SONOLUMINESCENCE IN LIQUIDS UNDER VARYING CONDITIONS

THESIS

submitted for the Degree of Doctor of Philosophy in the University of London and the Diploma of Membership of the Imperial College.

Robert David Finch, M.Sc. February 1963. ABSTRACT

A study has been made of the sonoluminescence and of the cavitation produced by a magnetostrictive window-type transducer coupled to a double quarter wave horn. The effect of excess static pressure, applied by gas and also hydraulically, on sonoluminescence of tap water has been imestigated in the range from 0 - 100 p.s.i. An optimum value of hydraulically applied pressure for maximum yield of sonoluminescence, and a higher value at which sonoluminescence was almost suppressed were established. The values of static pressure at which the light yield was a maximum and a minimum both varied with the applied acoustic power. Similar results were obtained with applied gas pressure except that the pressure corresponding to maximum luminescence was displaced on de-pressurising. This hysteresis effect is believed to be correlated with variations in the nucleation of the liquid. Some evidence of this corr. Jlation is afforded by corresponding measurements of the variations of acoustic power absorbed, of the resonant frequency and of the number of sonoluminescence pulses.

By taking photographs of single sweep oscilloscope traces, sono- luminescence pulses were found to occur always at roughly the same phase of the sound cycle, but not with every sound cycle, the frequency of their occurrence being random. Photographs of many sweep oscilloscope traces showed a statistical averaging process whereby the sonoluminescence appeared as a discrete pulse with every sound cycle, as found by other authors,

Evidence: of the high pressures arising from cavitation was obtained using "carbon paper pressure detectors". Curves of temperature v. time during cavitation showed the presence of a periodic oscillation, particularly pronounced in carbon tetrachloride.

A comprehensive review of the literature on sonoluminescence and allied topics is given, and a discussion of the origin of sonoluminescence is appended. It is shown that the differences in 'sonoluminescence yields from a liquid saturated with various gases can be accounted for qualitatively in terms of the ratios of specific heats, the molecular velocities , the solubilities and the excitation potentials of the gases concerned. ACKNOWLEDGEPENTS

The author is indebted to many people for their assistance in the work described in this thesis, In particular he wishes to thank

Dr. R.W.B. Stephens for his very helpful supervision, and Mr. E. A. Neppiras for generously given advice on numerous theoretical and experimental aspects of the subject.

My grateful thanks are due to the Admiralty for the financing of the research and to Messrs. Mullards for the loan of a transducer.

I should also like to express my gratitude to various members of the workshop staff and in particular to Mr. T. Shand, Mr. A. Davis and

Mr. O.R.Milbank for their most helpful cooperation in the design and manufacture of parts of the apparatus.

I record also my thanks for the useful, candid comments freely given by other members of the Acoustics Group.

The skill of Mr. E. Sparkes in photographing some difficult subjects was much appreciated.

Finally the author wishes to record the patient assistance of his wife in producing this thesis. "Particles of Light appeared plentifully, about the bigness of small pinheads, vory vivid, resembling bright twinkling stars ti

Francis Hauksbee, 1709.

CONTENTS

Page No.

CHAPTER I : Survey of Sonoluminescence and Other Cavitation Phenomena. 1.1* Introduction. 1.1.1. Definitions and Historical Review. 1 1.1.2. Instrumentation of Observing Sonoluminescence. 2 1.2. Dependence of Sonoluminescence on Various Parameters. 1.2.1. Frequency. 6 1.2.2. Acoustic Power and Pressure. 7 1.2.3. Static Pressure. 9 1.2.4. Temperature. 10 1.2.5. Time. 12 1.2.6. Physical Properties of the Liquid. 19 1.2.7. Physical Properties of the Solute Gas, 26 1.3. The Spectra of Sonoluminescence. 28 1.4. Sonoluminescence in Hydrodynamic Cavitation. 31 1.5. Light from Collapsing Bubbles. 1.5.1. Light from Agitated Mercury. 33 1.5.2. Collapsing Glass Spheres. 35 1.5.3. Implosion of Bubbles by Shock Waves. 38 1.6. Theories of Sonoluminescence. 38 1.7. Other Effects of Cavitation. 43 I.7.1. Chemical Effects. 44 1.7.2. Erosion. 46 1.7.3. Biological Effects. 47

References in Chapter 1. 49

CHAPTER 2 : Apparatus and Preliminary Experiments. 2.1. Objectives. 2.2. Transducer and Velocity Transformer 53 2.3. Energising Circuit. 57 2.4. Some experimental Observations of Cavitation. 63 Page No.

CHAPTER 2 2 -contd. 2.5. Measurement of Acoustic Power. 73 206. Preliminary Observations of Sonoluminescence:.. 82 2.7* The Housing and Sample Holder. 84 2.8. Detecting System. 88

References in Chapter 2. 93

CHAPTER 3 s Observations of the Dependence of Sonoluminescence upon Static Pressure. 3.1, Hydraulic Application of Pressure. 97 3.2. Application of Air Pressure. 109

CHAPTER 4 : Discussion of Experimental Results. 4.1. Observations of Cavitation. 122 4,2. Changes in Noise Level and Temperature Oscillations. 124 4.3. Preliminary Observations of Sonoluminescence. 126 4.4. Variation of Sonoluminescence with Static Pressure. 4-4.1. Theories. 126 4,4.2. Discussion of theories. 129 4.4.3. A Modified Theory. 132 References in Chapter 4. 137

PlOWW1010 ..... CHAPTER 5 : Sugrestions for Further Work. 5.1. Sonoluminescence and Nucleation Problems, 138

5.2. The Origin of Sonoluminescence. 140 References in Chapter 5. 141

Mel 011.11.04.11.••••••.••••••••• 1/•malmarlimi.m. •••1•.••11.11, APPENDIX 1 : Thermal considerations in the design of the sample holder. 142 APPENDIX 2 : A PROPOSED THEORETICAL EXPLANATION OF SONOLUYJNESCENCE AND ASSOCIATED EFFECTS.

Page.

A.2.1. Introduction. 145 A.2.2. Basic Features. 145 A.2.2.1. : Cavitation Bubble Dynamics. 145 A.2.2.2. : Pressure Distribution. 147 A.2.2.3. : Temperature Distribution. 150 A.2.2.4. : Mass Transfer. 151

A.2.3. The Effect of Thermal Conduction Losses. 151

A.2.4. The Effect of Mass Transfer. 161 A.2.4.1. : In the Bubble Growth. 162 A.2.4.2. : In the Bubble Collapse. 166

A.2.5. The Mechanism of Sonoluminescence 170 A.2.6. The Mechanism of Chemical Effects. 174 A.2.7. The Role of the Liquid in Sonoluminescence. 178 A.2.8. The Effect of Dissolved Salts on Sonoluminescence. 180 A.2.9. The Effect of Organic Additives on Sonoluminescence.182

REFERENCES in Appendix 2. •• APO .. 184

GLOSSARY .. •• •• 186

LIST OF SYMBOLS . •• 188

LIST OF FIGURES.

NO: Page

1 Luminescence in water solutions, as a fune'on of !ound intensity 8

2 Relatlon between sonoluminescence and 2 VT 8

3 Sono:Luminescence of water as a function of applied pressure 11

Temperature dependence of sonoluminescence 4 from various aqueous solutions 11

5 Schematic rpresentation of time effects 13

6 Relaxation time variation of sonoluminescence 13

7 Apparatus of Meyer and Kuttruff 16

8 Growth and collapse of cavitation bubbles 17

Volume change of cavitating bubbles and 9 sonoluminescence 20

10 Sonoluminescence as a function of physical

properties of liquids 23

11 Sonolumin.sscence as a function of electrolytes dissolved in water 25

12 Spectra of sonoluminescence 31A

13 Radiation strength of light impulses from collapsing glass spheres as a function of filling gas and pressure 37

14 Radiation strength of light impulses from collapsing glass spheres as a function of immersion liquid 37

15 Horn and transducer

16 Circuit for impedance loop measurements 58 INTO s Page.

17 Impedance loop bo

18 Limiter 62

19 Driving voltage as a function of limiter voltage 64 20 Block diagram of driving circuit 65

21. Mounting of crystal pick-up 66

22 Photograph of cavitation 67

23 Construction of carbon paper pressure detectors 70

24 Photograph of exposed carbon paper pressure detectors 71 25 Photograph of atomisation of a water droplet 74 26 Photograph of atomisation of a flow of water 75 27 Glass calorimeter 76 28 Calibration of thermocouple 77 29 Heating curves (water) 78

30 Acoustic power as a function of pick-up voltage 80

31 Heating curves (carbon tetrachloride and glycerine) 81 32 Oscillograph traces of, pick-up voltage and photomultiplier anode voltage (many sweep) 83 33 Oscillograph traces of pick-up voltage and photomultiplier anode voltage (Many sweep) 83 34 Oscillograph traces of pick-up voltage and photomultiplier anode voltage (Single sweep) 85 35 The Housing 87

36 Spectral sensitivity of photomultiplier 89

37 Potential divider 90 No2 Page

38 Integrator 91

39 Circuit for calibration of integrator 92

40 Calibration of integrator 94

41 Photograph of general assembly 96

42 Sonoluminesconce as a function of hydraulically applied excess pressure (6.5 watts) 99

43 Acoustic power absorbed as a function of hydraulically applied excess pressure 100

44 Sonoluminescence as a function of hydraulically applied excess pressure 102

45 Sonoluminescence as a function of hydraulically applied excess pressure (pick—up voltage constant) 103

46 Sonoluminesconce as a function of hydraulically applied excess pressure (8.2 watts) 104

47 Sonoluminescence as a function of hydraulically applied excess pressure (6.95 watts) 105

48 Sonoluminescence as a function of hydraulically applied excess pressure (5.2 watts) 106

49 Sonoluminescence as a function of hydraulically applied excess pressure (power values in region for which optimum excess static pressure = 0 p.s.i.) 107

50 Sonoluminescence as a function of hydraulically applied excess pressure (3.3. watts) 108

51 Shift of maximum with power 110

52 Shift of suppression point with power 111

53 Sonoluminescence as a function of gas applied excess pressure (6.5 watts) 112

54 Sonoluminescence as a function of gas applied excess pressure (5.4 watts) 113 NO: Page.

55 Sonoluminescence as a function of gas 114 applied excess pressure (4.15 watts)

56 Sonoluminescence as a function of gas applied excess pressure (2.13 watts) 115

57 Resonant frequency as a function of gas applied excess pressure 118

58 Single sweep oscillograph traces of pick—up voltage and photomultiplier anode voltage. (0 p.s.i. excess pressure) 119

59 Single sweep oscillograph traces of pick—up voltage and photomultiplier anode voltage. (6 p.s.i. excess pressure) 119

60 Single sweep oscillograph traces of pick—up voltage and photomultiplier anode voltage. (20 p.s.i. excess pressure) 120 61 Maximum liquid pressure and maximum bubble radius as a function of static pressure 128

62 Spectrum of nuclei sizes in tap water 131 63 Acoustic power absorbed as a function of static pressure 133 64 Hypothetical variation of sonoluminescence with static pressure 133

65 Radius—time curve and adiabatic temperature 148 66 Low temperature approximation 159

67 High temperature approximation 160 1 SURVEY OF SONOLU1aNESCENCE AND OTHER CAVITATION PHENOMENA

1. 1.1 Definitions and Historical Review.

During an investigation of emulsification by ultrasonic cavitation

Marinesco and Trillat (1) in 1933 and Marinesco and Reggiani (2) in 1935 observed the production of latent images in silver halide emulsions on photographic films and plates immersed in water. They ascribed this action to an acceleration of the chemical process of oxy-reduction brought about by the acoustic radiation, but Frenzel and Schultes (3), having made similar experiments, believed that the effect was actually due to exposure to light. Chambers (37) first called this light "sonic-luminescence" and the contracted term "sonoluminescence" is generally used although the evidence now points to its being of thermal origin i.e. an "incandescence" and not a "luminescence" which according to current definitions is light not primarily caused by conversion of thermal energy. The term

sonoluminescence" will however be used throughout this thesis to conform with current practice.

In over thirty publications on experimental work no report has been given of the appearance of sonoluminescence without the simultaneous occurrence of cavitation, except in the case of "luminol" (tri-aminophthalic hydrazine) when a very bright light is observed which persists for about a twentieth of a second after cavitation ceases. This is attributed mainly to chemiluminescence excited by oxidation products of cavitation. Sono- luminescence may thus be defined as light which appears during the cavitation of liquids.

Cavitation is the process of production of cavities or bubbles in a

liquid and can be caused by boiling, by passing steam into cold water,

by the flow of a liquid through a narrow orifice or around an obstacle, by

the rotation of ships' propellers or by the application of acoustic fields 2 of a few watts/cm . Cavitation can occur without the presence of sono-

luminescence, as Harvey (4) showed in the case of boiling and Polotskii (5)

by passing steam into cold water. It is also probable that'sonoluminescence

does not occur in those instances of hydrodynamic cavitation mentioned

above, but this question will be discussed further in section 1.4. Even in the case of ultrasonic cavitation, sonoluminescence does not always appear,

for instance engassing water with hydrogen causes its suppression.

The luminescence is only just discernible in cavitated tap water by

a well dark-adapted eye as a faint bluish glow, but it is stronger in

glycerine and much stronger in mercury. The addition of a few drops of

carbon tetrachloride or carbondisulphide to tap water or its saturation

with inert gases enhances the luminescence.- Previous reviews of the literature have been given by mw 'Jarman (6) and El'piner (7).

1.1.2 Instrumentation for Observing Sonoluminescence.

Much of the earlier work was carried out by visual inspection, although

some workers have used photography to obtain quantitative measures both of

the total light intensity and its spectral distribution. More recently

photomultipliers and photocells have been employed. The use of photo- TABLE 1 : INSTRUMENTATION OF SONOLUMINESCENCE STUDIES.

Abbreviations:

D.A. : Displacement amplitude E. t Eye E.M. : Electromagnetic m/s : Magnetostriction P.A. : Pressure Amplitude P.C. : Photocell Ph. : Photography P.M. t Photomultiplier. uo AUTHOR REFERENCE DATE METHOD OF FREQUENCY ACOUSTIC OBSERVATION PRODUCING POWER INSTRUMENT. CAVITATION

Marinesco and Trillat 1 1933 Quartz 4.28 ke/S 80 w/cm2 Ph. 1.43 Mc/s

Frenzel and Schultes 3 1934 Quartz 500 kc/6 — Ph. 2 Marinesco and Reggiani 2 1935 Quartz 428 kc/s 80 w/cm Ph. Chambers 27,37 1936 m/s 8.9 kc/s — E Levshin and Rzhevkin 28 1937 Quartz

Pasunoff 15 1939 Quartz . 4)0 1cc/s — Ph. Harvey 4 1939 Quartz 550 kois — E. Pinoir and Pouradier 16 1947 Owarz 330 kc/s — Ph.

AUTHOR REFERENCE DATE METHOD OF FREQUENCY ACOUSTIC OBSERVA- PRODUCING POW at TION CAVITATION INSTRUMENT.

Polotskii 5 1948 36-97 w Ph. generator

Prudhomme 25 1949 Quartz 960 kc/s 76 w Prudhomme & Bus so 43 1952 Quartz 800 to/- s 9) w P.C.

Griffing and Sette 9 1955 Quartz /1 m/c 8 w/cm2 • i 2 WC

Srinivasan 39,40 1955 Quartz 800 kcis Parke and Taylor 10 1956 Quarti 0.50,2 Mcis 7.- Prud.howhie and Guilmart 29 1957 Quartz 960 kcis 90 w P.C.

Gunther et al 8 1957 Quartz 30,80,175 ' 300,1000 kcis 13.5 wicm Ph.

CUnther et al 33 1957 30 kc/s Wagner 13 1958 B44.0 50-260 kc/s 3 w/cm2 P.M. 3 Schmid. 48 1959 Chestorman Technique - - P.M. Jerman P.M. 4.1 1959 m/s 25 kcis 35 w AUTHOR REFERENCE DATE METHOD OF FREQUENCY ACOUSTIC OBSERVATION PRODUCING INSTRUMENT CAVITATION

Meyer and Kattruff 22 1959 m/s 2.5 kc/s 0.03cm D.A. P.M.+Ph. Gunther et al 44 1959 Quartz 294 kc/s 7.5 w/cm2 P.M. Heim 45 1960 Quartz 294 kc/s 7.5 w/cm2 Ph, Negishi 12 1961 Ferrite 28'keis - P.M. BaTiO 470 kc/s 3 Kattruff and Plass 24 1961 BaTiO, 30 kcis 1.8 at P.A. P.M. \JI + Horri 1 Degrois and Badilian 32 1962 Quartz 1 Mc/s 5w/cm2 P.M. Rosenberg 14 1962 Quartz Arrar 5 Mc/S 3000 w/cm2 P.M. Schmid 52 1962 Collapsing Glass Sphere - - P.M. Kattruff 38 1962 BaTiO + 25 kc/s - Ph. Glass Horn Mercury Agitation - - Ph. multipliers led to the discovery that sonoluminescence occurs as discrete flashes which are periodic with the sound field.

At first ultrasonic cavitation was produced by quartz crystals working

at frequencies up to the order of 2 Mc/s. Magnetostrictive and piezoelectric

ceramic transducers operating at frequencies from 1 — 30 Kc/s have also been

employed. Cavitation produced "hydrodynamically" in glycerine has also been

observed to produce sonoluminescence. When a glass sphere containing gas

at reduced pressure is broken in a liquid the ensuing collapse gives rise to

a flash of light. Bubbles of gas at atmospheric pressure can be caused to

collapse by the sudden incidence of a high pressure pulse, and this process

also entails the production of a light pulse. In these latter types of

investigation the light has the same origin as sonoluminescence in all

probability. A summary of the methods of production and observation of

sonoluminescence used by various workers is given in Table I.

1.2 Dependence of Sonoluminescence on Various Parameters.

The details of experimental findings on the variation of sonoluminescence

with the various parameters, frequency, power etc., will now be summarised.

1.2. 1 Frequency: No worker has so far made a deliberate study of the

variation of sonoluminescence over the complete acoustic frequency range.

A decrease in the luminescence intensity with frequency was reported by

Gunther et al (8) who made observations at 30, 60, 80 and 100 Kc/s. A

similar conclusion is to be drawn from the work of Griffing and Sette (9)

who used frequencies of 0.66, 1 and 2 Mc/s. Sonoluminescence has not been observed at frequencies greater than 2 Mb/S,

1.2 2.Acoustic Power and Pressure:

Griffing and Sette (9) observed a linear relation between sonoluminescence and acoustic intensity (Fige1) and this was substantiated by Parke and.

Taylor (10), who however reported that it was the equilibrium value which was involved and this was only attained after a few minutes of irradiation with a given acoustic power. Jarman (11) also reports that the luminescence yield increases with power up to values of about 35 watts.

Whilst those workers found an increase of luminescence intensity with 2 power, Negishi (12) reports a sudden cut off at only 2w/cm y in luminol as well as other liquids producing sonoluminescence. He found that the luminous flux varied in the same way both for increasing and decreasing p s t'a.cL power except that with decreasing power the luminescence tqgmainod below the threshold value for increasing power. Wagner (13) obtained oscillograms of luminescence pulses whose height increased with increasing acoustic pressure amplitude.

Recent work in Russia by Rosenberg (14,31) with a he.mi—spherical array of quartz transducers operating at 0.5 Mc/s, and producing a power flux of 2 120 K w/cm at the centre of a focal region has been used to determine the power dependence of sonoluminescence over a range far in excess of that possible hitherto. The results of these measurements are shown in Fig.2.

Here q7 is the collapse time and T the sound period, and the power flux

W=f.1:k ( T )2 where k is a constant:P.:1103 w/cm2. Sirotyuk (30), working 8

+Distilled water,CCI4 , A 0Distilled water,CC14 ,C0 Tap water

0 Tap water, CCI4

FIG.1 : LUMINESCENCE IN WATER SOLUTIONS AS A FUNCTION OF SOUND INTENSITY, FREQUENCY 1 Mc/s (Griffing and Sette)

1.5 0

0 I anode 1.0 voltage 0.5

0• . 0 0.5 10 1-5 2-0 2%/T------> FIG.2: RELATION BETWEEN SONOLUMINESCENCE

AND 2`C/ T ( Rosenberg) with Rosenberg, has also found that sonoluminescence starts to appear at a lower threshold value of acoustic pressure, which corresponds to that of cavitation itself.

The dependence of sonoluminescence upon power is consistent with its appearance at pressure maxima in standing wave fields. Parallel regions of luminescence in plane standing waves have been reported by Marinesco and Reggiani (2), Pasunoff (15), Pinoir and Pouradier (16), Gunther et al (8,17), Wagner (13) and Macleay and Holroyd (18). It is generally agreed that these luminescent planes occur at the maxima of pressure amplitude, although cavitation bubbles can appear at pressure nodes due to the effect of radiation pressure (19,20) or, possibly, Bjerknes (21) forces.

Sound focussing systems have been employed by Jarman (11), Negishi (12) and Rosenberg (14), and the luminescence then occurs at the focus where the pressure variation is a maximum. For large amplitudes of excitation of a transducer, cavitation and luminescence occur at the face of the transducer as was found by Meyer and Kuttruff (22) and Negishi (12). The use of a solid horn rigidly attached to the transducer face in order to increase the energy flux similarly produces cavitation and luminescence at the stub of the horn as was found by Jarman (23) and Kuttruff and Plass (24).

1.2. 3 Static Pressure.

