon of sonoluminescenco is concerned with the cavitation process in liquids and has been explained in terms of two main theories, the so-called hot-spot' theory and the ' electrical' theory. The latter is concerned with the assumed existence of the electrification of a bubble the collapse of which leads to an electrical discharge and consequent luminosity. The existence of sonoluminescence in electrically conducting liquids would appear to provide evidence against this theory as compared with the hot-spot' theory which is based on adiabatic gaseous compression considerations and the consequent development of a high temperature — 104 °c. Conference on the Properties of Liquid Metals 521

Measurements of the luminosity of the phenomenon at various temperatures near and above the melting point have been made with the objective of obtaining some insight into the cohesion properties of the liquids. The Jarman (1959) parameter a2/py, where a is the surface tension and p, the vapour pressure, led Kuttruff (1962) to expect a sonoluminescence from mercury 75 000 times that from water, and he did find a very strong sonoluminescence. We cavitated 5 ml. of the metal in a stainless- steel furnace pot by means of a 30 kc/s lead zirconate titanate cylindrical transducer having a glass velocity transformer bonded to it (fig. 4). The system was adjusted to deliver a constant acoustic power of 4w over an area of 0.8 cm2. The transducer was monitored by an oscilloscope and valve voltmeter connected across it. The sonoluminescence was measured by a 13-stage E.M.I. photomultiplier tube, 6255B', sensitive from 1650 A and 6500 A, and the signal was detected by a high-impedance valve voltmeter.

Fig. 5

100

0 MERCURY 13 GALLIUM TS A INDIUM VOL V TIN R GP BISMUTH CE DU ANS TR CE Bi ESCEN IN UM NOL 50 10 -

-50 50 100 _150 200 250 IER42,02.41URE

Variation of sonoluminescence with temperature for several liquid metals.

Figure 5 shows a general decrease of sonoluminescence with increasing temperature similar to that reported by Jarman (1959) for organic liquids. Table 2 gives the various parameters which might correlate with the sonoluminescence. With the exception of bismuth, thermal diffusivity appears to give an inverse correlation with sonoluminescence. 522 Conference on the Properties of Liquid Metals

Table 2. Sonoluminescence and other parameters for liquid metals

Hg Ga In Sn. Bi Sonoluminescence at 20°0 above m.p. 92 51 24 24 29 m.p. (°c) —39 30 156 232 269 Surface tension of pure metal (dyne cm-1) 475 735 560 575 390 Vapour pressure at 20°c above m.p. (dyne cm-2) 10-14 10-44 10-28 10-3° 10-1° Thermal conductivity (cal em-1 sec-1 deg-1) 0.021 0.081 0.060* 0.074 0.026 Density (g em-3) 13.6 5.9 7.3 7.3 9.8 Specific heat (cal gm-1 deg-1) 0.034 0.095 0.061 0.060 0.036 Thermal diffusivity (cm2 sec-1) 0.045 0.144 0.133 0.169 0.074

All values are from ' The Structure of Liquid Metals and Alloys ' by J. R. Wilson, Metallurgical Reviews, Vol. 10, No. 40 1965, Institute of Metals, London ; except * which is from The Rare Metals Handbook by R. A. Hampel, Reinhold Publishing Corporation (Chapman & Hall), and is from 0°c to 100°c.

REFERENCES BEYER, R. T., and COPPENS, A. B., 1965, Int. Commn. Acoust., Congre. 5th, Liege. GITIS, M. B., and MucumLov, I. G., 1966, Sov. Phys. Acoust., 11, 372. HILL, J. E., and RUOFF, A. L., 1965, J. chem. Phys., 43, 2150. JARMAN, P., 1959, Proc. phys. Soc., 73, 628. KUTTRUFF, H., 1962, Acu.stica, 12, AB 230. LANDAU, L. D., and LIFSHITZ, E. M., 1959, Fluid Mechanics (London : Pergamon Press). Runxicx, I., 1958, .1. acoust. Soc. Am., 30, 564. STEPHENS, R. W. B., 1963, Proc. Int. School Phys., 27, 393 (New York : Academic Press). WEBBER, G. M. B., 1965, Int. Commn. Acoust., Congre. 5th, Liege. WEInum, G. M. B., and STEPHENS, R. W. B., 1966, Physical Acoustics, Vol. 4B, edited by W. P. Mason (New York : Academic Press) (to be published). ZIMAN, J. M., 1964, Principles of the Theory of Solids (Cambridge University Press). &la:mile, L. K., 1960, Soy. Phys. Acoust., 6, 38. 118

APPENDIX.

