the splashing morphology of liquid-liquid impacts

JAMES COOK UNIVERSITY

SCHOOL OF ENGINEERING

The Splashing Morphology of Liquid-Liquid Impacts

Thesis submitted by David Cole BE (Hons) JCU

In July 2007

Thesis submitted to the School Of Engineering (Mechanical) in partial fulfilment of the requirements for the degree of

Doctor of Philosophy

STATEMENT OF ACCESS

I, the undersigned author of this work, understand that James Cook University will make this thesis available for use within the University Library and, via the Australian Digital Theses network, for use elsewhere. I understand that, as an unpublished work, a thesis has significant protection under the Copyright Act and; I do not wish to place any further restriction on access to this work

_____________________________________ ______________ Signature Date

STATEMENT ON SOURCES

Declaration

I declare that this thesis is my own work and has not been submitted in any form for another degree or diploma at any university or other institution of tertiary education. Information derived from the published or unpublished work of others has been acknowledged in the text and a list of references is given. …………………………………………….. ……………………… (Signature) (Date)

ELECTRONIC COPY

I, the undersigned, the author of this work, declare that the electronic copy of this thesis provided to the James Cook University Library, is an accurate copy of the print thesis submitted, within the limits of the technology available. _______________________________ _______________ Signature Date

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ACKNOWLEDGEMENTS

This project could have never been completed without the assistance of many people.

The first group of people I would like to thank are the technical staff. Dave Kauppila

and Kurt Arrowsmith in the mechanical workshop for their prompt service whenever I

needed something to be made. Warren O’Donnell for letting me steal literally hundreds

of litres of his fine steam distilled water. The lads in the electrical workshop John

Renehan, John Becker and Llyod Barker for sorting out all my electronic/electrical

problems and keeping me generally entertained over the proceeding three years. John

Ellis for dealing with all my purchasing requests. Jihong Li for putting up with all my

tedious computing requests and dealing with them for me in such a timely manner.

Almost all technical advice for this project has come from my primary supervisor Dr.

Jong-leng Liow. There is no question in the world I would not be at this point if it were

not for the guidance and support of Dr. Liow. I would also like to thank Dr. JL Liow for

giving me the opportunity to work towards my PhD and giving me the privilege of

working with such advanced experimental equipment. I would also like to thank the

soon to be Dr. Paul Dylejko for putting up with some of my bitching and ranting and

giving my some stimulating engineering discussion over the past few years.

Finally a big shoutout to all my friends and family who have put up with me over the

past three years. However, the biggest shoutout must be reserved for all the guys and

gals in Clan Ethereal who have without question have kept me sane during my PhD.

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ABSTRACT

In this thesis, a systematic experimental study of the flow behaviour resulting from

liquid-liquid impacts has been conducted. Numerous new flow behaviours have been

identified including microbubble formation from floating drops, pre-entrapment jetting,

multiple primary bubble entrapment, downward jets penetrating the entrapped bubble,

the break-up of the downward jets to leave drops entrapped inside the entrapped bubble

and small vortex ring formation in the early stages of the post-entrapment jetting

regime. These new flow phenomena have been combined with existing flow behaviour

to produce the most comprehensive maps (both quantitative and qualitative) describing

the splashing morphology of liquid-liquid impacts to date. It was found that six different

flow regimes were required to adequately categorise all the flow behaviour.

The physics of the cavity formation and collapse were investigated with high speed

video and high framing rate particle image velocimetry. The formation and collapse of

the cavity can be described as a six stage process. Initially, the cavity expands due to the

inertia of the impact and the majority of the displaced fluid is driven into the wave

swell. After the energy of the impact has been dissipated, the side walls of the cavity

stagnate and the growth of the wave swell also stagnates. This causes the fluid

contained in the wall swell to begin flowing downward under the influence of gravity.

As the fluid flows down, the base of the cavity stops growing and begins to retract.