The first experimental determination of the effect of static pressure on sonoluminescence intensity was made by Harvey (4). He applied pressure to water hydraulically by means of a piston and found by visual inspection that the luminescence and cavitation became intermittent at about 1.3 — 10 —

atmospheres excess pressure and disappeared at pressures above this value. On decreasing the pressure the light did not re—appear until about 0.8 atmospheres excess. Harvey also found that at slight excess pressure

(0.3 to 1 atmosphere) the light was brighter than with no pressure,while Pinoir and Pouradier (16) found an extinction at a reduced pressure. This latter result was also confirmed by Prudhomme (25) who also found an

extinction at excess applied gas pressure. Later Dusnel and Degrois (26)

found an extinction of the luminescence from luminol with, excess pressure, but the only quantitative work on the.subject was due to Polotskii (5)

who measured the optical density of photographic plates exposed to

luminescence from water at different gas applied pressures and at different acoustic powers. The form of his results is shown in Fig. 3.

1.2. 4 Temperature Chambers (27) was the first to report that the luminescence decreases

with temperature to extinction with the liquids investigated. Harvey

reported an extinction temperature of 40°C in water, the luminescence being

strong at 0°C. Parke and Taylor (10) found a linear temperature dependence from 5-50°C. Jarman (11) also found an almost linear decrease

from 25 — 80°C with several liquids, but a puzzling feature of his work is a sharp drop in luminescence at temperatures below about 25°C. anther

et al (8) found that the logarithm of the light intensity was linearly

related to the temperature from 0 — 35°C although the slopes of the lines

were less for 2N electrolytic solutions. Their results are shown in Fig.4. 11

1; 36.3w: glass window 1 optical density 2:36-2w:quartz window 040 3:63.2w: quartz window

0.30 4: 97.0w: quartz window 0.20

0-10

o 0 3s. 7691 40 Ku, 2.290 3040 pressure.-----).

FIG.3: SONOLUMINESCENCE OF WATER AS A FUNCTION OF APPLIED PRESSURE ( POlotskii)

log. units log. un it s . units

2.0 N .X , 2 nKCl2-0 2-0

Ng 1.5 1.5 Kr 2nNaCIN1 K

* 1.0 1.0 1.0 , 2. c' itt ill -.....„02,1n NaCI 0.5 *---...... * 05 0.5

N* -0.5 0 10 20 30 t ,0 20 30 0 10 20 30

FIG.4: TEMPERATURE DEPENDENCE OF SONOLUMINESCE NC E FROM VARIOUS AQUEOUS SOLUTIONS (Gunther et al) — 12 —

1.2. 5 Time Effects.

Sonoluminescence consists of discrete flashes of light whose appearance is periodic with the stimulating sound field. The eye cannot generally distinguish such rapid fluctuations and will actually register an average value of the luminescence intensity. This average intensity can however vary with time, and Fig.5. is a schematic diagram to illustrate the various time effects that can•be observed. (i)Variation of average intensity of luminescence on initiation of cavitation.

Levshin and Rzhevkin (28) were the first to report that the luminescence took some minutes to develop and this time dependence was also observed with water by Parke and Taylor (10) who found that the luminescence rose gradually to an equilibrium value. They ascribed this process to de—gassing. The same effect was found by Jarman (11). Prudhomme and Guilmart (29), however, found that the luminescence declined for the first few minutes of irradiation, but it should be noted that the water in their experiments had been first de—aerated and then saturated with various pure gases.

(ii)A ReIaxatio.n. Time Variation.

Recent papers by Degrois and Badilian (32) report the occurrence of what is termed a "relaxation phenomenon ". They found that the cavitation noise, the yield of iodine from a KI solution, and the occurrence of sonoluminescence undergo sharp changes periodically. The nature of the changes in the sonoluminescence is shown in Fig. 6. They

'IL (2 A

onoluminescence

time

initial variation of mean intensity FIG.5 :SCHEMATIC short time periodicity REPRESENTATION OF sound field TIME EFFECTS

luminescence

10 15 20 t(min.)

FIG.6 : RELAXATION TIME VARIATION

OF SONOLUMINESCENCE (Degrois& Badilian) - 13 - ascribe the effect to changes from "gaseous" to "vaporous" cavitation caused by small temperature changes.

(iii) Short time periodicity

Gtnther et al (8) were the first to report a short time periodicity of the light emitted from irradiated water. They did this by photographing the oscillogram of the anode voltage of an eleven stage photomultiplier, receiving light emitted at the pressure antinodes of a standing wave in water irradiated at 30 Ko/s and then at 80Kc/s. The light was found to fluctuate at double the frequency of the sound, and it was therefore concluded that the emission of sonoluminoscence has a fixed phase with respect to the alternating sound pressure. The work was extended by

Gunther et al (33) with a view to establishing this phase relation.

They also observed the light from a standing wave in water at 30 Kcis, using a separation of 21 cm between a magnetostrictive oscillator and a reflector and so allowing the light from five pressure maxima to be investigated. They then compared the anode voltage from a photomultiplier,

"trained" on each maximum in turn, with the driving voltage of the transducer by displaying them on a double beam oscilloscope. They corrected for phase shift between the anode current and the oscilloscope trace by subsidiary experiments and also correlated the driving voltage with the pressure at successive maxima. They found that for odd numbered planes a light pulse occurred shortly before the end of the pressure phase of the sound pressure variation. For the intermediate even — 14 — numbered planes there was a phase shift of 180° relative to the driving voltage, which again suggests that the light occurs before the end of the pressure phase. With a greater resolution they found that the pulse in fact consisted of a number of discrete flashes whose duration they concluded must be less than 10-7 sec. It is interesting to note that

Harvey (4) in 1939 observed no movement of the luminescent region with fluid velocities of up to 200-300 cm/sec in water and concluded that 3 the luminescence could not have persisted longer than 10 sec.

Wagner (13), also investigating the short time periodicity of sonoluminescence in a plane stationary wave, similarly found the light was emitted from the pressure antinodes, and that it had a duration of less. than 4.10-7 sec. In contrast to anther et al, however, he found that the light was emitted shortly before the instant of minimum sound

pressure. He arrived at this conclusion by simultaneous observation of oscillograms of the luminescence pulses from one pressure antinode and the output of a small Barium titanate microphone in the same pressure antinode. He also found that there was an optimum acoustic pressure

amplitude of from 1 - 2 atmospheres for producing luminescence, and that this maximum value of luminescence depended very much on the gas content of the liquid.

Jarman (11) observed luminescence pulses from a number of liquids

and reported in 1959 his agreement with Wagner that the light was emitted at the time of minimum sound pressure, which he confirmed with the use of a hydrophone. As will be shown in section 1.6 the phase of the 1, luminescence pulse is an unequivocal test of theories upon the origin of sonoluminoscence and thus the disagreement in the results of Tanther et al on the one hand and Wagner and Jarman on the other stimulated several other workers. The uncertainties in this work lay in the use of hydrophones to deduce the bubble radius from the pressure variation and to determine the phase of the luminescence flash with respect to the

pressure variation.

For this reason Meyer and Kuttruff (22) sought to make a direct correlation between the phase of the luminescence flash and the volume

of the cavitation bubbles, by producing cavitation bubbles on the end face of a nickel rod magnetostrictively - excited at 2.5 Kcis. At this frequency the bubbles were large enough to be seen and they used the

actual sonoluminescence flash to produce a voltage pulse which activated

a flashlight. The end surface of the nickel rod (12 mm diameter, 1 m in

length) (Fig.?) was thereby illuminated and by delaying the activating

pulse by various amounts, a series of photographs showing the life cycle

of the cavitation bubbles was obtained. These photographs (Fig.8)

showed clearly that cavitation bubbles started to appear half way through

the sound period, grew to a maximum and collapsed rapidly. The sono -

luminescence flash occurred at the and of the collapse.

This work of Meyer and Kuttruff was extended by Kuttruff and Plass (24)

at 30 Kc/s using a barium titanate rod coupled to a Mason horn. The

method of photographing the bubbles at various phases was similar to that

employed in the earlier work. Again the luminescence was observed at the 16

FIG.7:APPARATUS

OF MEYER AND KUTTRUFF

\i'l amplifiers V 2 P:phaseshifter IG: impulse generator F.spark light source (detail below)

0,IIN f§V0 #51N

10

PL36 _i_ #410V F _Lei

O ,T -750V MM IOW

0 :10 60' 900

4111112w

120- 1500 1800 210'

41C. hmaw

240- 270' 3110 330-

FIG.8 GROWTH AND COLLAPSE OF CAVITATION BUBBLES (Meyer and Kuttrufl) SONOLUMINESCENCE FLASHES AT O° and

360° OF SOUND FIELD. v 360 - 18 -

end of the collapse.

The appearance of the luminescence at the minimum bubble volume was also demonstrated by Negishi (12,34) who used a photomultiplier, to

measure the amount of light scattered by cavitation bubbles at right

angles to an incident light beam. A high anode current thus denoted

a large bubble volume and so an oscillogram record of the bubble volume

was obtained. When the source of illumination was turned off a trace

of the luminescence was obtained instead. By means of doubly exposed

photographs these'two traces could then be compared.

Two further determinations of the phase of the luminescence flash

with respect to the pressure cycle were also reported. One by Gunther

et al (35) using a new experimental arrangement, and one by Maclean and

Holroyd (18) who used a light guide to obtain histograms of the light

distribution in a standing wave field at 400, 600 and 1200 Kc/s. They

correlated this distribution with the sound field using the Debye-Sears

effect.

Another technique that has been used to show that the luminescence

flash occurs at the end of the bubble implosion is by demonstrating the

simultaneity of the flash and the creation of the liquid-borne shock.

This technique was first employed by Gunther et al (35) who were able

to demonstrate the simultaneity of the flash and the peak of the pressure

pulse.

The occurrence of secondary flashes has been reported by Wagner (13), -19

Jarman (11) and Negishi (12). The latter found that the secondary flashes occurred at the same time as a secondary pressure peak appeared in the sound pressure, detected with a miniature barium titanate hydro- phone, and as a small dip appeared in the curve of the bubble volume. (Fig.9). He explains the phenomenon, on this evidence, as being due to a rebound and second collapse by some of the bubbles.

1.2. 6. The Physical Properties (Surface Tension Viscosity and Vapour Pressure of the Liquid Medium.

(i) Pure Solvents.

Zimakov (36) in 1933 was the first to observe that sonoluminoscence occurred in some liquids, but not in others, as was confirmed by Levshin and Rzhevkin (28). In 1936 Chambers (37) investigated 36 pure liquids and found 14 which showed sonoluminescence, the light being brightest in glycerol and nitrobenzol. He concluded that there was a correlation between the luminescent intensity and the product of the molecular dipole moment and the viscosity of the liquid, although as has been pointed out by Jarman (11) this relationship only appears to hold for a particular homologous series of alcohols with similar dipole moments and viscosities.

Jarman investigated some 20 pure liquids with widely different properties and values of the relative intensities with different liquids are given in Table 2. He found that the best correlation was obtained 2 between sonoluminescence flux and the square of the surface tension, S 20

Fig. 9. Volume change of cavitating bubbles with small dips and sonoluminescence with secondary flashes (indicated by arrows). — 21 —

TABLE 2: Relative intensity of sonoluminescence from various liquids at three different temperatures.

Relative intensity of sonoluminescence

Liquid 25°C 40°C 55°C Dimetbyl phthalate 16 6.6 2.4 Ethylene glycol 12 3.4 0.5 Tap water 3.6 1.0 Chlorobenzene 0.84 0.43 0.20 Isoamyl alcohol 0.54 0.28 0.18 0—Xylene 0.36 0.24 0.14 Secondary butyl alcohol 0.30 0.17 0.086 X. butyl alcohol 0.21 0.10 0.030 Isobutyl alcohol 0.17 0.088 0.046 A k. Propyl alcohol 0.21 0.076 0.038

Toluene 0.15 0.074 0.050 Benzene 0.23 0.060 0.010 Tertiary butyl alcohol — 0.050 0.025 Isopropyl alcohol 0.054 0.028 0.012

2N NaCl 25 2N EDI 20 2N MgC1 2 15 2N lInC12 5 1N N aCl 10 Sea water 10 -22— divided by the vapour pressure, pv, of the liquid, as is shown in

Fig.10.

The discovery ofTthis empirical relationship drew the attention of Kuttruff (38) to the case of Mercury, for which the ratio S2/pv is

75,000 times greater than for water. In order to observe the luminescence it is necessary to procure cavitation adjacent to a transparent surface, which Kuttruff did by employing a quartz Mason horn coupled to a tubular barium titanate transducer operating at 25 1c/s. The light then travelled up the horn and through the hollow transducer to be registered on a photomultiplier. It was found that the intensity of the luminescence

of mercury was much greater than that from ethylene glycol observed under

the same conditions. Kuttruff points out however that it should be remembered that this value would not be so great, but for the fact that

mercury reflects light that would not otherwise reach the observer.

(ii) Solutions and Liquid Dispersions.

Those liquid media may be considered to fall into four classes :

electrolytic solutions, suspensions and colloidal solutions, solutions of organic compounds, and gaseous solutions, the last two being considered in the following section.

Harvey (4), investigated visually the luminescence from various inert suspesnions (zinc stearate, talc, infumrial earth, pumice and kaolin) and concluded that, the intensity of the luminescence was independent of the suspended substance. He also found no appreciable change with an olive 1.dirnethyl phthalate 23 2.ethylene glycol 3 .tap water 4.0-xylene 10_ th 5. isoamyl alcohol 6.chlorobenzene 0 7.n butyl alcohol E 8. isobutyl alcohol E 9. tol uene c\i": 10. secondary butyl alcohol 1 11.n propyl alcohol —No 12. isopropyl alcohol 0 13.ethyl alcohol 2 14. benzene 7:3 15.tert iary butyl 0 alcohol

4 o0 o o 6 7 8o 001_ 9 1111 °° °10i0 120 o 014 F IG.10 13 15 Sonol uminescence Flux at 40°C (JARMAN) 0001 I 0.01 01 1 10 -24-

oil emulsion or colloidal solutions of ferric hydroxide or starch, but

that the luminescence from a mercury emulsion was 'rather bright'.

He found that fairly weak electrolytic solutions (1 Normal) of

various acids, alkalis and salts again showed little dependence on the

nature of the dissolved substance, and that an increase in the strength

of aqueous solutions of NaCi, NH4C1, CaC12 (to saturation) did not affect

the luminescence except in the case of ammonium sulphate, which was

'rather bright'. Parke and Taylor (10) also found that the dissolving

of H2SO4,01, KNO3, K2SO4 and KH2PO4 caused no significant change in

luminescence. ainther et al (8) investigated the effect of electrolytes

on the spectrum, and as was discussed in section 1.2.4 on the temperature

dependence of the total intensity, they found an increase in the intensity

with addition of an electrolyte• Jarman (11) found that low salt

concentrations initially depressed the luminescence yield which then

returned to about that of tap water. He found however that 2N solutions

of various salts could increase the luminescence yield by factors of up

to seven in the case of NaCl, as is shown in Table 2. Negishi (12) also

found that 2N NaC1 solution showed enhanced luminescence, but only by a

factor of two. He also found that increasingly strong solutions of NaHCO 3 progressively inhibited luminescence. Negishils results are shown in

Fig.11. 25

luminous flux (relative) 20 1.0 0.5 0.2 2 0.1 3,45 i,7 0.05 8 0.02 001 I is I 1 0 10 20 30 40 vibrometer output (volts)

FIG.11:INTENSfTY OF SONOLUMINESCENCE FROM AQUEOS SOLUTIONS OF VARIOUS SODIUM SALTS AS A FUNCTION OF VIBROMETER OUTPUT (Negishi)

1. tap water 2. 2n Na2CO3 3. 2n NaCI 4. 2n Na 5 0 2 2 3 5. 2n NaNO3 6. 2n NaSO3 7. 2n Na NO2 8. 1n Na2SO3 9. 0.5n NaHCO3 10. in NaHCO3 -26-

1.2. 7 The Physical Properties of the Solute Gas

(i)Low Boiling Point Gases.

Harvey (4) was the first to study the effect of the dissolved gas on sonoluminescence, observing that it appeared with air, oxygen, neon and weakly with nitrogen. It did not howover appear with hydrogen or carbon dioxide. The luminescence from even quite dark bromine water was however comparable in intensity with the bright sonic chemiluminescence of luminol. Chlorine water also luminesce(' more brightly than distilled water, but iodine solution showed no enhancement. Pasunoff (15) reported only finding luminescence with air or oxygen and not with carbon monoxide, hydrogen or nitrogen, a result confirmed by Polotskii (41). Griffing and

Sett° (9) using aqueous solutions of carbon tetrachloride saturated with various gases also made qualitative estimates of the intensity of sono- luminescence and found it to be strong for Argon and neon, medium for nitrogen, weak for CO and SF6, quite weak for freon 114 and non- existent in the cases of hydrogen and carbon dioxide.

Srinivasan and Holroyd (39), Parke and Taylor (10) and CAnther et al (8) obtained measurements of relative intensities using photomultipliers and their results are presented in Table 3 using oxygen as a standard. Prudhomno and Guilmart (29) used a photocell sensitive in the ultra- violet to investigate the luminescence from water saturated with light gases, and their results are also shown in Table 3.

(ii) Volatile Organic Additives.

A number of volttile organic compounds influence the nature of sono- 27

TABLE 3: Effect of dissolved gas on the intensity of sonoluminescence from water.

Relative intensity of sonoluminescence

A

Gas

Xenon 540 6700 Krypton 180 2000

Argon 54 95 290 Nitrogen 45 20 35 Oygen 35 35 35 35 Air 20 77 Neon 18 Helium 1 5.5

A: Prudhomme and Guilmart (29) B: Srinivasan (40)

C: Gunther et al (8) D: Parke and Taylor (10)

Oxygen was used as a standard to compare the results of

the various authors. -28- luminescence when present in solution. Such effects were first studied by Harvey who added 1 drop of a number of fluids to 10 cc of water and found that propyl, butyl, amyl and capryl alcohols, ethyl butyrate, amyl acetate, ethyl ether, P.P-dichloroethyl ether and 1.4-dioxane prevented luminescence, that toluene, thiophene, petroleum ether and aniline allowed a faint luminescence, while carbonYbetrachloride, chloroform, 0-:wlene, nitrobenzene, benzyl alcohol, paraffin oil, olive oil, n-butyl phthalate, bromoform and bromobenzene did not effect the sonoluminescence of water.

With carbon disulphide in water the luminescence was brighter than with pure water alone. Griffing and Sette (9) reported that carbon tetrachloride had an enhancing effect on the luminescence. Parke and Taylor (10) reported that with CS2 the luminescence was twelve times greater than with oxygen. They also made spectral measurements on the luminescence of CS2 which will be discussed in the next section. Jarman (11) found with CS 2 an increase of ten times the value from tap water, and of three times with

CC14. Negishi (12) also obtained quantitative values of relative luminescence from a number of aqueous solutions of organic solvents and these are shown in Table 4.

1.3 The Spectra of Sonoluminescence.

Spectral photographs of sonoluminescence from petroleum with exposure times of 12 - 48 hours, were made by pasunoff (15) who found a region of relatively intense continuum of luminescence between 4450 and

5580 R. Kling (42) found that the spectrum of the luminescence from bromine -29—

TABLE 4: Relative intensity of sonoluminescence from aqueous

solutions of organic liquids.

Liquid Relative intensity of Formula Name s ono lumi ne s o enc e

CS Carbon disulphide 11 2 Br Bromine 10 2 CH I Methyl iodide 3 7 001 Carbon tetrachloride 4 3.5 C HC1 Trichloroethylene 2.7 2 3 C6H5Br Bromobenzene 1.0

C H NH 0.75 6 5 2 Aniline (H20) 0.40 C H Benzene 0.25 6 6

o0o - 30 - water contained the bromine emission spectra with its two prominent bands.

This result was confirmed by Parke and Taylor (10) who also found a band starting at 3700 2 and stretching to the limit of resolution of the spectrometer in the spectrum of luminescence from 082 solution. Parke and Taylor believed the absence of an ultra-violet component was suggested by the fact that the luminescence from air saturated water measured with a photomultiplier sensitive down to 2200 R showed no change on adding sodium salicylate which fluoresces when excited by light of from 950 to 3400 However Polotskii (5) was able to show that when sonoluminescenco was viewed through a quartz window, the intensity was much greater than when viewed through a glass window. Prudhomme and Busso (43) used a photocell sensitive to the ultra-violet and found measurable intensities of light from solutions of various gases. Gtinther et al (8) using various optical filters were able to demonstrate the presence of wavelengths from the infra rod increasing in intensity through the visible to a maximum in the ultra-violet. They also demonstrated an absorption diminution of ultra- violet radiation with increasing hydrogen peroxide concentration. As hydrogen peroxide is frequently created during cavitation this might explain the earlier reports of the absence of an ultra-violet component.

The spectrum of sonoluminescence is generally a continuum as has been found photographically by Pasunoff (15) and Gunther et al (8). The latter found that the addition of electrolytes to the cavitated solution caused the emission of lines and bands characteristic of the metal radicals, as well - 31 - as a general enhancement of the background continuum, as is shown in Fig.12, The sodium D lines appear very clearly but showing a typical assymmetrical broadening on the long wavelength side. Irradiation with p particles considerably reduced the intensity of these lines. Studies of the spectral intensity distribution- using photomultipliers were made by Srinivasan (39, 40) and Uanther et al (44). Srinivasan found that this distribution fitted closely to the curve of black body radiation for 8800°K in the case of oxygen and nitrogen and for 1100°K in the case of argon and helium. Onther et al investigating xenon and argon solutions found an equivalent black body temperature of 6000°K however. Further investigations of the assymmetrical broadening of the sodium D lines with 2N xenon saturated NaC1 solution was made photo.;,- graphically by Heim (45) using a reflection grating giving a dispersion of 24 2/Mm Heim used a 500 hour exposure time, taking precautions to ensure that the temperature of the spectrograph did not vary by more than half a degree, A photometer was used to give a trace of the intensity distribution. This showed that on the short wavelength side the D lines wore sharp but that there was a gradual fading over some 120 a on the long wavelength side.