Effect of Thermal Conductivity of Gas on Sonoluminescence from the Rare Gases dissolved in Water.

Finch (1) considered the case of a collapsing bubble where the temperature within the bubble is uniform but drops linearly over a distance of 3X(1\is the mean free path) to Tom , the liquid temperature. He derived the following equation

T- T exp - I' v(12 (-1 — ) t-1 Ad 6 R T i

where T = temperature of gas with thermal conduction 3(S-1) T = To 110 = adiabatic temperature that would be (--R ) reached without thermal conduction.

R = radius at maximum volume R = radius at any instant

To = liquid temperature 0.92= 2 from kinetic theory= 44l--6.9° -

= 0092,(3S,

where R. = gas constant per gram.

Assume Rayleigh's equation for the bubble collapse 0,

dRj j 1\ where P. = liquid pressure (d.t.)=, 3j oi. ) = liquid density R = radius at maximum volume R =radius at any instant

119

d.R Now dt = dR14, —/dt (2PL. _ i\ 3.p. R'

SubtitutingSub tituting this in 0 we get for the integral s ) A 1 = j i oiorf (i ... -...-.Ts; . dR R ' T2L2K..... (R,; _ i) R. 4 3/1. kiT.1 I

and we now have a differential equation in R. .R 1-1 T, dR NR3 B.

Approximating,

I= T (1 - R dR 6 R

As T>N> To, neglect — R Then I dR Rai o R 0

:120

To solve this equation, assume a series solution between R and. T of the form

R. - a + a .111 + 4;). 2 R 3( - 1 ) T + + Then a- R ) as T Ad Ad = RI" and W= 3 for a monatomic gas

T To R

7. R, 2. 1 Rt. R. 2a a + a l -0.• 0 + 2a a 7.-R + 2ac a R— + a R .4. ' R 'J- ••••••••••••••••=0 R,

I 31z R R 1 a - + 2a a + (2a,s az + a .2" + 2a a -u + az •• • • • • el. TAd. R". s • 2. Rr.

Substituting the expression for T in 0 we have, fR -172 exp 50( a R +a R +aR R- .dR Ad 12Pi: R o o 3-PL R 0 4. 4.2 4, 23,13.4- 2a,s• 1/, = exp -k[ --- + a RoR + 2a R R -.-- 0 2a R Itila l . z o 3 Ro .- a' R Ro .- o o

Siz 2a,R 1f = exp -k + a R R + 2a R R 2a:, + al + 2a )R 33! 0 0 1. 0 121

If the sonoluminescence can be largely regarded as black body radiation,

Light Intensity Itix Tif iX e from

where k vt r4 D(

where R, is gas constant per gram and M is molecular weight of the gas and f is a constant.

If (a is photomultiplier tube signal,

g loge Ix, log I 4ka

—4171:-}A

Hence a plot of logD againstpi7 should be a straight line

1 i. , 11 112 log(& x '10 )

He 4..0 2.0 0.500 0.065 Ne 20.2 4.5 0.222 0.505 A 39.9 6.3 0.159 1.48 Kr 83.7 9.15 0.109 1.70 Xe 131 11.4. 0.088 2.10

(0 from Fig. 25)

Fig. 65 shows that the values for helium, argon, krypton and. xenon

lie on a straight line within the ts of the experimental error.

The low position of the point for neon may be due to the fact that :122

Much of the light from neon is in the red region of the spectrum and this would not be registered by the photomultiplier tube which had an 0 upper limit of 6500 A .

References

(1)Finch, R.D., Ph.D. Thesis, Imperial College, London, p.154. (1963). (2)Rayleigh, Lord, Phil. Nag., 34, 94- (1917).

123

ozi(a),18°)

Z. 0

0.0 0.0 0-1 o-a 0.3 0.4 0.5

F19. (Sor,z, k.A.,w,c_.rcev,ce) aqa.msi- 1-or et a s J. A lecu.kr