These actions give rise to a vortex mid way down the cavity and acts to collapse the

cavity. The fluid driven by the vortex then converges at the base of the cavity along the

axis of symmetry.

The formation of the vortex was shown to be centred around a stationary line that forms

on the cavities interface. Several interesting properties of this stationary line were

discovered. The depth at which the stationary line forms is almost constant for the same

drop size and is independent of impact velocity. The dimensionless width of the cavity,

Dw' was shown to scale to 31Fr . The formation of the stationary line was also shown to

influence how the flow converges at the base. The wider the cavity grows, the greater

the rotation the fluid undergoes before converging along the axis of symmetry. Thus, for

small width cavities the flow tends to converge while the fluid is being directed

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downward. While for larger width cavities, the flow tends to converge with a strong

upward component. This has lead to the formulation of three different flow convergence

criteria: downward convergence, parallel convergence and upward convergence. All

jetting modes or lack of jetting can be described using one of the three convergence

criteria.

For cavities that are small and thus have a downward flow convergence condition, no

jetting occurs. This type of flow convergence occurs in the primary vortex ring regime

and may assist in the development of strong coherent vortex rings. A parallel flow

convergence condition is responsible for forming high-speed jets in both the pre-

entrapment jetting and primary bubble entrapment regimes. Here, the flow is similar to

two parallel jets impinging on each other. This action forms a stagnation point and a

significant rise in the local pressure around this zone follows. This leads to a strong

inertial force that drives a small jet of fluid back up into the cavity. Cavity retraction

acceleration was measured as high as 90 000g during this time. The maximum exit

velocity of the secondary drops formed from the break up of the thin high-speed jets

was measured to be in excess of 30 m/s. In the primary bubble entrapment regime it was

postulated that multiple stagnation points would form and interact with each other to

produce variable jet velocities across the regime. The retraction velocity of the cavity

was also shown to have a direct correlation with the exit velocity of the first drop. An

upward flow convergence condition was found to be responsible for the thick slow

moving jets observed in the post-entrapment jetting regime.

All modes of bubble entrapment were investigated and the quantity of air each mode

can entrap has been estimated. It was found that the most efficient method to produce

microbubbles was by forming jets in the post-entrapment jetting regime that pinch off

secondary drops with Weber numbers ranging from 6 to 20. This produces drops that

fall into the primary microbubble entrapment regime to produce thin films that rupture

into thousands of microbubbles. Methods for determining the volume of entrapped air

from the break up based on the rupture velocity of the film are presented. The entrapped

air in the bulk fluid is equivalent on average to 0.3% of the original drop volume.

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TABLE OF CONTENTSSTATEMENT OF ACCESS................................................ i

STATEMENT OF ORIGINALITY.............................................................................. ii

ELECTRONIC COPY DECLARATION ...................................................................iii

ACKNOWLEDGEMENTS .......................................................................................... iv

ABSTRACT..................................................................................................................... v

LIST OF SYMBOLS ...................................................................................................xiii

LIST OF FIGURES..................................................................................................... xvi

LIST OF TABLES..................................................................................................... xxvi

CHAPTER 1 - LITERATURE REVIEW .................................................................... 1

1.1 Introduction................................................................................................... 1

1.2 Thesis Focus ................................................................................................. 1

1.3 Background................................................................................................... 2

1.4 Theoretical Preliminaries .............................................................................. 6

1.4.1 Theoretical Flow Description......................................................... 6

1.4.2 Scaling Analysis.............................................................................. 7

1.4.3 Dimensionless Groups, Length Scales and Time Scales ................ 9

1.5 Liquid-liquid Impact on a Deep Pool ......................................................... 11

1.5.1 Total coalescence ......................................................................... 11

1.5.2 Coalescence Cascade ................................................................... 12

1.5.3 Air film formation and rupture ..................................................... 15

1.5.4 Thoroddsen bubbles...................................................................... 17

1.5.5 Oguz-Prosperetti bubble rings ..................................................... 18

1.5.6 Cratering dynamics ...................................................................... 19

1.5.7 Vortex Rings ................................................................................. 20

1.5.8 Jets without bubbles...................................................................... 23

1.5.9 Primary bubble entrapment and thin jets ..................................... 24

1.5.10 Downward Jets ............................................................................. 26

1.5.11 Crown formation........................................................................... 27

1.5.12 Thick Jets ...................................................................................... 30

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1.5.13 Secondary bubble entrapment ...................................................... 32