1.4. Sonoluminescence in Hydrodynamic Cavitation. Harvey (4) studied cavitation induced by flow through Reynolds and

Venturi tubes but was unable to detect any luminescence. Bresler (46) and Rasmussen (23) have also stated that they were unable to detect any

FIG.12. 31A. a)Continuous spectra for film calibration. Three sensitivity maxima. wilmosm.. mom NoikoNFXd b)Sonoluminescence of satura- ted solution of xenon in water. 96 hour exposure time. 650 600 5 111111Ki.g c)Xe-aiMgC12 solution. (12 hours)

.- Mk. 656 600 550 501 4-50 400 d)Kr-2nMe12solution. (30 hours)

65C •CO) 550 450 400 e)Xe-2nLiC1 solution. (12 hours)

m 650 600 550 501 450 400 f)Kr-2n NaC1 solution. (24 hours)

650 600 550 500 450 400

g) Xe-2n NaC1 solution. (12 hours)

650 600 550 500 450 .do

h)Xe-2n CaC12 solution (12 hours)

650 600 350 500 450 400

i)Xe-2n SrC1N 2 solution (24 hours)

65C 600 550 500 j)Xe-2n BaC12 solution (24 hours)

556 600 559 k)Xe-2nNaCl solution + 0.05gm (6 hours) SrC12/100 cm3 ._ 650 .00 550 500 450_ 40.) 1)Xe-2n NaC1 solution + 40m Curie 0 irradiationa line suppressed. g7; 1.17177;:l 50* - 4.40 4, ' -32— luminescence during hydrodynamic cavitation. Jarman (23) reports observations made with a photomultiplier of cavitation around an aerofoil but found that if there were any luminescence present that it was scarcely detectable.

On the other hand KonstantinoV (47) who observed cavitation from the trailing edge of a cylindrical obstacle reported the occurrence of 64%40. flashes of luminescence some 0.2 — 0.3 mm long bed the obstacle. These flashes were bright with a bluish tinge. Around the junction of the caviikation region flaeles with a diffuse yellowish tinge occasionally appeared. Those phenomena appeared with a critical cylinder length, a critical water velocity and not when the cavitation separated from the cylinder.

So far only one indisputable example of sonoluminescence occurring during hydrodynamically induced cavitation has been reported. The

Chesterman technique of inducing cavitation consists essentially of imparting a rapid upward momentum to a vertical tube closed at the bottom and filled with a 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, Schmid (48) was able to obtain a single bubble which grew to over a centimetre in diameter, before collapsing rapdily.

When the liquid medium was glycerine, luminescence was observed. 1.5. Light from Collapsing Bubbles. 1.5.1. Light from Agitated Mercury.

Some recent experiments by Kuttruff (38) on luminescence associated with mercury recall the researches described in Harvey's "A History of Luminescence " (49). The first barometer was constructed by Toricelli and Viviani in 1643. In 1675 Jean Picard noticed a glow above the mercury in a barometer when carried about in a dark room. One of the remarkable dharacteristics of the light was its appearance when the mercury moved downward but not when it was moving upward. In 1700 Johan

Bernoulli described finding that pure mercury in a clean phial well exhausted of air gave a brilliant light whenever the tube was shaken.

In 1701 with particularly clean mercury and a particularly clean phial he was able to obtain light even when the phial was full of air. The light "appeared only like separate sparks, which arose successively and perished almost at the same time, whereas the light in the vacuum is like a continual flame which lasts incessantly while the quicksilver is in agitation".

Another description of the phenomenon was given by Francis

Hausksbee in 1709. When mercury was shaken viblently in a globe containing air at atmospheric pressure "Particles of Light appeared plentifully, about the bigness of small pinheads, very vivid, resembling bright twinkling stars.." When the same vessel was exhausted, "the mercury did then appear Luminous all round, not as before, like little - 34 - bright sparks, but as a Continued Circle of Light during that motion".

A rolling motion of the mercury was necessary in the latter case.

A number of publications on this type of phenomena appeared during

the year 1710 - 1719 and notably a dissertation by J.M. Heusinger in 1716.

Heusinger noted that small air pockets sometimes observed along the sides

of a barometer tube could emit light. He found that evacuation was

generally preferential, and that water inhibited the luminescence. He

found that a lead-mercury amalgam could also produce light.

The phenomena has recently been re-examined by Kuttruff (38)

who concluded that there were two emission processes involved:(i) a

bluish light which can be continuously excited by a rolling of mercury

in a partially evacuated tube and (ii) a reddish light of short duration

arising from bubbles created and collapsed by shaking the tube.

Kuttruff was able to show that the two types of light were not only distinguishable by their duration but also in their spectral structure.

A spectral analysis of the bluish light obtained with a two hour exposure of the light from a tube continuously rotated by a motor showed lines, the 4360 R line being particularly bright, with littlo background continuum. The reddish light however showed a strong continuum with a maximum in the red. On this basis Kuttruff concluded that the first typo was electroluminescence, whilst the second was sonoluminesconce. -35-

1.5. 2. Collapsing Glass Spheres. It is interesting to note that glass spheres containing air at reduced pressure when broken in air were observed to emit luminescence by Beccaria (171-6-1781) a description of whose experiments was given by

Priestley (49) in 1769: "Signor Beccaria observed that hollow glass vessels, of a certain thinness, 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 dashi of the external air against the inside, when it was

broke".

Work of a similar nature to Beccarials experiments has recently been carried out at the Armour Research Foundation (50), flashes of light

having been observed upon the breaking of glass tubes containing gas

at reduced pressure. Some work on converging spherical shock waves

obtained by breaking glass spheres in air has also been reported by

Glass (51).

With the object of overcoming difficulties inherent in ultrasonic

investigations of the influence of gases on sonoluminescence a technique

has been developed by Schmid (52) to model the collapse stage of

cavitation under more certain conditions. A thin—walled glass sphere

(radius 7.0cm) immersed in a liquid was evacuated and then filled with

various gases at low pressure. On breaking the glass wall an implosion — 36 — occurred which resulted in the emission of light. It was established that no triboluminescence occurred when the glass broke, and that the sphere truly imploded and did not gradually fill with liquid. A high speed cinematographic record of the event showed that during the collapse, which lasted for 4 ms altogether, the bubble walls accelerated until the imploding volume divided into a number of parts which continued to implode, giving rise to strong shock waves in the liquid and regions of luminescence. Unfortunately, the glass fragments of the sphere made it difficult to distinguish the imploding bubbles.

The time dependence of the total intensity was displayed on the screen of an oscilloscope. In general there were several light impulses from one implosion. The breadth of these impulses increased from less than 20 n sec for a fully evacuated sphere to about 20 u sec for 30 mm 'filling pressure', the pulse height varied also from 19 units with a fully evacuated sphere to 0.8 units at 30 mm filling pressure.

Thus for observing luminescence there was an optimum range of filling pressures of from 10 — 20 mm.

Using glycerine as an experimental liquid a number of experiments were made with different filling gases. Due to the instability of the spherical form of the collapsing sphere there was a large scatter in the results and some 275 individual measurements were made, and average values taken. The results are shown in Fig. 13. Other experiments were made with mixtures of gases. 37 radiation strength 100 CCI

10

0.1 C2 Hs)a0

filling y, 10 20 30 60 pressure(torr)

FIG.13: RADIATION STRENGTH OF B.R1GHTEST LIGHT

IMPULSES AS A FUNCTION OF FILLING GAS AND

PRESSURE (Schmid) 100 tradiation strength

lycerine 88°/o

10 glycerine 30°/o

11/4:

\1--water ‘1, filling 0- 10 10 20 30 40 pressure (torr) FIG.14:RADIATION STRENGTH OF BRIGHTEST LIGHT

IMPULSES AS A FUNCTION OF LIQUID (Schmid) - 38 -

The results of experiments made with different experimental liquids are displayed in Fig.14, These experiments showed that a low vapour pressure and high viscosity were desirable for bright luminescence, although the intensity of the luminescence did not depend so critically on the liquid as on the gas.

1.5.3. Implosion of Bubbles by Shock Waves.

It is also possible to collapse a small bubble in a liquid whore the bubble content is at atmospheric pressure by the incidence of a powerful shook. Light is thereby evolved and the effect has been used by Travis (53) to mark the entry of a shock on smear camera photographs of detonations of liquid explosives.

1,6 Theories of Sonoluminescence.

A number of theories upon the origin of sonoluminescence have been proposed :

a) The electrical microdischarge theory of Frenkel (54) who postulated the abrupt creation of lens-shaped cavities as the liquid:Ipressum decreases. Charges of opposite sign arising on the walls of the cavity due to statistical fluctuations of the charge distribution in the liquid are then supposed to give rise to a microdischarge within the cavity as the electric field increases due to the cavity becoming spherical. It is this discharge which is thought to give rise to the luminescence. — 39 —

b)The triboluminescence theory of Chambers (27,37) who suggested that when the quasi—crystalline structure of a liquid is broken triboluminescence occurs, as in the case of the rupture of certain crystals such as cane sugar. c)The balloelectric theory of Harvey (4) according to which potentials occur in the surfaces of bubbles similar to those observed on liquid droplets by Lenard and which explain the appearance of waterfall luminescence. A discharge within the bubble would occur according to Harvey when the field was greatest, i.e. when the bubble is near collapse. d)The mechano —chemical theory advanced by Weyl and Marboe (55,56,57) and according to which a chemiluminescence arises due to reactions between ions mechanically created at the nascent surfaces of the cavitation bubbles. o) The hot spot theory of Noltingk and Neppiras (58,59) who suggested that adiabatic compression of the bubble contents could result in very high temperatures with a consequent incandescence. They suggested black body radiation as a possible form of incandescence. f) The therm° —chemical theowof Griffing and Sette (9,60,61) who proposed that adiabatic heating would cause thermal dissociation and the subsequent emission of chemiluminescence due to recombination. -40—

Criticisms of the Foregoing Theories.

The microdischarge theory presupposes the production of a non- spherical cavity whereas all high speed cinematographic records show cavities spherical from their inception. Charges can be formed on bubble walls, but they are highly dependent on the conductivity of the liquid whilst sonoluminescence output is often enhanced by the addition of electrolytes and is particuarly strong in mercury. Lines and bands might also be expected in the spectrum of sonoluminescence if it were due to a discharge. It would seem that a discharge and luminescence would be most likely to occur when, according to Frenkel the field is greatest due to the cavity becoming spherical, and when the pressure inside it is a minimum, i.e. at the maximum radius. This has been shown not to be the case as was mentioned in section 1.2.5 (iii).

A further criticism of the microdischarge theory and of the triboluminescence theory is that most evidence suggests that cavities do not arise due to molecular ruptures but rather by growth from 4uul stabllehcd gaseous nuclei.

Tho fact that sonolminescence is accompanied by chemical changes might suggest that sonoluminoscence is in fact a chemiluminescence.

The simplest processes that can give rise to luminescence in general are

A + B —>AB + h V ( I )

and A + B + C + C or AB + C* (2) the asterisk representing an excited state. - 41 -

Apart from recombination of electrons and positive ions, two

body reactions of type (1) might be caused by the recombination of dissociation products of diatomic or pblyatomic molecules, or from the

interaction of two molecules or a molecule and a radical. The cold light or bioluminescence of animate mater is due to the two- body reaction of luciferin with the enzyme luciferase. (The spectral distribution of this light is often a continuum resembling that of a

black body radiator at 10,000°K). Two body reactions of this sort

only occur readily with peIyatomic molecules. In the case of recombination of dissocation products of molecules the light is weak,

often in the infra-red and not usually a continuum. Three body reactions are more likely but these give rise to line and band spectra.

The mechano-chemical theory is also subject to the severe criticisms that luminescence should occur during the growth stage of cavitation

and that chemical yield should be independent of the gas content of

the bubble. This leaves the thereto-chemical theory of Griffin& and

Sotto. It seems that chemiluminescence cannot account for all sonoluminescence, although undoubtedly there is a large chemiluminescent component in the sonic luminescence from luminol and perhaps from carbon disulphide,

According to the hot spot theory the light is incandescent or basically thermal in origin, due to a physical process such as black body radiation. Neppiras and Noltingk based this suggestion on -42— their theory of cavitation bubble dyhamics. Neglecting the vapour pressure of the liquid,which was assumed incompressible, and assuming the gas content of the bubble to remain constant in time, they derived a differential equation of motion of the bubble wall which was solved by computer. They found the cavitation conditions (high .., pressures within and without the bubble) would only occur for nuclei of loss than resonant size. They also .concluded that cavitation is not only restricted to a finite range of frequencies wand nuclear sizes, Ro, but also to a fixed range of variation of hydrostatic pressure PA as found by Polotskii (5), and alternating pressure amplitude Po as found by Rosenberg (14). It is thus to be expected that if sonoluminescence is duo to adiabatic compression of the bubble contents, high temperatures and pressures will be attained within the bubble, furthermore the intensity of the luminescence should vary with the basic parameters in the same way as the intensity of cavitation, as measured by the liquid pressures for example. Thus sonoluminescence should decrease withW(R6P0 and PA being constant), only appear for nuclei of a certain range of radii R0( w,P0 and PA constant), show a sharp threshold at low Po (and power) and decline above certain critical values of Po and PA. These conclusions agree at least qualitatively with many of the observations of sonoluminescence reviewed in section 1.2. -43—

If vapour pressure is taken into account the decrease of sonoluminesconce intensity with ambient temperature, described in section 1.2.4, can be accounted for since the condensation of the vapour during the collapse stage would remove energy that would other— wise be radiated. The same effect would explain the low light output vola.taft, from liquids. The theory could not, however, be used readily to

explain the effects of various impurities and dissolved gases on sonoluminescence.

Jarman (62) has pointed out the similarities between shock tube luminescence and sonoluminesconce. Both are most intense in rare gases

and lines and bands can be produced in the spectra of both by the

addition of inorganic impurities. The addition of carbon disulphide

or carbon tetrachloride causes luminescence enhancement in both cases.

Jarman therefore suggested that shocks propagated inwards within the collapsing cavity could be the cause of luminescence. Heim (63)

alsolhought that such shocks could occur and suggested that the continuum was due basically to the excitation spectra of the gas

broadened by high pressure conditions. He thoughtthat recombination and bremstrahlung continua could also be present and suggested that the

emission of the sodium D lines would be Completed before the emission of the continua due to the low excitation potential of the sodium atom.

1.7. Other Effects of Cavitation.

Besides the appearance of sonoluminescence a number of other - 44 - effects accompany the cavitation process. The experimental observations of these effects have boon reviewed by Webster (64,87), and Noltingk (65) and a brief summary emphasising the comparisons and contrasts with sonoluminescence will now be made.

1.7.1. Chemical effects.

Depolymorisation of solutions of polymers is a common occurrence

and polymerisation of some solutions and emulsions has also been observed. Changes of non-Newtonian viscosity and optical rotation of some solutions are a consequence of this process. Non miscible liquids can be rapidly emulsified and some suspensions peptised. Many

of these effects can be explained by the action of the liquid shock

arising from collapsing cavities.

A number of chemical reactions occur. Cavitation of water leads

to the production of hydrogen peroxide. Iodine is liberated from

potassium iodide solution, this renction being accelerated by the

presence of carbon tetrachloride. Chlorine is liberated from carbon

tetrachloride solution. Hydrolysis, addition and oxidation have been

observed. The inversion of sucrose has been reported. Aqueous chloroform is dissociated into the gases carbon monoxide and carbon dioxide and a number of other liquid and solid products, according

to Karpovitch (66). The maximum acceleration of reactions by

cavitation occurs when one of the reaction products is a gas.

Certain explosives are detonated by cavitation. Weissler (65) found -45- that, in any reaction, the number of molecules produced by cavitation was many hundreds of times smaller than that yielded by gamma radiation for the same amount of energy absorbed in each case.

Nitrous and nitric acids are produced slowly in water containing

dissolved air (68,69,70).

Most chemical processes do not appear to depend on frequency

although some reactions are reported to be slower at increased frequency.

An optimum frequency, depending on particle size, exists for the disperskn, of barium sulphate or clay in water.

With increasing power, chemical reactions start with the onset

of cavitation and several authors report that the reaction rate

increases approximately linearly with intensity, although other workers

have found optimum values of intensity above which the chemical yield decreases. Weissler (71) has shown that such maxima occur when the volume of the solution is small.

Since sonoluminescence is also related linearly to low .power values

a correlation between sonoluminescence and chemical yield is to be

expected. This has been found to be the case for H202 production by

Parke and Taylor (10) and for liberation of chlorine from CC1 solution 4 by Griffing and Sette (9).

Yield of chemical products is generally linear with time of.

application until the reactants are exhausted, the initial reaction rate usually being high. — 46 —

The occurrence of an optimum value of static pressure for various chemical effects has been observed (68 and 72-77). Chemical yield decreases with increasing liquid temperature, although there is disagreement over the extent of this decrease.

The gas content of the solution influences the chemical yield of cavitation, There is disagreement hs to whether oxygen is necessary for the process of oxidation, but it is agreed that the presence of rare gases in solution increases the yield of chemical products, as

from has been shown by Fitzgerald et al (78) for liberation of Cl2 C Cl solution and by Prudhomme (79) for liberation of hydrogen 4 peroxide from water. Carbon dioxide and nitrous oxide completely inhibit the carbon tetrachloride reaction. Prudhomme and Grabar (80) found that as little as one part of ether in a thousand of water would

inhibit oxidation.

1.7. Q. Erosion. Erosion of metal surfaces by cavitation decreases the harder

the metal. Erosion is also found to proceed faster when the surface is rough. Loss of weight per unit time due to erosion increases with

temperature up to a certain critical value and then decreases, On

performing experiments with water tunnels some authors found that

erosion occurred where the cavitation bubbles were expanding and others found it where the bubbles collapsed. The presence of permanent air

bubbles in water prohibits erosion, probably by increasing the _47_ compressibility of the liquid.

The mechanism of cavitation erosion is still in dispute.

It has been suggested that chemical corrosion plays a major part in the process, Wheeler (81,82) has suggested that the initial damage is due to shearing strains induced by the collapsing cavities. The resulting slip raises the temperature, causing corrosion in suitable circumstances. In a metal not previously cold worked, strain centres and hence anode potentials are set up, giving rise to further corrosion, which effect was demonstrated by Callis (83) and Petracchi (84), the latter finding that erosion could be reduced by making the specimen cathodic. It has also been suggested by Poulter (85) that cavitation erosion is caused by the forcing of liquid under pressure into the pores of the material and its subsequent escape carrying small particles with it.

1.7. 3. Biological Effects.

The destruction of blood corpuscles, yeast cells and bacteria in liquids can be brought about by cavitation, by rupture of the cell wall.

At low intensities growth in bacteria cultures is stimulated, possibly due to dispersion, but at a certain intensity destruction sets in and increases with increasing power. This threshold is lower than that measured by other means. The death rate is approximately logarithmic with time, and increases with temperature rise. The latter effect, which apparently contradicts the decrease of sono— -48— luminescence and chemical effects with temperature rise, could be because the bacteria themselves act as cavitation nuclei and, at higher temperatures, intermolecular bond strength decreasing, there is a higher incidence of cavitation.• The sensitivity of bacteria to cavitation is dependent on the medium in which they are suspended, proteins exerting a protective action, Certain enzymes and antigens are released from bacteria, even when the organism itself is killed.

Recent investigations by Neppiras (86) have shown that there is an optimum value of static pressure for the disintegration of yeast cells. - 49 — REFERENCES. 1. MARINESCO,M and TRILLAT,J.J.: C.R. Acad. Sciaaris 196 (1933) 858 N 2. MARINESCO, M. AND REGGIAN11, M: C.R. Acad. Sci. Paris 200 (1935) 548 3. FREN71 rivi and SCHULTES,H Z.f. physik. Chem B:27 (1934) 421 4. HARVEY, E.N. : J. Am. Chem. Soc. 61 (1939) 2392 5. POLOTSKII, I.G. : Mur.Fiz.Ghim. U.S.S.R. 22 (1948) 787 6. JARMAN, P.D.: Science Progress No: 184 (1958) 632 7. ELTPINER, I.E. : Soviet Physics (Acoustics) 6 (1960) 1. 8. GUNTHER, P. et al : z.f. Elektrochem 61 (1957) 188 9. GRIFFING, V and SETIE'D : 3. Chem. Phys. 23 (1955) 503 10. PARK, A.V.M. and TAYLOR,D.: J. Chem. Soc. 4 (1956) 4442 11. JARMAN, P.D. : Proc.Phys.Soc. 73 (1959) 628 12. NEGISHI,K. : J. Phys. Soc. (Japan) 16 (1961) 1450 13. WAGNER, W.U. z.f. ang.Phys. 10 (1958) 445 14. ROSENBERG, L.D. Acustica 12 (1962) 40 15. PASUNOFF, P. : C.R. Acad. Sci. Paris 209 (1939) 33 16. PINOIR, R. and POURADIER, J.: J. Chim. Phys. 44 (1947) 261

•• 17. GUNTHER, P et al : z.f. Naturforschg. A 11 (1956) 882 18. MACLEAY and HOLROYD J. App. Phys. 32 (1961) 449 19. YOSIAKA and KAWASIMA : Acustica 5 (4955) 167 20. YOSAIKA et al : Acustica 5 (1955) 173 21. BLAKE, F.G. : J.A.S.A. 21 (1949) 551. — 50 — 22. MEYER, E and KUTTRUFF, H z.f. ang. Phys. 11 (1959) 325 23. JARMAN, P. : Ph.D Thesis London (1959) 24. KUTTRUFF, H and PUSS, K. Acustica 11 (1961) 224 25. PRUDHOMME, R.O. : J. Chim. Phys. 46 (1949) 318 26. BUSHEL and DEGROIS ; J. Chim. Phys. 52 (1955) 279 27. CHAMBERS, L.A. : J. Chem. Phys. 5 (1937) 290 28. LEVSHIN, V.L. and RZHEVKIN, S.N.: Dok.Akad.Nauk. U.S.S.R. 16 (1957)407 29. PRUDHOMME, R.O. and GUILMART, T : J. Chim.Phys. 54 (1957) 336. 30. SIROTYUK, M.G. : Proc. 4th Int.Conf.Acoustics (Copenhagen 1962) 026 31. SIROTYAH, M.G. : Soviet Physics (Acoustics) 7 (1962) 405 32. DEGROIS, M and BADMAN, B: C.R. Acad.Sci.(Paris) 254 (1962)231, 837, 1213, 1943. 33. GUNTHER, P et al : z.f. Naturforschg. 12 (1957) 521

34. NEGISHI, K Acustica 10 (1960) 124. 35. GUNTHER, P et al : Z. Ang. Physik 11 (1959) 274 36. ZIMAKOV, P.V. : C.R. Acad. Soi. U.S.S.R. 3 (1934) 450

37. CHAMBERS, L.A. ; Phys. Rev. 49 (1936) 881 38. KUTTRUFF, H. Acustica 12 (1962) 230 (Akutische Beihefte) 39. SRINIVASAN, D and HOLROYD : J. App. Phys. 32 (1961) 446

40. SRINIVASAN, D Ph.D Thesis, University of Missouri (1955) 41. POLOTSKII, I.G. Zhur. oh. Khim. 8 (1938) 1691 42. KLING : Rev. Sci. (Paris) 85 (1947) 364 43. PRUDHOMME, R.O. and BUSSO C.R. Acad. Sci. (Paris) 235 (1952) 1486 44. GUNTHER, P et al : z.f. Elektrochem 63 (1959) 43 — 51 — Haim. a.: Z. Ano. Pigs. tiz 6960) 423 45. OUPITIIER, P et ea a w.f ElekteeeNetw. 43 (1959) 43 46. BRESLER, S.E. s Acta Physicochim. U.S.S.R. 12 (1940) 323 47. KONSTANTINOV, V.A. Dok. Akad.Nauk. U.S.S.R. 56 (1947) 259 48. SCHMID, J : Acustica 9 (1959) 321 49. HARVEY, E.N. a "A History of Luminescence" Am. Philosophical. Soc. Philadelphia (1957) 50. Private Communication. 51. GLASS, T.I. U.T.I.A. Review (1960) No:17 52. SCHMID, J. : Acustica 12 (1962) 70 53. TRAVIS, J.R. et al : "Les Ondes de Detonation" Centre National de la Recherche Scientifique (Paris) 1961

54. FRENKEL, J : Acta Physicoehim. U.S.S.R. 12 (1940) 317 55. WEYL, W.A. and MARBOE, E.C. : Research 2 (1949) 19 56. WEYL, W.A. and MARBOE, E.C. : J. App. Phys. 21 (1950) 937 57. WEYL, W.A. : J. Colloid Sci, 6 (1951) 389 58. NOLTINGK, B.E. and NEPPIRAS, E.A. : Proc.Phys.Soc. B 63 (1950) 674 59. NOLTINGK, B.E. and NEPPIRAS, E.A. : Proc. Phys. Soc. B 64 (1951) 1032 60. GRIFFING, V : J. Chem. Phys, 18 (1950) 997 61. GRIFFING, V : J. Chem. Phys. 20 (1952) 939 62. JARMAN, P.D. : J.A,S.A. 32 (1960) 1459 63.HEIM, E : Proc. 3rd I.C.A. (1959) page 343 64. WEBSTER B.S. : MSc Dissertation (1961) London 65. NOLTINGK, B.E. : "Handbuch der Physik". Vol XI/2 : Acoustics 2 (1962) p.259 "The Effect of Intense Ultrasonics in Liquids". — 52 — 66. KARPOVITCH J.A.S.A. 30 (1958) 678. 67. WEISSLER, A J.A.S.A. 32 (1960) 283, 1208 68. POLOTSKII, I.G. Zhur. Ob. Khim. 17 (1947) 1048 69. FLOSDORF et al : J. Am. Chem. Soc. 58 (1936) 1069 70. VIRTANEN and ELLFOLK : Acta. Chem. Scand. 4 (1950) 93 71. WEISSLER, A. et al : J. Am. Chem. Soc. 72 (1950) 1769) 72. BONDY and SOLLNER : Trans. Faraday. Soc. 31 (1935) 836 73. SCHMID and ROMMEL z.f. Physik. Chem. 185 (1939) 97 74. CHAMBERS and FLOSDORF : J. Biol. Chem. 114 (1936) 75 75. FREUNDLICH and GILLINGS Trans. Earaday Soc. 34 (1938) 649 76. FREUNDLICH and SOLLNER : Trans. Faraday Soc 32 (1936) 966 77. ONO Rev. Phys. Chem, Japan 14 (1940) 25 78. FITZGERALD, M.E. et al : J. Chem. Phys. 25 (1956) 926 79. PRUDHOMME, R.O. : Colloquium Over Ultrasonore Trillinger (1952)182 80. PRUDHOMME, R.O. and GRABAR J. Chim. Phys. 46 (1949) 667 81. WHEELER, W.H. D.S.I.R. Mech. Eng. Res. Lab. 46 (1957) 49, 50 Fluids Rep. 44 (1956) 82. WHEELER, W.H. N.P.L. Symp. "Cavitation in Hydrodynamics" H.M.S.O. 1956 83. CALMS, G.T. Inter—Service Met. Res.Counc. 1248, 1954 84. PETRACCHI : La Metallurgia Italiana 41 (1949) 1 85. POULTER : Frontier 10 (1947) 7 86. NEPPIRAS, E.A. : Private communication. 87. WEBSTER, B.S. : Ultrasonics 1 (1963) 39 -53-

2. APPARATUS AND PRELIMINARY EXPEr, N S.

2.1. Objectives.

The possibility of using a system producing single bubbles, such as the Chesterman technique, was considered but it was felt that luminosity from the collapse of such a bubble would be low. The necessarily low rate of repetition of the collapse would make studies of the variation of sonolnminescence with various parameters extremely tedious. On the other hand the more usual method of producing many bubbles ultrasonically with a frequency of collapse equal to that of the sound field still appeared to be capable of exploitation for several investigations, such as"the dependence of sonoluminescence on static pressure, on the amount and nature of dissolved gas, and on the types of nuclei present in the cavitated liquid. All of these measurements would necessitate the use of a closed sample holder, so that either a transducer has to form part of the wall of the sample holder or sound has to be radiated through the wall.

2.2. Transducer and Velocity Transformer.

As sonoluminescence is most intense at relatively low frequencies it was decided to use a magneto—strictive transducer. Cylindrical transducers of the type employed by Jarman (1) have the advantage of producing cavitation in regions remote from solid surfaces, but in order to produce cavitation in a closed sample holder the walls of the latter need to be made of polythene to ensure good acoustic matching. Such an arrangement would lead to difficulties if it is desired to pressurise the -54— sample and control its temperature. Furthermore, the cavitation region cannot be precisely located with a cylindrical transducer, which is a disadvantage if spectral analysis is contemplated. Thus, it was decided to use a commercial window type transducer, of nickel laminations, whose dimensions are given in Fig.15. The transducer was driven by a Midland L275 power oscillator, the system being designed to operate at about 20 kc/s and to dissipate some 50-60 watts of electrical power. Other data concerning the transducer is given in Table 5.

In order to couple the transducer to the liquid sample it was decided to use a velocity transformer. The double quarter wave type was selected since it has a velocity step-up ratio approximately equal to the inverse ratio of the end areas, whereas in the case of an exponential or conical

transformer the step up ratio is equal to the square root of the ratio of the end areas (2). Furthermore the double quarter wave transformer is

somewhat easier to machine, since it does not require the accurate location

of flanges for purposes of clamping. The horn was made of titanium

because of its high strength and resistance to chemical and cavitation

erosion.

The ratio of the end diameters of the velocity transformer was chosen

to be about 6 s 1, giving a velocity step-up ratio of 36 : 1 the resultant stresses being still reasonably below the fatigue limit of titanium. The

transducer and velocity transformer were mechanically coupled together

by hard soldering onto the end of the transducer a steel plate which

was then tapped, enabling transducer and horn to be firmly screwed together 55

464 F I G. 1 5: HORN AND TRANSDUCER: FULL SIZE

displacement antinode

Zi_

displacement node • three holes at P.0 D " ta B .;(

displacement antinode 7" - 56 -

TABLE 5.

PROPERTIES OF THE TRANSDUCER AND HORN.

Amber of Nickel Laminations about 90

Thickness of LaMLnations .006 inches.

Number of turns of wire about 80

Resonant Frequency of Transducer and Horn. 21200 cps unloaded) and Horn. 21000 cps (loaded)

Electro-mechanical Q of Transducer and Horn at resonant frequency 700

D.C. Polarising Current 3 amps

A.C. Resistance of Transducer 50 ohms unloaded) and Horn at resonant frequency. 20 ohms loaded)

...... ----o0o------57 - with a piece of steel stubbing, as shown in Fig. 15. Silicone grease was smeared onto the mating surfaces to improve matching. It was also found desirable to minimise rusting by coating the whole of the exposed surface of the steel plate with silicone grease when operating in a water bath. The rusting which otherwise occurred readily is an example of the acceleration of chemical processes by vibration without the accompaniment of strong cavitation. A certain amount of weak cavitation was observed on the exposed part of the large end of the horn, when it was immersed in a water bath, and to prevent this energy loss some closed cell sponge rubber was stuck onto this part of the horn, to provide a pressure release medium.

2.3. Energising Circuit.

The oscillator consisted of a multivibrator, power amplifier and a source of polarising current, but this equipment had to be modified to permit better matching to the impedance of the horn—transducer system and also to overcome instability in the driving frequency. The first of these modifications was carried out after plotting a form of impedance loop, which was determined in the following manner.

In Fig.16 the part of the diagram enclosed by the dashed line represents the output stage from the power amplifier, C being a decoupling 1 capacitor which is followed by an output transformer, a blocking capacitor,

C and the actual transducer, T, the cooplete arrangement having an 29 effective impedance Z. The purpose of C2 is to block the backward flow of 58

Signal Generator

Oscilloscope

1 r F

Stub'

0.44441,

44

FIG.16 -59- the polarising current which enters the circuit at the point A. The mismatch of the electrical impedance of the transducer system to the output stage of the power amplifier led to a failure of the output transformer.

This was probably due to the appearance of a large reactive component in the output impedance of the power amplifier causing large voltages to. develop on the primary side of the transformer. Measurements on an A—C bridge at 10 kc/s confirmed that there was a large inductive component.

A signal generator was then joined in series, through a switch K, with a variable capacitance C and Z (Fig.16). The potential at the point B was recorded on an oscilloscope, the resistance R0 being much greater than Z, this potential was then proportional to the combined impedance of C and Z, for a given output from the signal generator.

Keeping this output and the frequency constant the value of C was adjusted until the signal displayed on the oscilloscope was a minimum, thereby rendering the system purely resistive. The magnitude of this resistive load, R, was then determined by switching K to a variable resistance, r, and adjusting the latter to give a signal of the same amplitude as the minimum value found previously. The values of R and X were found at a series of different frequencies and the results are plotted in Fig.17.

The departure from the ideal circular loop is probably due to the absence of a polarising current, and reflections from the walls of the beaker in which the horn probe was immersed. However, the results confirm that the main resonant frequency is of the order of 21200 c/s and that the X 60 (ohm)

5500

50 00

4 500

40 00

21•(9

3500

3000 parameter : 18.o frequency (Kc/s)

2 500

2000 w I I I I I 0 200 400 600 800 1000 1200 1400 R(ohm)- FIG.17 -61- electro-mechanical Q-factor is of the order of several hundred. They also showed that for correct matching an impedance of 3600 ohms was required, and accordingly C , was altered to a value of 0.002pF, no subsequent failure in the output transformer occurring.

A second modification to the energising circuit was made to overcome instability in the driving frequency produced by the multivibrator of the oscillator. Whilst the latter is sufficiently stable to drive machine tools, the purpose for which the oscillator was intended, the high 4-factor0 of the present arrangement caused the system to go "off tune" readily. Attempts were made to produce self-maintained oscillations by fixing a crystal pickup to the top of the transducer and feeding the signal from this back into the power amplifier after suitable amplification and phase changing. These efforts however proved unsuccessful, although the reason for this is still not apparent. Recourse was eventually made to the use of a highly stable Muirhead-Wigan decade oscillator. A limiter was also incorporated into the circuit so that the signal entering the power amplifier, could be set to any value between 1.5 to 3.1 volts peak to p,ak amplitude, thus providing a control over the power delivered to the transducer. The use of a Neon tube in this limiter, whose circuit diagram is given in Fig.181 ensured that the signal entering the power amplifier remained constant, whatever changes might occur in the impedance of the remainder of the circuit. The relationship between the peak to peak voltage amplitude set on the limiter, and the driving voltage 62 i

240 v

to 16K power amplifier >

OA 71f\ 47 K VOA 71 o _ 150 i._2 10K 198 K

>' 200/1

100f1

_1

FIG.18: LIMITER -63— obtained from the power amplifier, was determined under loading conditions and is shown in Fig.19. It can be seen that the power amplifier is approaching saturation at high settings of the limiter. A block diagram of the complete energising circuit is shown in Fig.20.

A lead zirconato—titanate crystal was stuck onto the top of the transducer, where it acts as an accelerometer, the pick—up signal being used to monitor the performance of the transducer as will be described later.

Some difficulty was experienced in obtaining a permanent bond between the crystal and the transducer. The method of bonding which eventually proved most satisfactory is illustrated in Fig. 21.

2.4. Some experimental Observations of Cavitation.

The design of the sample holder was decided on by the results of some preliminary observations on the patteinof cavitation and the dissipation of acoustic power during cavitation, so that these experiments will be described before continuing with the account of the apparatus.

Fig.22 is a photograph of cavitation occurring at full acoustic power in a beaker of fresh tap water. Immediately below the stub of the horn can be seen a cloud of bubbles too small to be distinguished individually.

The density of this cloud diminishes sharply in lateral directions, and more gradually along the projection of the axis of the horn whilst larger bubbles appear, moving at high velocity away from the stub, and thus appearing as streaks in the photograph. The photograph is only slightly greater than actual size, and as the exposure time was 0.01 sec it can 190

driving voltage 180

170

160

150

140 FIG.19 •

130

120

limiter voltage 110 12 1.4 1.6 1.8 2.0 2.2 2.4 2.6

65

FIG. 20: BLOCK DIAGRAM OF DRIVING CIRCUIT

SIGNAL POWER

GENERATOR LIMITER AMPLIFIER

blocking SOURCE OF capacitor POLARISING T CURRENT

.111•11•11• light weight mft l axial cable insulati on silver loaded solder

lead zirconate titanate crystal silver coating

fd, AI/APIAFAI/WerAIRACCIMIA hot setting araldite layer of silicone grease steel base plate

/// transducer

FIG.21 cm 0 1 2 3 4 5

FIG.22 :CAVITATION IN A BEAKER OF WAT ER -68- be seen that some of the bubbles are moving at velocities of at least

20 cm/sec. Moreover a close inspection of the photograph shows that there are streaks present at all orientations. Whilst visual observation is not very reliable in observing these rapid events it appears that in fact these larger bubbles are stable and execute a spiralling motion away from the stub. At large distances (5-10 cm) from the stub this motion ceases and the bubbles are carried out of the radiation field and rise to the surface of the water.

When their escape from the radiation field is precluded by employing as a container a tube of diameter 1-2 cm, the larger bubbles become trapped at the bottom where they can attain a diameter as large as 3-4 mm. The cavitation pattern was observed in a series of narrow, flat—bottomed glass tubes of various lengths so that the distances between the stub and the bottom of the tube were multiples of a half wavelength of sound in water

(about 3.2 cm at 20 kc/s), up to 2 wavelengths. In each case the cavitation pattern was the same :. a cloud of small bubbles directly beneath the stub and larger bubbles agglomerating at the bottom of the tube. With very short tubes the bottom of the tube was eventually broken off. With the longer tubes streamers of bubbles could occasionally be observed originating at points well below the stub and moving away from it. The points of initiation of these streamers did not occur at any definite distances from the stub (e.g. half wavelength intervals ) and the streamers were also sporadic in their time of appearance. The nature of -69— the cavitation was subject to abrupt changes when the large bubbles trapped at the bottom of the tube were suddenly released and rose to the surface. A simultaneous drop in cavitation noise level was heard and during these periods of reduced noise level the activity in the vicinity of the stub resembled a boiling liquid. An attempt was made to correlate these transitions in the nature of the cavitation with temperature changes, using the apparatus described in section 2.5, but the phenomena were not readily reproducible. However, periodic changes in noise level could sometimes be heard when using the metal sample holder and housing described in section 2.7. The period of these changes varied from about

20 to 90 secs. A discussion of these phenomena will be reserved until chapter 4, but whatever their explanation might have been, it was clear that the size of the sample holder did not affect the cavitation pattern i.e. standing wave effects were negligible.

There is some evidence that the bubbles immediately below the stub of the horn were subject to a motion directed radially inwards during the course of their collapse. In the first place erosion occurred on the end face of the stub (initially machined flat) leaving a thin outer rim apparently unscathed. Superimposed on this eroded crater some relatively deep pitting was also observed.

The author is indebted to Mr. S.D. Howkins (3) for the provision of a number of "carbon paper pressure detectors", whose construction is illast;rated in When immersed in n-liquid. baTtcketiais,--oceurs to a. degree which is a function of the applied pressure. Fig. 24 shows the 70

melinex

0 blotting paper 0 carbon paper 0 emery paper

melinex

FIG.23: EXPLODED DIAGRAM OF CARBON PAPER

PRESSURE DETECTOR 71

FIG. 24s• - CARBON PAPER PRESSURE DETECTORS EXPOSED TOs

A : 492 ATMOSPHERES STATIC PRESSURE APPLIED HYDRAULICALLY

B ; CAVITATION, FOR 3 MINS., 1 mm BELOW STUB

C CAVITATION, FOR 3 VTNS.. 2 mm BELOW STUB

D : CAVITATION, FOR 3 MINS , 3 mm BELO STUB

E UNEXPOSED - 72 - blackening on detectors placed for 3 mins in the cavitation region at distances of 1,2 and 3mm from the stub of the horn. Assuming this blackening to be caused by shock waves arising at the end of the collapse of the cavitation bubbles, it follows that the bubbles must collapse at the centre of the stub, since the diameter of the region of blackening on the detector placed closest to the stub is less than the diameter of the horn itself. It can also be seen that the attenuation of the shocks must be extremely rapid.

Further, a visual comparison of the blackening observed in these cases with that obtained on a series of detectors at calibrated pressures, suggests that the shocks arising from the collapsing cavities have peak pressures of the order of several hundred atmospheres at least. The effect of enclosing the probe of the horn in the stem of a glass

T-piece with a water flow across the stub in the piece of the T was also tried,but no appreciable cavitation could be observed. During this experiment the probe of the horn happened to rub against the glass wall,and a small bright red region of luminescence was observed,which may have been due to triboluminescence. Later an attempt was made to observe the tribolum- inescence of zinc sulphide crystals embedded in araldite on a glass plate, immersed in a light transparent oil,which was then irradiated with a probe.

A photomultiplier was used to detect luminescence but it was concluded that any triboluminescence which might have been present was masked by sonolumin- escence caused by cavitation in the oil.An attempt was also made to produce cavitation in water below a polythene platel heavy engine oil above the plate serving as a coupling medium for the horn.However, intense cavitation was produced in the oil and no cavitation was observed in the water.

Finally a drop of water was placed on the stub of the horn when it was not operating. Upon energising the transdUcer the water was almost - 73 -. instantaneously dispersed as a cloud in the surrounding atmosphere, When

a non-absorbent solid surface was placed under the probe droplets with a

wide spectrum of diameters ranging from the microscopic up to a few

millimetres were found to be present. (Fig, 25). A continuous process of

atomisation could be seen when water was allowed to run down the side of

the stub (Fig. 26).

2.5. Measurement of Acoustic Power.

Some measurements of the power radiated from the horn were made with

the apparatus illustrated in Fig. 27. This consisted of a glass container

made so that the transducer and the upper part of the horn could be cooled,

while the probe of the horn heated a fixed mass of water. The "shoulder"

of the horn, which is a displacement minimum, was set in a plasticene

seal. It was assumed that the energy leaving the system in the form of

noise was negligible compared with that converted into heat within the

water, A copper-constantan thermocouple was pre-calibrated in terms of

the deflection produced on a scalamp galvanometer, the calibration curve

being shown in Fig. 28. The thermocouple junction was then immersed

in the volume of water to be irradiated and the galvanometer deflection

noted at half minute intervals after energising the transducer. The

experiment was repeated a number of times with different acoustic power

levels, obtained by adjustment of the "limiter" previously described.

Typical heating curves so obtained are shown in Fig. 2-ci- In each case

the best straight line has been fitted to the.earlier part of the curve,

to eliminate the effect of heat losses as explained in the theoretical

appendix 1. Then from measurements of the geometry of the container and 137d0HC d31VM V JO NOLLVSMOIV CE C:J31\iM ~O MOl.=1 \:;f .=10 NOI1VSllAJ01'd 929.=1 76

cooling ,.. water

FIG. 27: GLASS CALORIMETER 77

4 1 1 2 4 5 6 7 galvanometer reading (scale FIG.28 divisions) temperature (°C) 70 - .,„x---- x

60

50 -

4 0 -

x x-----x-----% X-----X 3 0 - ____x ___.x x...... _.-X---->: FIG.29 x X-----X x,--x----7---- 20 I 0 1.0 2.0 3-0 4.0 5.0 6.0 7.0 8'O time (mi n) -79— height of the water column the acoustic power was calculated and Fig.30 shows these power values plotted against the peak-peak voltage of the signal from the crystal pick-up. It can be seen that the apparatus is capable of supplying from 3 to 10 watts of acoustic power, this being radiated from the stub whose diameter is inch, so that the power flux 2 across the stub can be varied from 9.5 to 32 watts/cm The theory of the method assumes a uniform temperature distribution within the water volume. This was felt to be justifiable because of the efficient stirring due to cavitation, and to confirm this some 1runs' were made with the thermocouple in various positions in the tube, no appreciable changes in the heating curves being observed.

Finally one truni was made with carbon tetrachloride as a liquid medium and with the limiter at its highest setting, and another with glycerine and the limiter at its lowest setting. The heating curves so obtained are given in Fig, 31. The power dissipations agreed well with those found for water at the same settings of the limiter. However a phenomenon which had been suspected in the case of water was clearly evidenced in the case of carbon tetrachloride. Superimposed on the trend to be expected from the theory (appendix 1) there was an oscillation of temperature with time, too large and regular to be due to random errors of observation. Closer inspection of the heating curves for water revealed the presence of a similar oscillation on each curve, although smaller in amplitude than that found with carbon tetrachloride. In the case of

-10 acoustic power (watts)

8 x

6

-4

FIG.30 X 2

I I I I I i I I I I I 0.4 0.8 1.2 1.5 2.0 2.4 2.8 3.2 3.6 4.0 4-4 4.8 pick up voltage (volts) 81

..--.. U 0 ...... Q) L. n .4- cu L. 70 _ w a E aJ 4, 60

carbon tetrachloride'

50

40 x

30 gl ycerine

20 /

10

0 1 i i i 0 2 4 6 8 10 t ime (m in)

El G.31 -82- glycerine no oscillation was apparent. A discussion of this phenomenon will be given in chapter 4.

2.6. Preliminary Observations of Sonoluminescence.

After an examination of the cavitation pattern in the narrow glass

tubes mentioned in section 2.4. a series of examinations was made with a

well dark-adapted eye when sonoluminescence could be observed in tap water

as a faint bluish glow immediately below the stub of the horn. In one or

two cases extremely faint flashes, appeared to be associated with streamers

or fast moving bubbles. Brighter luminescence was observed with aqueous

carbon tetrachloride solution or with glycerine which had been exposed to

the atmosphere Some rough measurements made with a photomultiplier

showed that the luminescence from glycerine was about twelve times:that

from tap water, while the latter was slightly brighter than that from

pure carbon tetrachloride and ethyl alcohol. Bubbling argon through tap

water for a quarter of an hour was found to enhance the luminescence about

ten times. It was also possible to obtain evidence of the periodicity of

the sonoluminescence by connecting a 5 Kohm resistor in the anode lead of

the photomultiplier and displaying the voltage developed across it on an

oscilloscope. Figs. 32 and 33 are photographs of such a trace displayed

on a double beam oscilloscope. The other trace shown in this photograph

was obtained from the crystal pickup. It can thus be seen that the

luminescence is periodic with the sound field. An interesting feature of

the trace of the pick-up voltage is its non sinusoidal character. 3

MWOMMINIM woor iffiffirim

FIG. 32: OSCILLOGRAPH TRACES OF PICK-UP VOLTAGE 1.11111111110.1 AND PHOTOMULTIPLIER ANODE igiorivirilsOPROmrpo VOLTAGE (MANY SWPAP) ZWAMINVWX

.01111nftlaslrllPlomisrrillmnmrillroiwr

V1NVWV\

• JVVVVVVVV\

FIG. 33: OSCILLOGRAPH TRACES OF PICK-UP VOLTAGE AND PHOTOMULTIPLIER ANODE VOLTAGE (MANY SWEEP) NNINMAWONSMII

41/` ••••• • • • • ••••• ..... - 84 -

When the transducer is energised this trace could be observed to grow

in amplitude as a perfect sinusoid until the onset of cavitation, which

usually occurs quite sharply, when the distortion at the peaks of the

trace would also appear. Fig. 34 shows some traces obtained with

single sweeps on a Tektronic oscilloscope.- It can be seen that

luminescence pulses are not obtained with every pressure maximum.

2.7. The Housing and Sample Holder.

The results of the preliminary experiments were used as a guide to

the design of a sample holder and housing suited to the investigations

mentioned in section 2.1. It was decided to make the sample holder of

stainless steel, firstly because of its high mechanical strength (for

(static-pressurel measurements) and secondly for its high thermal

conductivity. As shown in appendix 1, this ensures that there cannot

be a temperature difference of more than 0.02°C across the metal wall

with an adequate supply of cooling water on the outside. This is an

important point since sonoluminescence is temperature dependent. Thirdly,

stainless steel is chemically inert as opposed to most common metals.

The dimensions of the sample holder were chosen to minimise the chance

of cavitation erosion at the walls. Fig. 35 shows the sample holder and

housing in cross-section. The quartz observation window at the bottom

of the sample holder was 4 mm thick and a thin steel backing plate in

the form of an annulus was mounted behind it to increase mechanical

strength. The window and backing plate were secured at the bottom of the 85

FIG. 34: OSCILLOGRAPH TRACES OF PICK-UP VOLTAGE AND PHOTOMULTIPLIER ANODE VOLTAGE (SINGLE SWEEP) - 86 -

Fig. 35. Tho Housing. is a brass cylinder 191 inches high, 4 inches in diameter and t inch thick.

1. Container of cooling water for ~;ransducer.

2. Contain~r of cooling water for sample holder. 3. Housing for photomultiplier. 4. Phosphor-bronze locking nut. 5. Sample holder in stainless stoel. 6. stainless stoel lid for sample holder. 1. Brass support for sample holder. 8. Transducer. 9. Horn. 10. steel backing plate.

11. Photomultiplier.

12. Quart z window. t••• 00

-a --Zlz 222 2 2 72 W. / A rAr r)11 lq. X X kr' Zr ir.,%/Ar AV .1" Ar

' A 01i l ,' war.' "Pr_ZIZZZLZZL/ z x 011; /' / \\ \X \ , r=ereal=4*" ,.., II / 1/

k P tt //7,7;0z %MUT v • ' I' \ XVI kr z, %, NN ( t 0 (30 - 88 - sample holder with a phosphor bronze locking nut. (Phosphor bronze was used for this purpose as steel components bind when screwed together).

The horn was mounted with three screws at its displacement node. Pressure sealing was achieved with rubber '01 rings.

2.8. Detecting System.

Sonoluminescence was detected with a photomultiplier (E.M.I. type

6256 B) having 13 dynodes, an antimony—caesium photocathode and an anode collector. The calibration as carried out by the makers using a tungsten source at a colour temperature of 2850°K, showed an overall sensitivity of 30 microamps/lumen (cathode) and 2000 amps/lumen (anode) for an overall voltage of 2KV. The dark current was 0.01 microamps. The tube has a quartz window and is sensitive to ultra violet light, a calibration of relative sensitivity of the tube at different wavelengths being given in Fig, 36. It can be seen that the tube is insensitive to light of wavelength greater than about 6000 a. The voltage 'steps' were supplied from a stabilised E.H.T. generator and a potential divider decoupled with 0.1µF capacitors over the last six stages (see Fig. 37). Since the instantaneous value of the anode current obtained during the observations of sonoluminescence was subject to a certain amount of fluctuation, a modified Miller integrating circuit was employed with a microammeter. The rate of current rise through the microammeter was proportional to the average anode current fed into the integrating circuit over an interval of a quarter to a half a minute.

Fig. 38 is a circuit diagram of the integrator and Fig. 39 shows the 89

100

/ / 80 / / / / / 60

40

20

0 -f- I I I I 1 02 03 0.4 0.5 0.6 0.7 Wavelength in p

FIG.36 90 Potential Divider

5

HT— A r 1.4MSL ...... i____ R 1 Ka

13 ••••• MOO ,m•• 4.IMP 4 ••.. =Mg •••• 4=IM c 0.1pF 11 eamM Ii• 4=6 MM. 18 NO= .• mIll 11•1

9 ..... vai Milo mon

recww• •••• ... I.E. 7 ••••• VP.. •••• •••• 6 5 man •••• •••. IMO nim. 4 maw* a. 4 3 :MID Mum •=l• ... Memi• 4MO• ONO 011•• 2 1 M. .•••• MM. .1M. -----i-- K F1G.37

Photom ultiplier 91

FIG.38

HT+

411.• ..III MID 19put, MPS . lb NMI ,••• •I0 ••••/0

A R 7 'C AS

INTEGRATOR

R 1.2 Mn, R 25 ka C 250 NF" 1 7 220 ksl, R8 150 kr. V ME 1400 R2 1 R 1803. R 100 kJ V 6SN7 3 9 2 R4 200s), A 250pA pot meter R 5R6 47 kit S switch 92

.

1M INTEGRATOR

FIG.39: A pPARATUS FOR CALI BRAT ION OF INTEGRATOR - 93 - circuit used for its calibration. This was found to be linear

(see Fig. 40) such that a rate of rise of 1.82 microamps/sec corresponds to an input current of 1 microamp. Fig, 41 is a photograph of the complete apparatus. The glass ware shown in this photograph is basically a water still designed to produce pure water. As time did not permit its use for this purpose, it will bo futhor discussed in Chapter 5.

References : 1. JARMAN, P.D. : Proc. Phys. Soc. 73 (1959) 628. 2. NEPPIRAS, E.A. : Conference on Technology of Engineering Manufacture (1958). Session /V Paper 6. "Design of Ultrasonic Machine Tools".

3. HOWKINS, S.D. : Ph.D. Thesis (London) 1962. 94

36 t dV /dt 32 (NA/sec)

2e

24

20

16

12

slope=1.82 sect 8

4

I I I 4 8 12 16 20

FIG. 40 -95-

Fig. 46 General Assembly.

1. The Housing, shown in detail in Fig. 35. 2. Buffer resevcir. 3. Pressure gauge.

4. Distillation flask. 5. Heating mantle. 6. Condenser. 7. Calibrated vessel. 8. Connection for evacuation. 9. Mercury manometer. 10. Unit containing potential divider and integrator* 11. E.H.T. Unit. 12. Cable carrying leads to photomultiplier. 13. Muirheac' oscillator.

14. Limiter. 15. Mullard oscillator* 16. Greaseless stop-cock. 17. J.and S.stainless steel valve. 18. Speedivalves. to On — 97 — CHAPTER 3 : OBSERVATIONS OF THE DEPENDENCE OF SONOLUMINESCENCE UPON STATIC PRESSURE.

3.1 Hydraulic Application of Pressure.

The general procedure was to pressurise the water sample in steps observing sonoluminescence at each stage by means of the photomultiplier and integrating circuit. The pressurisation was effected by means of a force pump (not shown in Fig.41.), the pressure being initially observed by means of a dial gauge which could read from 2 p.s.i. to 800 p.s.i. with fair accuracy. The light output was measured by timing with a stop watch the rate of rise of the reading of the micro-ammeter incorporated in the integrater circuit. With rapid rates of rise two or three readings were taken and their mean value derived. It was found impossible to release the pressure in the system steadily, so that no measurements were made with decreasing hydraulically applied pressures. An initial experiment showed that sonoluminescence decreased with excess pressure values up to 120 p.s.i.

On re-pressurising the same sample the sonoluminescence yield was found to have decreased. Tap water, usually freshly drawn, was used in this and in all subsequent experiments.

In order to measure the lower pressures more accurately, the pilot experiment was repeated with a Budenberg gauge (0-100 p.s.i). The voltage from the pick-up accelerometer was carefully monitored and the oscillator was re-tuned when necessary using the maximum attainable pick- up voltage and the maximum attainable loudness of cavitation noise as the criteria of resonance. -98—

The results are shown in Fig 42. Apart from the value of the anode current at zero excess pressure the current readings at lower pressures follow a continuous curve with a maximum at above 6.5 p.s.i. excess pressure and tending towards a suppression point at about 22 p.s.i excess pressure. Scattering readingsof anode current (far in excess of the dark current) were however obtained at pressures up to 40 p.s.i. excess pressure.

It was noted that the crystal pick—up voltage at resonance varied as the pressure was increased, which it was assumed was due to a variation in the impedance of the liquid medium. In fact, for a given voltage setting of the limiter, the acoustic power, as determined from the pick—up voltage, (see Fig. 30), showed a variation with static pressure

(Fig.43) similar to the variation of sonoluminescence. However, it should be noted that the calibration curve Fig. 30 was made at atmospheric pressure, pot4-er so that Pposourc estimates on the basis of pick—up voltage become increasing unreliable as the ambient pressure departs from atmospheric.

Subject to this reservation it was nevertheless felt that the measurements in the low range of excess pressure gave a reasonable indication of the power—pressure relationship. An attempt was made to obtain calibration curves relating pick—up voltage to power at various ambient pressures using the metal housing. This attempt was unsuccessful however since the high thermal conductivity of the housing walls prooluded the attainment of temperature rises of more than 1°C. To carry out such an investigation

99

anode current (NA)

FIG.42 0.8

0.6

x

0.4 x /4----..--r------S---2------

0.2

I I I I 0 0 5 10 • 15 20 25 30 35 40 excess pressure(p.s.i.) acoustic power ( watts)

I I I I I i 1 I I 10 20 30 40 50 60 70 80 90 100 excess pressure (p.s.i.) -101 - an entirely new apparatus would have been required. This possibility is further discussed in Chapter 5.

As sonoluminescence intensity is proportional to the acoustic power, an attempt had to be made to correct for this variation (Fig. 43).

This correction was generally made by diviling each value of the photomultiplier anode current by the corresponding value of acoustic power, determined from the calibration of Fig. 30. Thus Fig. 44 shows the results of Fig. 42 when corrected in this way, and it is to be noted that even when the correction was applied the same trends were present.

This would seem to imply that the maximum in the sonoluminescence pressure curves does not arise simply due to the maximum in the power- pressure curves. A further indication of this was obtained by making a series of readings of sonoluminescence at different pressures, adjusting the limiter until the pick-up voltage reached a certain predetermined value at each pressure value. The results of this experiment (Fig.45) still show the presence of a maximum.

The procedure of dividing by the corresponding acoustic power was adopted to make a series of determinations of the variation of sono- luminescence intensity with applied pressure at various values of the power,(as measured at atmospheric pressure) and the results are shown in Figs. 46-50. The position of the maximum shifted towards higher values of excess pressure as the power was increased. It appears that 102

anode current//acoustic power (microamps/watt)

016

014XN-2(

FIG.44: power 6.5w x 0.12

010

x x x 008

x x

006 x

0.04

0.02

00 5 10 15 20 25 30 40 excess pressure (p.s.i.) 103

dI d t a cou st i c power r A. seelw-1 )

0 O

1st run 0.5

0.4

0.3

0.2

0.1

0 0 2 4 6 8 10 12 excess pre ssure(p.s.i) •104

F IG.46 : pOWER 8.2watts

•

PR ESSURE ( P.S.f.) --'›

90 100 dt acoustic n►er

0-14

FIG.47 : power 6.95w

0.08

0.06

0.04 0

0.02

excess pressure (p.s.i.)

00 10 20 30 40 50 60 70 80 90 100 dI d t acoustic power FIG.48 : power 5.2w 0.11 ( r A .sec-.1w-1)

0.08

0.06 0

0041- )(4

0 1 I I t I I I t I 0 10 20 30 40 50 60 70 80 90 excess pressure (p.s.i.) 107

dI acoustic power dt -1 - ( tJA.sec. w 1)

4-7w 1st run

013 4.7w 2nd run

012

011

x 4•4 w

010

0.09 0 excess pressure (p.s.i.)

FIG.49 .• 108

'13

•+-t(AI 12.

ul li Q. FIG.50: POWER 3'3 watts

CC ce .09

O -0$ U- .07 URRENT/ C DE

x ANO

•o1 P.RESSURE 0 1.0 2.0 ao qo so 60 7o to .90 100 -109— below 4-5 watts of acoustic power there was no maximum in the curves and to confirm this point some measurements were made with power values in this region and applying pressure with a water column, to permit accurate measurement (Fig.49). The shift in the position of the maximum with variation of input acoustic power is shown in Fig.51.

A tendency towards suppression was also frequently present, and the suppression point, extrapolated from the curve, was also found to shift with power (Fig.52).

The decline in sonoluminescence intensity after pressurisation, suspected from the pilot experiment was confirmed (Fig. 45-49), Fig. 47 showing the effect of two successive pressurisations. It is to be noted that no appreciable shift occurred in the position of the maximum after pressurisation.

3.2. Application of Air Pressure.

Since, according to Henry's Law, the solubility of a gas in a liquid is proportional to the applied gas pressure, it is to be expected that some differences in sonoluminescence might result depending on whether pressure is applied hydraulically or with an air cylinder. This expectation was confirmed by several experiftents in which the force pump was replaced by an air cylinder (Fig.53-56). With increasing values of pressure these curves are similar to those obtained with hy040W1Oryseur showing an initial high reading, a maximum, a tendency towards suppression and then a "tail" at high pressure values. However, using the air 110

FIG.51 :SHIFT OF MAXIMUM 111

pressure at suppression point (p.s.i)

30 r i

20 I

ft.

10

0 1 2 4 6 8 10 acoustic power (watts)

FIG.52 N

3.6 d 1 at acoustic power C FiA.sec-.1w-1) 3°2 FIG. 53: power 6.5w

2.E

X..s...",--- X 2.4

2.0 )(------X

1.6

1.2

1.0 I J 0 10 20 30 excess pressure (p.s.i.) 113 dI dt acoustic power

w1) 0 quA. sec-.1 2-4

2.2

2.0 FIG.54 X /7\ \. 1.6

0

-.-

1.2

excess pressure (p.s.i ) 1.o 0 10 20 30 114

dI dt acoustic power (FA.sec.1 w-1 ) 3.8 X

3.4

3.0 FIG.55:power 4,15w

2.6

x

2.2

1.8

1.4

1 ,3 0 10 20 30 excess pressure(p.s.i.) t 115 dI d t acoustic power

( 1A.secT1w 1 )

FIG.56: power 2.13w

1 J 0.5 0 10 20 30 excess pressure (p.s.i.) - 116 - cylinder it was possible to reduce the pressure gradually so that measurements of sonoluminescence could be made along a return path. It was found that the sonoluminescence intensity was greater on this return path than with increasing pressure and that the maximum in the curve was displaced towards higher pressure values. In one case

(Fig. 56) a further pressurisation was made and then the curve followed a path intermediate between the first pressurisation and the return.

This phenomenon might be described as a hysteresis effect. The increase

in sonoluminescence yield with applied pressure was clearly time dependent, as is shown in Table 6. in which are listed the results upon which Fig.55 was based. The rate of rise of the microammeter reading,

at a given pressure, can be seen to: increase with successive readings. As has been mentioned it was necessary from time to time to "re-tune" the apparatus, using the Muirhead oscillator. Fig.57 shows

the variation of the resonant frequency observed whilst taking the

results shown in Fig.53. A number of photographs of single sweep oscilloscope traces were taken with 0, 6 and 20 p.s.i. excess gas pressure applied (Figs.581

59 and 60). By counting the number of luminescence pulses and dividing

by the number of cycles undergone by the sound field, a measure of the

probability of a luminescence pulse arising during a given sound cycle was obtained. These probabilities were 0.261, 0.282 and 0.050 at 0, 6

and 20 p.s.i. excess pressure respectively. -117—

TABLE 6 : Variation of Sonoluminescence with Static Pressure.

Pressure Resonant Frequency Time to rise 100RA on microammeter (p.s.i). (c/s) (secs)

0 21530 9.0; 9.3, 9.1 3 21510 14.2, 14.9, 5 21510 16.3, 16.5 6 21510 18.3, 18.3 8 21430 21.8, 19.7, 20.3 10 21430 24.3, 3.0, 23.8 14 21410 29.8, 28.8, 18 21320 34.1, 32.3, 301.031.0 2 22 21320 31.9, 25.0, 124.7 ..6 26 21230 22.7, 21.8, 18.4 30 21230 23./2. 22.12. 21.2 Return 25 21230 28.0, 30.8 22 21230 30.3, 21.8 18 21230 27.2, 27.0, 25.2 14 21290 18.7, 17.6, 16.9 10 21330 16.2, 16.1, 1 4.7 821380 8.8, 8.7, 8.6 6 21460 9.4, 9.5, 9.5 4 21460 8.3, 8.7, 8,4 3 21470 7.8, 7.7, 7.8 2 21470 7.5, 7.7, 8.3 0 21470 8.1, 9.0, 8.9 9.9, 10.1, 11,6 readings at 11.3, 12.6, 12.5 1 minute intervals 11.5, 11.4 118

resonant frequency(c/s)

0 0 xx 0 x x 21500

o FIG. 57

x x 21_400

0 0 0 0

x x x 0 2130 0 x

21200 10 20 30 excess pressure(ils.1-) 119

FIG. 56: SINGLE SWEEP OSCILLOGRAPH TRACES OF PICK—UP VOLTAGE AND PHOTuMULTIPLIER ANODE VOLTAGE. SAMPLE AT EXCESS rstLbSURE

NAIWVWWWWVINVWV1

WANWWWVVVIMMW

WWWWWVWVWWVW

FIG. 59: SINGLE SWEEP OSCILLOGRAPH TRACES OF PICK—UP VOLTAGE AND ANWWWWWWAAWA, PHOTOMULTIPLIER ANODE VOLTAGE. SAMPLE AT 6 P.S.I. EXCESS PRESSURE ,WWWWWWWWAIWIt 120

ANIANVAIWVInowwwwwwmip

1WWWVMMilMAMMIlf f

"WWWWWVINVV:mmiwy

W1111.11111WWW:Ahowww100

41All yyte

FIG. 60: SINGLE SWF.,,T OSCILLOGRAPH TRACES OF PICK—UP VOLTAGE AND PHOTOMULTIPLIER ANODE VOLTAGE. SAMPLE AT 20 P.S.I. EXCESS PRESSURE. - 121 -

Finally a phosphor bronze pressure tight spacer,or washer, of -e thickness was made to raise the height of the stub in the sample holder, with a view to seeing if the 'tail' on the sonoluminescence curve was due to the establishment of standing waves. Fig.54 was obtained using this spacer, and it can be seen that at 30 p.s.i. excess pressure the sonoluminescence intensity is lower in this case than in the other 'runs' using Gas pressure (Figs. 53, 55 and 56). Unfortunately, the construction of the spacer was somewhat faulty and time did not permit a more thorough investigation of this point. -122-

41 DISCUSSION OF EXPERIMENTAL RESULTS.

4.1. Observations of Cavitation. Two types of cavitation bubble were encountered: (i) bubbles too small to be distinguished individually but which appeared as a 'cloud' below the stub of the horn, and (ii) large stable bubbles which moved rapidly away from the stub (Fig.22). The distinction between these two types is often made by the use of the terms 'vaporous' and 'gaseous' cavitation respectively. The small cavities which contain a predominance of water vapour at their maximum radius both grow and completely collapse during the sound cycle, whereas the larger bubbles always contain a predominance of foreign gas and are merely subject to a pulsation during the sound cycle. In the latter case it is possible for the bubble to grow by a process of rectified diffusion until it is of resonant size.

Yosiaka and Kawasima (1) have shown that, for bubbles resonant to a source of progressive waves, the radiation pressure on the bubble shows a sharp maximum. The diameter (d cm) of resonant air bubbles in water at (c/s) by atmospheric pressure is related to the resonant frequency fr the formula :

f d = 657 cm/sec r which can be derived from the results of Minnaert (2). Thus at 21.2 Kc/s, the frequency of the transducer, the diameter of a resonant bubble is 0.31 mm. Inspection of Fig. 22 shows that the large bubbles have diameters of the - 123 - order 0.2 - 0.6 mm. It is therefore surmised that they are air-filled bubbles of approximately resonant size in rapid motion due to the radiation

pressure of a progressive wave.

It is also interesting to note that when the liquid sample was

contained in a narrow tube, so that these large bubbles could not escape

laterally from the radiation field that they were held at the bottom of

the tube where they would sometimes grow to several millimetres in diameter.

Yosiaka and Kawasima (1) also showed that the direction of the radiation

pressure was reversed for bubbles above and below resonant size in a standing

wave system* Thus the fact that these large bubbles always congregated

at the bottom of the tube, whatever its length, is some evidence for the

absence of standing waves. Of course had standing waves been present,

the appearance of clouds of vaporous cavities at other places as well as

under the stub might have been expected.

The fact that the larger bubbles appear to be moving at all

orientations in Fig. 22, and are possibly executing a spiralling motion

might be accounted for by Bjerknes'forces (3). Bjerknes' forces are

manifested as attractions between spheres pulsating in phase and as

repulsions between spheres pulsating in anti-phase.

A movement of cavitation bubbles directed radially inwards over the

surface of a horn has been observed by Meyer and Kuttruff (4) at 2.5 Kc/S

and by Kuttruff and Plass (5) at 30 Kc/s. The nature of the erosion

and of the pattern obtained with exposures of the "carbon paper pressure -124- detectors" both appear to support the observations of these workers. Meyer and Kuttruff ascribed the radial movement to a "quartz wind", but Lt could also be due to Bjerknes forces.

The atomisation of a droplet also appeared to be preceded by cavitation within the droplet so that presumably the effect depended upon shocks from the collapsing bubbles rupturing the surface film. At the same time the possibility of surface oscillations of such amplitude that instability resulted must also be admitted as an alternative explanation*

4.2. Changes in Noise Level and Temperature Oscillations. The periodic changes in noise level described in section 2.4 are reminiscent of the observations of Degrois and Badilian (6). These workers 2 used a quartz crystal of surface area 12 cm to irradiate a rectangular sided sample holder of 200 cm3 volume at 1 Mc/s. Various volumes of water and solutions were poured into the sample holder which was cooled so that the moan temperature was 25 ± 1°C. Thermocouples, hydrophones and a photomultiplier were employed to measure the ultrasonic intensity, the instantaneous temperature, the cavitation noise and the sonoluminescence.

The voltages at the terminals of these instruments were amplified and continuously recorded, Fig.6 showing their results obtained in the case of sonoluminescence, Similar results were obtained for the variation of intensity, instantaneous temperature and cavitation noise. The yield of free iodine from KI solution plotted as a function of time showed a step- like form. They also observed the alternate existence of two vibrational -125- modes of the cavitation bubbles. These modes could be distinguished by the number and diameter of the bubbles formed,their vibrations and movements in the volume of the solution, the height of the "geyser" formed at the surface and density of aerosol above the liquid surface, as well as by the parameters already mentioned.

During what Degrois and Badilian termed mode II there was an increase in noise, ultrasonic intensity and instantaneous temperature

(of 1-2°C) in comparison with mode I whilst chemical. effects and sono- luminescence appeared only during mode II. They found that mode I was permanent below a certain power threshold value P and that increase of power increased the duration of mode II until above an upper threshold power value P mode II was permanent. An increase in ambient temperature f' had the same effect as a diminution of power. For a given liquid, the curve of P or P as a function of temperature (transposed into the f vapour pressure of the liquid was shown to be a straight line.

Degrois and Badilian explain their results as transitions between

'gaseous' (mode I) and tvaporousl cavitation (node.II), but the mechanidm of the relaxation they describe appears to contain a number of questionable assumptions.

There can be no doubt however that some sort of relaxation effect can take place. The periodic changes in noise level and the sinusoidal oscillations on the heating curves described in section 2.5 are felt to confirm this fact. Moreover the enhanced amplitude of the oscillation in - 126- the case of carbon tetrachloride and its apparent absence in the case of glycerine seem to emphasise the role of vapour pressure as pointed out by Degrois and Badilian.

4.3. Preliminary Observations of Sonoluminescence.

The location of sonoluminescence below the stub of the horn would seem to indicate its origin in the very small or vaporous bubbles. The enhancement of the luminescence with aqueous carbon tetrachloride solution or with. glycerine or by saturation with argon is well known, if not well understood. The periodicity of the sonoluminescence flash with the sound field is also a well investigated phenomena. However the single sweep traces appear to be novel and of some interest. The fact that a sono- luminescence pulse does not occur with every pressure cycle would seem to indicate that there is not always a suitable nucleus in the vicinity of the stub when the pressure becomes negative.

4.4. Variation of Sonoluminescence with Static Pressure. Earlier experimental findings on the variation of sonoluminescence with static pressure have been summarised in section 1.2.3. The various theories that have been advanced to explain the experimental observations will now be summarised and discussed.

4.4.1. Theories of the variation of sonoluminescence with static pressure.

According to Harvey (7), who was the first to investigate the effect of pressure on sonoluminescence, such "a study.... becomes a study of the effect of pressure on cavitation". Harvey did not indicate what -127— precisely was meant by these words, and it was left to Polotskii (8) to make a more definite hypothesis of the mechanisms involved. He suggested that gas "dissolved" in a liquid provides nuclei to act as cavitation centres. Thus degassing under reduced gas pressure or engassing under applied gas pressure will decrease cavitation and sonoluminescence in the first case and increase it in the latter. Polotskii supported the electrical microdischarge theory and argued that the application of pressure would lessen the maximum radius of a cavity thus facilitating discharge across the bubble.

The effect of pressure on sonoluminescence has been observed qualitatively by several other workers but no explanations were

proposed. The only other theoretical indication of a possible mechanism comes from the general theory of cavitation put forward by Noltingk and

Neppiras (9) according to which there are upper and lower static pressure thresholds for the appearance of high pressures in the liquid surrounding the collapsing cavity. This process may be visualised in the following way : as the static pressure increases so does the velocity of collapse

of the cavity wall and similarly the transient liquid pressures developed.

On the other hand as the static pressure increases there is a lessening

of the maximum radius attained at the end of the growth stage, and finally

this growth is completely suppressed. Thus there is a static pressure

value at which these two opposing tendencies just counterbalance, and at

this pressure value the radiated shock wave pressure is a maximum. .:(See

128

maximum maximum

radius R fluid pressure P

(microns) (atmospheres x106)

1500 3

1000 2

500 1

I i 0 1 2 3 4 static pressure( atmospheres)

FIG.61:MAXIMUM RADIUS & FLUID PRESSURE

AS A FUNCTION OF STATIC PRESSURE

acoustic pressure: 4 at ms. angular frequency:9x104 4 radius of nucleus:1 6x10 cm ( NOLTINGK and NERNRAS) -129—

Fig.61). If the temperature and pressure of the cavity contents vary in the same way as the liquid pressure in the immediate neighbourhood of the collapsing cavity, then it might be supposed that sonoluminescence will also show a maximum at a certain value of applied excess pressure.

4.4.2. Discussion of theories of the variation of sonoluminescence with static pressure.

The following discussion of the theories of the pressure variation of sonoluminoscence has the aim of clarifying some points prior to an interpretation of the results given in the preceding chapter. The remarks of Polotskii are based on the microdischarge theory, which has, it is assumed, been superseded for the reasons given in section 1.6. Polotskii does not explain the appearance of a maximum and a suppression point in the curves which he himself obtained (See Fig. 3). His indication of the possible role of nuclei in the process is, however, of some interest. Polotskii does not report any evidence of a change in the impedance of the cavitated medium (or transmitted ultrasonic power) with pressurisation and his results, in contrast to those of the author, showed a clear suppression point.

The extrapolation from the thy of Noltingk and Neppiras indicates a possible mechanism for the maximum and tendency towards suppression.

However, the curve shown in Fig. 61 applies only to certain particular values of the parameters concerned, including the nuclear radius. In practice a liquid will contain a distribution of nuclear sizes, and — 130 — pressurisation is known to affect this distribution. Furthermore the extrapolation from the behaviour of the pressure in the liquid shock to that of sonoluminescence must be treated with some reserve.

Clearly, a satisfactory explanation of the variation of sonoluminescence with pressure cannot be divorced from the study of the state of the liquid medium as a whole, which introduces the complex question of cavitation nuclei. The existence of such microscopic inhomogeneities in liquids was first postulated to explain the discrepancy between experimental and theoretical values for the tensile strength of liquids. Gas bubbles and solid particles have been suggested as possible cavitation nuclei, although in the former case it is difficult to explain why such small bubbles should not rapidly dissolve and various mechanisms of stabilisation have been put forward. Cosmic rays have also been suggested as the means of creating small gas bubbles in liquids. The spectrum of nuclear sizes has been measured by means of acoustic absorption (which shows a sharp peak with bubbles of resonant size) e.g. by Iyengar and Richardson (10) using tap water, (see Fig 62).

Pressurisation of water has the effect of increasing the cavitation threshold, although even after considerable pressurisation relatively large nuclei can still exist, as was shown by Knapp (11).

In addition to these facts concerning the nuclei contained in water, there is certain other data regarding other parameters which vary during cavitation under pressurisation. As already mentioned in section 1.7. a 131

tabsorption 240

160

80 ....--4,--....--sa ,...... --b --v-..... c d 250 500 750 1000 frequency . 1 (Kcls) 50 20 10 7 equivalent bubble diameter (microns)

FIG.62:VARIATION OF ULTRASONIC

ABSORPTION AS WATER STANDS FOR

DIFFERENT TIMES (Iyengar and Richardson)

a : freshly drawn b : after 1/2 hour c: after 1 hour

d :after 20 hours - 132 - number of cavitation effects show a variation with static pressure similar to that of sonoluminescence. There is also the interesting evidence presented by Busnel and Degrois (12) that the acoustic absorption, for a given driving voltage, varies with static pressure in a similar way to sonoluminescence, as is shown by the solid line in Fig.63. This variation they measured both by thermocouples and by observing the height of the

"ultrasonic fountain". They made no suggestions as to why the power should vary in this way.

4.4.3. A modified theory of the variation of sonoluminescence with Static Pressure.

If this variation of acoustic power absorbed were caused by a variation in the impedance of the medium, due to the presence of cavitation bubbles

(which are of low impedance compared to quiescent water), then the number of cavitation bubbles present at any pressure may be surmised to have the form of the broken curve in Fig. 63. If sonoluminescence is then thought of as a number of pulses (this number being determined by the number of cavities) of heights determined by the power and static pressure (as in the theory of Noltingk and Neppiras) then the variation of time averaged sonoluminescence with pressure might be imagined as in Fig. 64.

The single sweep photographs (Figs, 58-60) afford some evidence that the number of cavitation bubbles do vary with pressure in the way shown in Fig. 63. The typical variation in resonant frequency shown in Fig.57 also supports this conclusion, since the overall variation is in the 133 height of geyser (cm;

IMa 1/1•\ FIG.63: HEIGHT OF GEYSER AS A FUNCTION OF PRESSURE (BUSNEL & DEGROIS) HYPOTHETICAL VARIATION OF CAVITATION EVENTS-- — \ (arbitrary units)

►

0 2 4 6 8 10 pressure Kgm(cm2)

sonolum nescence (arbitrary units) FIG.64:HYPOTHETICAL VARIATION OF LUMINESCENCE

pressure -134- direction of that obtained with a non-cavitating liquid load (see Table 5).

However, some explanation of this postulated variation in the number of cavitation events is required. According to Henry's Law the saturation gas content of a liquid is proportional to the applied gas

pressure. Vigorous stirring due to cavitation would accelerate the

attainment of an equilibrium in gas content due to the opposing tendencies of degassing and the operation of Henry's Law. So that if it is assumed that the number of entrained gas nuclei is proportional to the gas content, then the number of nuclei should rise with applied gas pressure. However the cavitation threshold increases with applied pressure; which will tend to decrease the number of nuclei that are actually expanded into cavitation bubbles. Thus it is not unreasonable to suppose that there should be a pressure value at which an optimum number of cavitation events occur.

(point M a in Fig. 63). Pressurisation is known to cause larger nuclei to dissolve more readily than smaller nuclei, and as the spectrum of sizes of nuclei in freshly drawn tap water contains peaks corresponding to larger nuclei it is reasonable to suppose that these could be readily suppressed by slight pressurisation, causing the initial minimum in the curve (point Mi). The fact that some samples had been allowed to stand overnight or for some days and then did not show the maximum in the power curve or the first minimum in the sonoluminescence curve would seem to indicate that these larger nuclei could also disappear on standing, without pressurisation. — 135 —

The displacement in the position of the maximum on the return, with gas pressurisation could be interpreted as a shift in the point Ma due to an accumulation of nuclei at higher pressures that can only be expanded into cavitation bubbles as the pressure is lowered. Presumably there is an equilibrium number of nuclei at each pressure value which is not immediately attained. This is supported by the fact that the intensity of sonoluminescence increased with successive readings at higher pressures (see Table 6) and decreased to an equilibrium on depressurising. The hysteresis effect would therefore presumably not occur if the sample were cavitated at each pressure for say 15 minutes before taking the sonoluminescence reading. As has been mentioned

Harvey found that sonoluminescence became intermittent at about 1.3 atmospheres excess pressure and disappeared at pressures above this value.

On decreasing the pressure the light did not re-appear until about 0.8 atmospheres excess. This would appear to be the earliest report of the hysteresis effect of pressure on sonoluminescence.

The shift in the maximum due to increasing power could be due to a shift in cavitation threshold, so that more nuclei can be expanded at a given value of static pressure. Similarly a shift in the suppression point towards higher pressure values might be expected on this basis and which might also be expected to be roughly linear, which agrees with the results shown in Figs. 52 and 53. - 136 -

The results obtained when pressure was applied by means of a water force pump present some problems in interpretation. The decrease in power absorbed would appear to indicate an increase in nuclei during pressurisation. However the drop in the value of sonoluminescence on subsequent pressurisation would appear to indicate a decrease in the number of 'permanent' nuclei. Almost certainly some pockets of air would be trapped in the apparatus during pressurisation, and these might have been sufficiently large to supply a temporary increase in the number of nuclei available during pressurisation, but not large enough to restore the reservoir of permanent stabilised nuclei depleted by pressurisation, or simply by standing.

The existence of the 'tail' on the luminescence curve at pressures well above the extrapolated suppression point is problematical. Although the evidence, as summarised in section 2.4 points to the absence of standing wave effects at atmospheric pressure, it is possible that they could exist at higher pressures, with the suppression of most of the cavitation.

In this case there could be an increase in the acoustic pressure amplitude sufficient io exceed the threshold value. On the other hand it is also possible that the effect is due to large nuclei surtiving or .13:91'rg :created despite the high degree of pressurisation. — 137 —

REFERENCES. 1. YOSIAKA, K and KAWASIMA, Y Acustica 5 (1955) 167. 2. MINNAERT, M : Phil. Mag. 16 (1933) 235. 3. BJERKNES, C.A. : Compt. Rendus 84 (1867) 1222,1309,1375,1446,1493. 4. MEYER, E and KUTTRUFF, H z.f. Any;. Phys. 11 (1959) 325. 5. KUTTRUPF, H and PLASS, K Acustica 11 (1961) 224. 6. DEGROIS, M and BADMAN, B: Compt. Rendus 254 (1962) 231, 837,1213,1943. 7. HARVEY, E.N. ; J. Am. Chem.Soc. 61 (1939) 1392. 8. POLOTSKII, I.G. Zhur. Fiz. Chim. USSR 22 (1948) 787.

9. NOLTINGK, B.E. and NEPPIRAS, B.A. : Proc. Phys. Soc. B63 (1950) 674 Proc. Phys. Soc. B64 (1951) 1032 10. IYENGAR, K.S. and RICHARDSON, E.G.: Brit.J.App.PhYs. 9 (1958) 154. 11. KNAPP, R.T. : Trans. Am. Soc. Mech. Engrs. 80 (1958) 1315. 12. BUSNEL, R.G. and DEGROIE,M.: J. de Chim.Phys. 52 (1955) 179. -138-

5, SUGGESTIONS FOR FURTHER WORK

Sonoluminescence depends on the physical characteristics of the cavitated medium, the number of nuclei, temperature, static pressure, acoustic power and frequency, and it also depends upon the nature, the temperature and pressure of the content of the cavity, The gross characteristics of the medium being easier to measure, their influence on sonoluminescence is better understood than that of the cavity contents.

There are possibilities in the application of the knowledge of the dependence of sonoluminescence on these grosser parameters eg. in studies of cavitation nuclei.

5.1. Sonoluminescence and Nucleation Problems.

As already mentioned in the preceding chapter the variation of acoustic power, the resonant frequency of a cavitating system, and the sonoluminescenc could all be connected with changes in the nucleation of the liquid sample.

Some further work might thus be devoted to investigate this possible correlation. A more reliable determination of the variation of the absorption of acoustic power with static pressure could be made with calibrations of vibration amplitude (i.e. pick—up voltage) against power absorption at various pressures with a calorimeter similar to that shown in Fig. 27, but modified to permit pressurisation. It would also be of some interest to decide if the 'tail' of the sonoluminescence — pressure curves is due to standing waves or to the creation of large nuclei. — 139 —

Further attempts could be made to ascertain if the number of cavitation events does vary with pressure as postulated in Chapter 4, firstly by a more comprehensive study of the luminescence pulses. If it were possible to make an analysis of pulse heights, then a distinction could be made between the effects of nucleation and of cavitation bubble Growth and collapse. The opposing tendencies of de—gassing by cavitation and en— gassing by pressurisation (aided by stirring) probably cause changes in the gas content of the water. A direct determination of gas content should therefore afford further evidence of the population of nuclei.

In addition to these pressurisation studies of nucleation, sono— luminescence could be a useful aid in counting the number of cavitation events after 'seeding' a sample of pure liquid with nuclei of various types, such as small bubbles, small solid particles, or by neutron irradiation. It might be useful to apply a sonoluminescence pulse counting technique to cavitation threshold measurements.

The glass apparatus shown in Fig.41 was designed to permit vacuum distillation of the liquid into the experimental system, and to operate magnetic stirring in order to produce water free of nuclei. It incorporates a calibrated vessel (which can be temperature controlled) and a manometer to enable determinations of gas content to be made by

Galloway's method ( 1). The apparatus should thus be fairly versatile and capable of a number of nucleation experiments. 5.2. The Origin of Sonoluminescence.

It may now be taken as established that sonoluminescence is broadly

of thermal origin. The details of the mechanism are, however, as yet unresolved and there is scope both for further theoretical and experimental work. As tes-;50 of the theory put forward in Appendix 2 some practical

propositions can be made, If the temperatures and pressures are both

extremely high, no spectral lines should be found that are not subject to considerable broadening. It would be of considerable interest to ascertain if the temperature and pressure distributions within the cavity are substantially uniform as iostulatod in Appendix 2. The dissolving of certain hydrocarbon gases_in water should substantially affect sono— luminescence if their action in shock tubes is any criterion.

The various methods of simulating the collapse stage of cavitation might be particularly useful in elucidating sonoluminescence meo7—JAism, as then the cavity content can be controlled (at least initially) and greater light output can be obtained per event, than with normal cavitation. An increase in light output might be obtained from collapsing glass spheres with pressurisation of the surrounding liquid.

On the basis of Appendix 2 sonoluminescence obtained from agitated mercury should be considerably enhanced if an atmosphere of xenon, krypton or argon (high r, low molecular velocity) is employed and possibly an optimum gas filling pressure could be demonstrated. Finally the collapse - 141 — of bubbles by means of liquid—borne shocks would appear to have considerable possibilities, since in the opinion of Travis (2) spectra could easily be obtained from such bubbles.

It would appear that the study of the origin of sonoluminescence is closely related to the study of isentropic compressions of gases, a comparatively unexplored field. The possibility therefore exists that eventually new information on gases and vapours at very high temperatures and pressures could be derived from sonoluminescence studies.

REFERENCES:

1. GALLOWAY, W.J. s J.A.S.A. 26 (1 954) 849 2. TRAVIS, J.R. s Private Communication. — 142

APPENDIX I : THERMAL CONSIDERATIONS

IN THE DESIGN OF THE SAMPLE HOLDER.

The intensity of sonoluminescence decreases with rise in temperature and hence it is desirable to operate at a constant low temperature if the effects of other variables are to be observed.

If the outside of the samplJ; holder'is maintained at a constant temperature Y°C, it remains to be assessed how the temperatureS°C inside the vessel will vary with time, t sec, after commencing irradiation, and with the thermal conductivity, k c.g.s. units, the' area, 2 A cm , and thickness, d cm, of the walls. Assuming that heat is generated uniformly within the liquid sample, which completely fills the holder, at a constant rate H cals/sec, and that the thermal capacity of the sample is W eels, then :

w (4$ H- k (,0 - A (1) - kA =- ga te 71 -1; If = (1) when r. Q0( Hci kA

- 143 -

It can be seen that the temperature rises eventually to an equilibrium value )e.- , so that :

(2) KR

If the time taken for I/e of this temperature rise to occur is t, then : t--vV ci (3) k

Comparing these results for glass and metal vessels, all other conditions being the same :

,b5)3 k ry, 6trn,

arhi

j 14,9 As :01."22.71()(N, the difference between the equilibrium temperature within the vessel and the constant temperature outside should be about

100 times smaller for metal than for glass and the equilibrium temperature should be attained 100 times as quickly.

If a sample holder is surrounded by air, conduction heat losses may be neglected at low temperatures, and equation (1) becomes d'D H ctt- - 144 -

Thus by measuring Wtt at low temperatures, as described in section 2.5, the value of H may be deduced. It was found that at full power H = 10 watts = 2.4 cals/sec., and substituting in equations

(2) and (3) using the dimensions of the sample holder described in section 2.7 Ct) 1::- 2.°C 0 -11.- - 02. 111 -- -E5 ZS "su, (AA 0 -145- APPENDIX 2 s PROPOSED THEORETICAL EXPLANATION OF SONOLUMINESCENCE AND ASSOCIATED EFFECTS.

A2.1: Introduction

A resume and discussion of previous theoretical explanations of sonoluminescence has been given in Section 1.6. It is presupposed that these effects are thermal in origin, as has been suggested by Noltingk and Neppiras (1), Jarman (2), Heim (3), Schmid (4) and others. There is some disagreement, however, as to the precise operation of this thermal mechanism and it is the purpose of this appendix to clarify certain points.

It is shown that, granted certain assumptions listed in the succeeding section, a number of aspects of the dependance of sonoluminescence on dissolved gases can be accounted for qualitatively in terms of the ratios of specific heats, the molecular velocities, the solubilities and the excitation potentials of the gases concerned.

A.2.2. Basic Features.

A.2.2.1. Cavitation Bubble Dynamics.

Theoretical predictions of the relationship of cavitation bubble radius with time have been made by Rayleigh (5), Noltingk and Neppiras (1) and others. These predictions, which agree in form have been verified experimentally by workers such as Guth (6), Knapp and Hollander (7) and

Harrison (8). The curves obtained can be replaced to a fair degree of accuracy by a growth stage in which the radius-time curve is linear and a collapse stage in which the radius-time curve is a parabola. Thus

146 in the collapse stage :

R= (1) where is the bubble radius at any instant, R.0 the radius at maximum volume, t the time and (A: is a constant. According to the theory of

Noltingk and Neppiras, the maximum fluid pressure, Pool is given by :

(

3 G2, / ( 2 ) where G/is the pressure within the cavity at maximum radius, and Pis the liquid pressure at which the collapse occurs i.e. the static pressure plus a component due to the sound field. For many purposes this latter component may be neglected. Noltingk and Neppiras used equation (2) to estimate the temperatures which might be attained within the cavity, assuming adiabatic conditions, and that the maximum pressure within the cavity is equal to the maximum liquid pressure. This temperature l; is then given by : p 3 o Try, T (ra' ( 3)

Noltingk and Neppiras quote as a typical case the growth of a nucleus 6 from 3 microns radius to 300 microns maximum radius i.e. a growth of 10 times in volume. If the equilibrium pressure in the nucleus isPa, then -147- a. .74. Po. t () assuming isothermal conditions and no gas diffusion during the growth stage. If rota': 2 atmospheres, (17zn: 2.10 6 atmospheres, and hence-T -M) 8.1012°K, assuming (!i* = 5/3, as for a monatomic gas. This amazing result leads to the conclusion that some heat loss mechanisms play a role, and that the conditions during the collapse are not purely adiabatic. It transpires, however, that the adiabatic temperature, i.e. the temperature that would be attained at any instant if adiabatic conditions did hold, is an important parameter in the subsequent analysis, and it is plotted in Fig. 65 in comparison with the radius-time curve drawn as a parabola assuming a collapse time of 311 sec.

To summarise these remarks : the results of Noltingk and Neppiras on bubble dynamics are assumed to be correct in the following analysis, except that a simplified form of the radius-time curve is adopted, and the assumption of a purely adiabatic collapse is discounted since it leads to unreasonably high predictions of final temperatures.

A.2.2.2. Pressure Distribution.

It is implicit in the theory of Noltingk and Neppiras that the pressure in the cavity is uniform, but the possibility that a shock wave could be generated within the collapsing cavity has been mentioned by

Jarman (2) and Heim (3).

Jarman (9) took Rayleigh's equation : 2..P I ‘) -37 ( (4) where U. is the velocity of the bubble wall, and P and f) the pressure and 148

300

200

100

0 0 1 2 t ( p sec)--o.

FIG.65

- 149 - density of the liquid. Jarman then showed, assuming adiabatic conditions, that the velocity of the bubble wall would exceed the velocity of sound in the bubble contents when This result is questionable Ro/oo. however since equation (4) was derived by Rayleigh assuming there was no gas present in the collapsing cavity. Later in his paper Rayleigh corrects equation (4) for the case of a gas filled cavity, assuming an isothermal collapse. To be consistent with Jarman's assumption of an adiabatic collapse the author derived a modified form of equation (4) :

.1.1•04. 34r U .114• 3f) for a gas filled cavity collapsing under adiabatic conditionslfrom which it can be shown that the velocity of the bubble wall does not exceed the f velocity of sound until "/t isa ratio much greater than 60. It may be concluded that whilst it is possible for the wall velocity to exceed the sound velocity, this will not occur until a late stage of the collapse.

However, it is not possible to assume on this basis that a pressure pulse will then be propagated as a converging "micro-shock" within the cavity, in the same way as in the conventional shock tube. It would appear to be possible that slight pressure disturbances could travel ahead of the bubble walls, long before they exceed the sound velocity. It seems reasonable to assume that the many wall reflections suffered by these pressure disturbances in a very short time interval will bring about a fair — 150 — degree of uniformity in the pressure distribution within the collapsing cavity.

A.2.2.3. Temperature Distribution.

It is also implicit in the theory of Noltingk and Neppiras that the temperature distribution within the cavity is uniform. It would be unreasonable, however, to expect a temperature of several thousands of degrees to exist in the cavity contents with the surrounding liquid remaining at its ambient temperature and no thermal conduction taking,pIdce. There must therefore be some temperature gradient at the wall of the bubble. It was found by Griffing (10) that the rate of inversion of sucrose, a reaction which is highly temperature dependent, was not affected by cavitation. It may be deduced from this that the liquid surrounding the cavity remains at the same temperature throughout the collapse. This will be assumed in the subsequent analysis, the liquid being regarded as a heat sink. The temperature gradient mentioned above is thus imagined to exist within the cavity contents. It will be assumed that this temperature gradient is linear over a distance of the order of a few mean free paths from the wall, and that the temperature is uniform within the remainder of the cavity.

This assumption greatly simplifies the subsequent analysis, and at least serves to illustrate the effect of thermal conduction. There are reasons however for believing that such an assumption is not so arbitrary as it might appear at first sight. Present (11)9 for example, discusses the well known effect of the "temperature jump". When a gas is conducting heat -151 - between two solid parallel plates at different temperatures, the temperature in the body of the gas is found to increase linearly with distance from the cooler plate, but generally the hotter wall is at a higher temperature and the cooler wall at a lower temperature than would be predicted by extrapolating the temperature variation found in the body of the gas.

Knudsen (12) calculated the distance over which this effect would occur as 0.95, where Xis the mean free path. Langmuir (13) using Knudsen's formula with improved data gave the value as 1.2X.

In the subsequent analysis it is assumed that this surface film is 3 )\ in thickness, but the form of the results would be the same for any chosen value of the order of a few mean free paths. The thickness of the postulated conducting layer will be of the order of a few percent of the bubble diameter throughout the collapse stage, since the mean free path decreases with increasing pressure.

A.2.2.4. Mass Transfer.

The first part of the analysis neglects the effects of mass transfer and of mixing of gas and vapour during the collapse stage, but further consideration will be given to these points in Section A.2.4.

A.2.3. The Effect of Thermal Conduction Losses.

If at any instant the temperature,T , within the bubble is uniform but drops linearly over a distance of 3Xto-ro, the liquid temperature, assumed to stay constant during the collapse, then the heat loss by conduction in an interval of time at is :

—152— R2 (T-To) dit 3 \

/ 2/0 , / / where . thermal conductivity of the gas (ergs/cm / C/cm/sec)

and ),4, = mean free path (cm)

In the same interval the heat made available through work done on the gas by the liquid is, ignoring work done by surface tension : P RI* d R) where = the instantaneous gas pressure. Thus the nett heat gain is mCvcT ci R 44-1 k R. (T —70) dyc 357

but ret where Yr). mass of the gas contained in the bubble, which is assumed to remain constant during the collapse and

= gas constant /gm

= C? Coi for a perfect gas.

Hence dividing (5) by y' 'C integrating,

-To v g 30-1Cv T

-vti3:4-4fq-7f)u1( 6) But according to Kinetic Theory :

9cv for monatomic gases

and k- Gv for diatomic gases

and

for diatomic gases. Now t> Y1114 where v = volume .14r M g -t) and To = adiabatic temperature: 1"Rd 2 that would ( be reached without thermal conduction or other heat losses. --14)ax] • • TA() )sitb t:STS0 FL also C) where ck is a constant. - 154 -

Thus -CAA -e)Y1 -f%

for monatomic gases. This is a non-linear integral equation, which was first solved by inspection. The possibility has recently been pointed out to the author of a series solution, which requires some further attention. The results of this series solution appear to vindicate tiose obtained by the inspection method. If the temperature is assumed to be a function-lAof time and is used to evaluate the integral in (7) then-17, on the left hand side of

(7) can be found as a function of time-T;(). Then if T1 (t)and1-2.(9 are consistent it may be taken that To is the solution. The form of the temperature-time relationship will be assumed to be given by :

T, (14 — -To) — To -•=. je-9 (8) i.e. the temperature rise is in reality a fraction of the rise that would be obtained in the adiabatic case. Equation (8) may be re-written :

— Cif,ci —Tv) lo (9) for convenience. Then, if X, is greater than unity - 155 - T TAA A (51

But —14114 tz To To I I 1 \ (a 10) i0% 1", C Substituting (10) in the integral of equation (7)

G kT 04. IT 6 lox T R R

At the start of the collapse IO • At the end of the collapse Ilr tr..] when C >To from (10) T 741 , so that fro /( 'LL . —1-161 =^ I D tlo ) . These are thus the two extreme cases, although the latter is probably the better approximation as the last part of the collapse contributes most significantly to the integral. Taking the low temperature approximation, --- ;Or —Of tF clic 1 (12) (0 D- 0 /S and for the high temperature approximation 3(Zr-12 (tP" ait

72. 2' .... --677717 /51) --____ ('13)13) 0

In equations (12) and (13) which apply to monatomic gases, V0 = mean molecular velocity at 300°K, For diatomic gases, for which de = 1.4, tf 0,3v-or at 3 ----;*c 43,A• (14) /0 0 IN

as a low temperature approximation and

I 0 (15) lOx Jb k3/2.t- -- v3)

as a high temperature approximation. The values of the integrals,

in the equations (12) - (15) are given by equations (16)- (19) respectively, after substituting for and tF I -4- -2 1° 6) ' 4.1e, g 12, c,14- -4 -2 e(-V+ i0 (12,1611 ( bG/1" tRir 5.11 — (17)

Vo in 10 + 0-4-%.10 0 59 01 (18) 10 - 4- t VD Rd 0-6 4 0i4r2)dp 3 10 xy 1.2 RI= (19)

157

The values of I were then evaluated numerically for a number of gases at a number of initial pressures, Q, using the relationship :

(20) which can be deduced from (2) and (3) and where KF is the radius at the end of the collapse. Equations (16) and (18) then reduce to the form: A. so that TA 4 105—)1 so that, for consistency, 106-1 -1741 TA 4 .145 lox tAy3;)c v; —x. (21) which can be solved graphically for 'X. . Thus the final temperature

can be found, and the results are shown for a number of gases at various initial pressures using the low and high temperature approxim- ations-in Figs. 66 and 67. As these curves represent extreme - 158 -

TABLE 7. Final Temperatures (°K) attained, evaluated using low temperature approximation (See Fig.66).

Initial Pressure,Q (atmospheres). 1 GAS 10 10 2 10 3 10 4 2 Xenon .6400 10 3.00 103 5.30 103 7.50 103 -..-..-.. Kryp+on 5.,30 9 2.12 103 4.24 103 6.00 103 2 2 Argon 3.00 10 9.48 10 1.68 103 2.12 103 2 Neon 2.12 10 6.72 10 1.20 10 3 1.50 103 Helium 1.20 102 3.00 102 5.31 10 7.50 102 -t------...... *...... NitrogenI N2 3.57 102 1.13 10 2.26 103 3.16 103 Oxygen, 02 4.03 102 1.26 10 2.26 '103 3.16 10 Hydrogen,H2 1.6 10 4.50 102 8.00 102 1.12 103

TABLE lg. Final Temperatures (°K) attained evaluated using high temperature approximation (See Fig.67).

Initial Pressure, Q (atmospheres) , .. 1 2 -3 -4 GAS 10 10 10 . 10 Xenon 6.00 102 2.40 104 6.00 105 1.20 107 2 Krypton 5.35 10 2.12 104 5.35 105 9.5o 106 Argon 4.80 102 1.90 104 4.20 105 8.40 106 2 Neon 4.20 10 1.50 104 3.30 10 6.00 106 2 Helium 3.00 10 9.60 103 1.89 105 3.00 106 Nitrogen,N 2 3.20 102 2.85 103 2 25 104 1.60 105 Oxygen, 02 2.00 102 2.80 103 2.40 104 1.60 105 Hydrogen,H2 2.00 102 1.40 103 .4 1.02 104 9.00 104

159

FIG. 66: LOW TEMPERATURE APPROXIMATION

xenon

7000

6500

6000 krypton

5500

5000

4500

4000

3500 oxygen, 3000 nitrogen

2 500 argon 2000

1500 neon hydrogen 1000 helium 500 1 1 1 0 Q (atmospheres) o -1 -2 3 4 10 10 10 10 10

I I t R (microns) 90 9 0.9 0.09

I I 1 I t 0.7 0.93 0.993 0.9993 1P 160 T (°K) xenon 7 10 krypton argon neon

helium

106

oxygen, nitrogen 105 hydrogen

104 FIG.67: H! GH TEMPERATURE APPROXIMATION

10

102 I Q (atmospheres) 0 10 10 101 10 2 10 3 104

RC microns) 90 9 0-9 009

0.93 0.993 0.9993 t/t t 2.F -161—

approximations, the true solutions will lie between these values so

that even if the family of curves for diatomic gases does not overlap

the family of curves for monatomic gases, there will be a closer approach

than that shown in Fig.67.

A.2.4. The Effect of Mass Transfer.

So far the processes of diffusion of gas through, and of evaporation

and condensation of the vapour at the bubble wall have been ignored, and

it is now necessary to give some indication of their effect, If there A n- were no heat loss due to thermal conduction, from (5) 100: GA

Now if an atom or molecule leaves the bubble and becomes

absorbed in the liquid by collision with the molecules of the liquid

it will deliver its energy to the liquid and not to the bubble content,

although the remaining gas molecules will not lose energy individually.

Thus the temperature of the bubble will not be diminished, although the

total energy of the bubble content will have been reduced, together with

the total mass and pressure. If the new mass and pressure are

and (1) respectively, then (IN\ vh)Cdy (12 -411)) 4 Ti RI- R

But =,. (V17 YN'N (r)A Yii) V whatever the mass, provided \ti/(m) , so that

oi

Ri -162-

i.e. I To i.e. the same final temperature will be attained even if mass is transferred from the bubble. The same argument can be used even when thermal conduction is present, since then

where I is not a function of mass.

A.2.4.1. Mass Transfer in Bubble Growth.

If the case of cavitation of a saturated aqueous solution of a gas is considered then it is clear that both gas and water vapour will diffuse into the bubble during the growth stage. Some estimate of the bubble content at the end of the growth stage can be made by assuming the entry of gas and vapour can both be represented by the diffusion equation :-

cNi sz 19roxi rt A de (22)

If further it is assumed that the partial pressure of the gas in the water falls to that in the bubble linearly over a distance of say three mean free paths, in the water, then

-n) 4-Tre 3\ (23)

- 163 - where r\,, and fl are the number of gas molecules in lcc. of the water and the cavity respectively,

11(5 S: (21 where .5 is the solubility of the gas in water at 2000, expressed as the

volume of gas, reduced to N.T.P. dissolving in unit volume of water, and M A is Avogadro's number. ..17. IV iliTt R3 where .4) is the total number of molecules of the same gas or vapour in the bubble.

Now from Kinetic Theory. 1111):M .\11\ hence

S NA 4:ii ( RI a 0.).,4)10 3 C\I J R If the growth stage of cavitation can be represented as linear

with time

i.e. (24)

so that ):!.):*(1!5 where tr is the time taken for the bubble to grow

to maximum radius go , and is about half a period i.e. 15µ sec at 30 Kc/s, then b 241; 2.103. Substituting for %, r1 andl in (23) and integrating over the

—164- growth stage, N0 3 4-II I 11(0(25) N (.2.1g 4)10 3 Jo t\I This is also a non-linear integral equation, similar to equation (7) and a similar procedure for solution by inspection can be adopted to obtain approximate values of the pressure at maximum radius, for a number of gases, these values being given in Tablet?. It was assumed in these calculations that the pressure in the nucleus was about 1.7 atmos- pheres, taking account of the excess pressure due to surface tension.

In the case of the water vapourentering the bubble,

11) V \\I so that substitution in (23) leads to 2

(IZNi cii" I , Ntk.1 3 If ts4 cbd (26)

Equation (26) is then equivalent to equation (25) for the case of gaseous diffusion. Following the same procedure, it is found that for water vapour

= 16 atmospheres. vapour This is well above the saturation/pressure for water and indicates that the water vapour in the bubble at maximum radius is at the saturation -165—

TABLE el : Partial pressures, Q, of bubble contents at maximum radius for saturated aqueous solutions of gases.

T GAS Q GAS Q (Atmosphera) (Atmosphere4

Xenon (2.6)10-3 Hydrogen (1.7)10-4

Krypton (1.07)10'3 Carbon (1.7)102 dioxide - .- - - Argon (6.7) 10 4 Water vapour (2.3)102

Neon (1.7) 104

Helium (1.06) 10-4

Oxygen (6.8) 10 4

Nitrogen (2.7) 10-4 I - 166 - value which will then be quoted in Table q.

A.2.4.2. Mass Transfer in Bubble Collapse.

During the collapse stage, the diffusion equation (23) may be written

In the later stages of the collapse the number of gas particles per cc within the bubble greatly exceeds the number per cc in the solution, so that 1); may be neglected. Hence, integrating over the period of the collapse

PAT3 N] No so that

N D or N F (27) N Now from Kinetic Theory,

p .3a N 13Cr (tz:,-37t/F so that P _77 CF 7ro1. ro (28) If water in equilibrium with water vapour at 3000K is hold in a container, and the volume of this container is then decreased isothermally - 167 - the vapour will condense so that its partial pressure remains constant.

If now the case is considered of a bubble collapsing so rapidly that only the molecules in the immediate neighbourhood of the wall can be cooled and condensed, there will be an increase in partial pressure of the vapour remote from the wall. Thus there will be a pressure gradient set up within the bubble, in the case of water vapour, as opposed to a gradient of partial pressure in the water, in the case of a gas. The extent to which the vapour pressure gradient builds up during the collapse is a diffusion problem which can be treated in the same manner as for gaseous 4160.0 diffusion using equation (28), save that V is an increasing function of temperature, and thus of time. It would thus appear that in the case of water vapour, from equation (28) thatiV6 is less than one. Clearly lo this situation could not arise since there would then be evaporation, and it is concluded that the molecular velocity of water vapour is sufficiently great in comparison with the velocity of the bubble wall to maiutain the partial pressure of water vapour at a constant value throughout the collapse. If the ratio of the partial pressure of the gas within the bubble to the partial pressure of the vapour is Cr at any time, then from (28)

if_ 4. 2R0 Q"o 7rc, •••••.ftim•••••••••...... (29)

-168—

If the gas and vapour are in thermodynamic equilibrium at any time during

the collapse it follows that

_No.v 9 where is a constant i3

and letting

W V (30) L 5 Ka

It is clear from equation (30) that the bubble will contain a mixture of

gas and vapour whose relative proportions will vary during the course of

the collapse. The ratio ROIt is in fact the 'averages velocity of

the bubble wall, so that the third term of equation (30) may be written (KA3 vvvi e.t which will be greater than unity provided : 3 7 4, /2. Vw > • ( 31)

This signifies that a pressure will be built up in the bubble, provided

the average wall velocity exceeds one sixth of the molecular velocity at -2 300°K. Using the values tF = 3.106 sec and go = 3.10 cm this

condition will be fulfilled by all the gases so far discussed except for

water vapour, hydrogen and helium.

Now it can be seen, from Tablet"? that the initial ratio of gaseous

to vaporous partial pressures will be small, varying from about 1 in the — 169 —

1 in the case of helium. It would seem that case of carbon dioxide to 100 the compression of a mixture of equal numbers of xenon and water molecules would attain a higher temperature than when the same compression is applied to a mixture of equal numbers of helium and water molecules. 'nasality the ratio of numbers of molecules in these two examples starts by being larger for xenon than for helium (see table Q) and increases considerably for xenon while probably only increasing a little, if at all, for helium.

In fact in the case of helium the ratio is so small that the temperature attained will probably be very close to that due to the compression of pure water vapour.

Referring back to equation (30) it can now be seen that there is a -- ‘14,Vyi "positive feedback" relationship between the third term RoA? ( 'NI.= and the first termT T . The second term L:7"being typically of the order of 10-1 or 10-2 will be relatively unimportant, so that it may be concluded that towards the end of the collapse, cavitation bubbles solution in an aqueous/of xenon will contain xenon predominantly.

Qualitatively, it can be seen that the presence of water vapour will generally depress the temperature curves for mon- and diatomic gases in

Figs. 66 and 67. Furthermore, the lower the curve lies in its family the further it will be depressed, so that the spread in the individual families will be increased, and the gap between the families will be decreased. In fact the oxygen-nitrogen curve might now lie above the neon curve, although it cannot roach the argon curve since the latter gas -170- has a lower molecular velocity than oxygen or nitrogen.

A.2.5. The Mechanism of Sonoluminescence.

When Nbltingk and Neppiras first suggested the possibility of a thermal mechanism as the origin of sonoluminescence they mentioned black body radiation as a possible example. There are two principal objections to such a mechanism. Firstly in the derivation of the formula for the spectral distribution of the. radiation it is assumed that the dimensions of the black body are large compared with light wavelengths, in fact it is assumed that there are differential segments of area on the surface of the body whose dimensions are large compared with light wavelengths.

However, at the end of the collapse the radius of the bubble might be orders of magnitude less than microns (10-4 cm) whilst light wavelengths are of the order of 10-5 cm. Secondly the derivation of the black body distribution law assumes the body to be at thermal equilibrium within a perfectly insulating enclosure, whereas in the case of cavitation there must be considerable heat losses due to thermal conduction, mass transfer and finally due to chemical reactions and radiation.

In order to find a better mechanism for explaining the spectra of sonoluminescence the actual state of the compressed gas must be considered.

Assuming as before that the results of Kinetic Theory may be applied it is clear that there will be a distribution of velocities within the bubble.

Thus distribution will probably not depart far from the Maxwellian form which is such that for molecules of mass $Y), of molecular density V‘/:c. - 171 - the number C14 with velocities lying between \I and V+41/ is given by :

111.1 R., 7141 N/ a V (32) ITN klairi

Let kinetic energy of a molecule and

)51 141. and X. --/a then 1`.-- ct x, --- (33)

It might be supposed that excitation will occur after collisions between high energy atoms or molecules. Thus the emission of sonoluminescence or the occurrence of chemical changes might be expected when the energy of the molecules becomes comparable with the critical potentials of the atom or molecule.

It seems likely that in the end stage of the collapse not only are high temperatures attained, but also high pressures. The work of krabinin (14) is of particular interest in this respect. He found that the ionisation potential of nitric oxide was lowered under conditions of high temperatures and pressures. He ascribed this phenomenon to perturbations arising from the proximity of atoms and it would thus seem that with high densities the discrete energy levels will become broadened into bands and finally a continuum. Such a process has also been described by Finkelnburg and Peters (15). It would also appear probable that the higher energy levels will be more perturbed than the -172- lower energy levels at the same atomic separation, as the effect of the

perturbing field will be stronger at the outside of the atoms. If,

in fact, the perturbation is such that the energy levels become virtually

a continuum above the first critical potential, E1 , then if an amount

of energy ai is delivered to the atom in this state such that A5-)T excitation or ionisation will occur followed by emission of a photon

when the atom returns to its ground state. On this basis, it might be

expected that the spectra of sonoluminescence would consist basically of

a continuum.

The probability of such an emission occurring will depend upon the

value of X hth.,:f , at any temperature T , Xi and the probability of excitation being related by equation (33). The values of Age =4:1 for the various gases at various temperatures are given in Table 16.

On the basis of the foregoing analysis it is possible to explain

the experimentally observed dependence of sonoluminescence on the nature

of the solute gas (see Table 3, Page 27) (i) Due to thermal conduction,

gases which have the same , will actually attain different final

temperatures. It is possible that some overlapping between familie6

of gases with the same (*will occur due to this cause alone. (ii) The

spread within a family in the temperatures attained will be enhanced due

to differing solubilities and molecular velocities, resulting in the

cavity contents being a mi2ture of gas and water vapour of different

proportions. (iii) Further spreading will appear, if relative values

of sonoluminescence are considered, due to differences in the excitation - 173 -

10 TABLES'.

x GAS E1* 1 (eV) 500oIC 1000115009k yafk 6000k 1200*2000e.

Xenon 8.3 190 104 49.5, 32.2 16.1 8.1 ' 5.2

Krypton 9.9 230 124 59.0 38.5 19.2 9.6 6.2

Argon 11.5 267 144 68.5 44.5 22.3 11.2 7.2 I,- Neon 16.65 365 196 93.2 60.9 30.4 15.2 9.8 . Helium 19.75 460 247 118 73.8 38.3 19.2 12.4 - Oxygen 7.9 184 99 47.0 30.6 15.3 7.2 4.9

ti .. . Nitrogen 8.5 198 106 50.5 33.0 16.4 8.2 5.3 1 - Hydrogen 11.15 260 139 66.2 41.5 21.6 10.8 6.9

* Mohler : Int. Crit. Tables vol. 6 p.69. -174-

potentials of the gases concerned. Although these remarks are

necessarily qualitative, it would appear that the experimental results

can be shown to be quite reasonable from a theoretical viewpoint.

A.2.6. The Mechanism of Chemical Effects.

There are definite critical potentials for the dissociation of

molecules and for the formation of new chemical products. Thus the

same factors which influence the yield of sonoluminescence from a given gas must influence the yield of chemical products of cavitation. A

number of these reactions will now be discussed.

(i) Reactions with air.

It is found in spectroscopic work that the dissociation potentials

are such- that oxygen starts to dissociate appreciably at about 4000°C.

At about 5000°C, nitrogen begins to dissociate, and at about 600000,

nitric oxide, NO is formed in appreoiable quantities. It would thus

seem reasonable to expect the formation of nitric oxide under cavitation

conditions. This would certainly be followed by the formation of

nitrogen peroxide, either within the bubble or the solution and finally

by the formation of nitric and nitrous acids, as observed by Virtanen

and Ellfolk (16). The whole scheme is thought to be :

0 01-0 .) 1\1 () No N 0 1.14 a z 2 IN1 4,. -+ H NO3 + H I\102. - 175 -

It is clear that in this case energy which is used in the formation of nitric oxide will not be available to cause further temperature rises.

Thus as the physical properties of air are intermediate between those of oxygen and nitrogen and consequently the final temperature attained might be expected to lie between those of oxygen and nitrogen, the chemical loss of energy might well be sufficient to reduce the temperature in air below that of either of its components in their pure state.

It is also to be noted that the luminescence from oxygen and nitrogen is in the reverse order from that to be expected on the basis of their ig6 wb molecular velocity, solubility' etc. This might be explained by the fact that the dissociation potential of oxygen lies below that of nitrogen, thus introducing an additional type of energy loss which will operate more strongly in the former case.

(ii) Reactions of the water molecule.

Duca et al (17) have proposed the following scheme for the effect of cavitation upon the water molecule : + 0 14 OH + I-1 1.01 k k The dissociation potential of the water molecule is quite low so that the initial part of this scheme at least appears to be feasible in the case of cavitation. If the yields of hydrogen peroxide are arranged in order of magnitude according to the nature of the gas dissolved in the water, the same order as for sonoluminescence might be expected. There are however -176- some interesting differences, which can be seen in Table.9:

It will be noticed in the first place that the yield from an oxygen saturated solution is greater than from a nitrogen saturated solution whereas from purely physical considerations the reverse situation might be expected. However it is very likely that oxygen will be able to enter into the hydrogen peroxide reaction when it is present, thus : * -101. 02. ---Nfr 141.01.

Discounting the cases of oxygen and air it is probable that the other gases, attain temperatures in the same order as their hydrogen peroxide yields since the number of water molecules will not be very different at any stage of the collapse whatever the nature of the rest of the bubble contents.

It may therefore be concluded that the yield of hydrogen peroxide affords a better indication of the order of temperature than sonoluminescences which is affected by the number of gas molecules present and their excitation potentials. It is interesting to note that if this is the cases the diatomic gases only overlap helium in the monatomic family.

One interesting feature of the water molecule reaction is that it does not occur to a greater extent than it does. The presence of water vapour in shocks and discharges has a marked quenching effect on luminescence, limiting the temperatures that can be attained to about 3000°C in shocks. -177—

of TABLE it o After Prudhomme and Guilmart (18) and

Prudhomme (19).

GAS No. of photons Yield of H202 in gm/cc in unit time. in unit time.

Xenon 540 27.5

Krypton 180 24

Argon 54 21.5

Nitrogen 45 2.5

Oxygen 35 13.5

Air 20 8

Neon 18 7

Helium 1 1

. ti — 178 —

(iii) The Carbon Tetrachloride Reaction.

Flosdorf (20) proposed that the first step in this reaction would be C, C.,L14 k 2.0 U Go -1- 2_14 U

Whether in fact this reaction actually occurs due to dissociation of either the carbon tetrachloride or the water is not clear. But in either case the order of the yield of free chlorine from aqueous solutions of various gases should depend on the temperatures attained, as in the case of hydrogen peroxide formation. The results of Fitzgerald et al (21) iz and Griffing and Sette (22) broadly confirm this finding (SQ.e table 1116).

It is interesting to note that the yield from carbon monoxide is less than from nitrogen, whereas the ratio of specific heats, the molecular velocity, and the solubility are all greater for the former. If however, the scheme proposed by Duca is correct it might be expected that the presence of an excess of carbon monoxide will act as a constraint on the reaction.

The three reactions discussed are among the more important from the cavitation viewpoint and serve as examples of how some chemical effects at least can be accounted for in a qualitative manner.

A.2. . The Role of the Liquid in Sonoluminescence.

In the discussion so far the liquid medium has always been assumed

to be water. By summarising the effect of water vapour on the sonolumin— -179-

11- TABLE III. After Griffing and Siete (22)

GAS Yield of free Chlorine in 6 min. a Argon 0.888

Neon 0.690

Nitrogen 0.534

Carbon-monoxide 0.330

SF6 0.276

Freon 114 0.060

Hydrogen 0.00

Carbon dioxide 0.000 -180—

°sconce it should be possible to infer how the luminescence will vary in different liquids containing the same dissolved gas. Firstly it has been shown that the process of evaporation during the growth stage will be sufficiently rapid due to the high molecular velocity of water vapour to allow the saturation vapour pressure to be readily attained within the growing cavity. Secondly, the temperature attained within the cavity will lie between the values that would be attained by the collapse of the pure gas and of the pure vapour 4— 1.33). Thirdly, during the collapse the pressure of water vapour in the cavity will probably remain constant, due to its high molecular velocity.

Almost all the liquids considered by Jarman (23) were polyatomic with low ratios of specific heats, in which case the criteria for a high luminescence yield must be a low saturated vapour pressure and a high moleculpr velocity. On the other hand, in the case of liquids, whose vapours have high ratios of specific heats, such as mercury, low vapour pressures might be expected to be prejudicial to the emission of sonoluminescence.

A.2.8. The Effect of Dissolved Salts an Sonoluminescence.

It has been shown by GUnther et al (24) that the addition of electrolytes to gaseous solutions causes the appearance of the principal lines of the spectra of the metal radicals as well as the enhancement of the background continuum. It was further shown by Heim (25), using higher spectral resolution that these lines were considerably broadened in -181 — an asymmetric manner towards the red.

If it is assumed that in the case of cavitation of NaC1 solution

some sodium radicles succeed in entering the cavity, it is very likely

that there will be sufficient energy to excite the D lines, whose

excitation potential is only about 2.1 eV. Indeed the ionisation potential

of the sodium atom is only about 5.1 eV, so that the appearance of a recombination continuum is also possible. The latter process would then

account for the observed strengthening of the continuum. It is very likely

that almost all the sodium molecules available will be excited, in which

case the temperature in the cavity may be reduced by a definite amount,

before the intensity of the light from the D lines diminishes, whereas any

reduction in temperature will cause diminution of the continuum. As has

been explained an increase in the temperature of the water generally

causes a decrease in the temperature within the cavity. Thus it might be

expected that the intensity of sonoluminescence from a purely gaseous

solution will decrease more rapidly than if an electrolyte is added to

the solution, as was observed by GUnther et al.

The asymmetric broadening of the spectral lines is particularly

interesting. A review of broadening and shift of spectral lines due to

the presence of foreign gases has been given by Chen and Makoto (26).

They describe theories which predict both broadening and shift of spectral

lines due to perturbations arising from dense packing of gaseous atoms

or molecules around the excited metal atom. They also summarise - 182 - experimental work under these conditions, showing that both alsorption and emission lines can be obtained, shifted either towards the red or the blue depending on the nature of the interacting atoms and broadened by amounts depending on the pressures employed. They show some spectra remarkably similar to those obtained by Onther et al and Heim, in respect of broadening. It is curious however that the D lines photographed by Heim do not show any marked shift, whereas according to the results of

Ch'en and Makoto, a half width of about 20 a as found by Heim should also be accompanied by a shift of about 10 2..

A.2.9. The Effect of Organic Additives on Sonoluminescence.

It has been found that the addition of certain organic compounds to cavitated water causes enhancement of the luminescence, whilst the addition of various other such compounds causes suppression. None of the authors who have investigated these effects mention precautions to remove dissolved air, so that it must be presumed that the collapsing cavities contain a mixture of molecules of the additive, air and water vapour.

It is to be noted that the ratios of speoific heats of all of these additives are less than that of air, so that it would appear that the temperatures attained would not exceed that of an air-water vapour mixture.

It is therefore of some interest that the luminescence obtained from a carbon disulphide solution should be ten to twelve times as great as that from a pure air solution, or three times as great in the case of carbon tetrachloride solution. — 183 —

The addition of carbon disulphide or carbon tetrachloride also causes enhancement of shock wave luminescence and the deposition of solid carbon is also observed (27). If in fact the enhancement of luminescence by these two additives can be explained as a combustion process, it is curious that ether, which is highly inflammable, should cause a suppression of luminescence. Perhaps this can be explained by the fact that ether is highly volatile and attains a high partial pressure in the bubble at the start of the collapse. This would tend to slow the collapse and stop it before very high temperatures are attained as also in the case of carbon dioxide. The very low ratio of specific heats of ether (1.024) would also prevent the temperature from rising appreciably if ether represents the main bulk of the cavity contents. - 184 -

REFERENCES.

1. NOLTINGK, B.E. and NEPPIRAS, E.A. s Proc.Phys. Soc. B,63 (1950) 674 Proc. Phys. Soc. B.64 (1951)1032

2. JARMAN, P.D. : J.A.S.A. 32 (1960) 1459

3. HEIM, E Proc. 3rd I.C.A. Conference (1959) 343

4. SCHMID, J. : Acustica 12 (1962) 70 5. RAYLEIGH : Phil. Mag. 34 (1917) 94

6. GUTH, W. : Acustica 4 (1954) 445

7. KNAPP, R.T. and HOLLANDER, A. : Trans. Am. Soc. Mech. Engrs. 70 (1948) 419

8. HARRISON, M : J.A.S.A. 24 (1952) .776 9. JARMAN, P.D. : Ph.D Thesis (1959) London.

10. GRIFFING, V. : J. Chem. Phys. 20 (1952) 939

11. PRESENT, R.D. 4: "Kinetic Theory of Gases". McGraw Hill (1958) 190

12. KNUDSEN : Ann. Physik. 34 (1911) 654

13. LANGMUIR J.Am. Chem. Soc. 37 (1915) 417 14. RYABININ: Y.N. "Gases at High Densities and Temperatures" Pergamon (1961)

15. FINKELNBURG, W and PETERS, T : Handbuch der Physik 28 (1957) "Continuous Spectra".

16. VIRTANEN and ELLFOLK : Acta. Chem. Scand. 4 (1950) 93. 17. DUCA, J. et. al : J.A.S.A. 30 (1958) 301

18. PRUDHOMME, R.O. and GUILMART, T s J. Chim. Phys. 54 (1957) 336.

19. PRUDHOMME, R.0. : J. Chim. Phys. 54 (1957) 332. -185-

20. FLOSDORF. et al. t J. Am. Chem. Soc. 58 (1936) 1069

21. FITZGERALD9 M.E. et. al : J. Chem. Phys. 25 (1956) 926 22. GRIFFING, V and SETTE, D s J. Chem. Phys. 23 (1955) 503 23. JARMAN, P.D. : Proc, Phys. Soc. 73 (1959) 628

24. GUNTHER 9 P et al : z.f. Elektrochem. 61 (1957) 188 25. HEIM, Es z.f. Ang. Phys. 12 (1960) 423.

26. CH'EN'S and MAKOTO, T s Rev. Mod. Phys. 29 (1957) 20 27. FAIRBAIRNI A.R. and GOWN, A.G. : Proc. Roy. Soc. A 239 (1957) 464. -186—

GLOSSARY

Acoustic or sound fields are taken to be synonymous throughout

this thesis.

Ultrasonic fields are taken to be acoustic fields of frequency

greater than 12 Kc/s.

Threshold.If one physically measurable quantity, A, can be shown

to be a function of another physically measurable quantity,B,

then with increasing or decreasing values of B, the

thresholds of A are those values of B at which A just

becomes appreciable.

The threshold of cavitation is generally defined so that A is the number of cavitation bubbles and B is the acoustic pressure amplitude.

In this case the number of bubbles is said to be just appreciable when there is one cavitation event per minute, but none at an amplitude 10% lower.

(GALLOWAY, W s J.A.S.A. 26 (1954) 849

Gaseous Cavitation is that type of cavitation in which the bubbles are

predominantly gas-filled. These bubbles generally pulsate

rather than collapse or implode, as do vaporous or 'true'

cavitation bubbles, which at maximum radius are predominantly

vapour filled. — 187 —

Rectified Diffusion is that process whereby gas which diffuses into

pulsating bubbles during the growth stage does not completely

leave the bubble during the collapse stage, so that there is

a nett gain in the bubble gas content over a complete sound

cycle.

Bjerknest Forces are hydrodynamic forces usually thought of as acting

on spheres when there is motion of the sphere or in the

surrounding medium.

- 188 - - 189 -

LIST OF SYMBOLS. temperature that would be attained within bubble if adiabatic conditions prevailed.

A 2 area. temperature of sample. diffusion coefficient. time a thickness of sample holder wall. collapse time of cavity. E kinetic energy of a molecule. bubble wall velocity. first excitation potential of an atom. v Mean molecular velocity. resonant frequency of bubble. fr: W thermal capacity of sample. rate of generation of heat due to cavitation, ratio of specific heats. k 1 thermal conductivity. viscosity. total number of molecules. mean free path, As Avogadro's number. ratio of partial pressure of gas to partial s number of molecules / cc. pressure of vapour. : mass. collapse time of cavity; time constant in instantaneous pressure. P sample heating. PA: hydrostatic pressure. temperature of sample. maximum liquid pressure. temperature of cooling water. : acoustic pressure amplitude. angular frequency. (),' pressure within cavity at maximum radius. R instantaneous bubble radius. cs maximum bubble radius.

tRo : gas constant / gm. —r-: period of sound field; temperature