1.5.14 Surface bubbles............................................................................. 33

1.6 Allied Splash Phenomena and Parameters.................................................. 35

1.6.1 Influence of impact angle ............................................................. 35

1.6.2 Influence of pool depth ................................................................. 37

1.6.3 Influence of temperature............................................................... 38

1.6.4 Influence of drop size.................................................................... 38

1.6.5 Surface Tension and Viscous Effects ............................................ 39

1.6.6 Apex drop...................................................................................... 41

1.6.7 Bubble acoustics ........................................................................... 42

1.6.8 Entrapped Bubbles Bursting at the Free Surface......................... 44

1.7 Particle Image Velocimetry (PIV) .............................................................. 45

1.8 Summary..................................................................................................... 46

CHAPTER 2 - EXPERIMENTATION ...................................................................... 49

2.1 Introduction................................................................................................. 49

2.2 Experimental Apparatus ............................................................................. 49

2.2.1 Drop generation and height control ............................................. 49

2.2.2 Impact Pool................................................................................... 50

2.2.3 Liquids .......................................................................................... 51

2.2.4 Digital Cameras ........................................................................... 52

2.2.5 PIV Laser...................................................................................... 53

2.3 High-Speed Video Configuration ............................................................... 56

2.3.1 Backlighting.................................................................................. 56

2.3.2 Photography down the cavity ....................................................... 58

2.3.3 Alignment and Calibration ........................................................... 60

2.3.4 Determination of imaging parameters ......................................... 60

2.4 PIV .............................................................................................................. 62

2.4.1 PIV configuration ......................................................................... 62

2.4.2 PIV Seeding .................................................................................. 65

2.4.3 PIV implementation ...................................................................... 68

2.5 Experiment Lists ......................................................................................... 70

2.5.1 Repeatability ................................................................................. 72

2.6 Analysis Techniques and Errors ................................................................. 72

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2.6.1 High speed video .......................................................................... 72

2.6.2 PIV analysis techniques................................................................ 75

2.6.3 PIV errors ..................................................................................... 80

2.7 Summary..................................................................................................... 80

CHAPTER 3 - SPLASHING MORPHOLOGY MAP .............................................. 81

3.1 Introduction................................................................................................. 81

3.2 Image Sequence Details.............................................................................. 81

3.3 Qualitative Splash Map............................................................................... 83

3.3.1 Flow regimes ................................................................................ 84

3.4 Primary vortex ring regime......................................................................... 85

3.4.1 Impact I (Fr = 41, We = 36, Re = 2341, tc = 2.54)...................... 86

3.4.2 Impact II (Fr = 53, We = 48, Re = 2692, tc = 2.24) .................... 88

3.4.3 Vortex ring development............................................................... 91

3.4.4 Bubble formation .......................................................................... 93

3.5 Primary vortex ring/Pre-entrapment jetting transition................................ 94

3.5.1 Impact III (Fr = 67, We = 62, Re = 3082, tc = 1.99) ................... 95

3.6 Pre-entrapment jetting regime .................................................................... 97

3.6.1 Small vortex rings......................................................................... 98

3.6.2 Impact IV (Fr = 76, We = 67, Re = 3178, tc = 1.85)................... 99

3.6.3 Impact V (Fr = 83, We = 77, Re = 3425, tc = 1.80)................... 101

3.6.4 Impact VI (Fr = 97, We = 90, Re = 3697, tc = 1.66) ................. 103

3.6.5 Jetting ......................................................................................... 107

3.7 Primary bubble entrapment regime........................................................... 108

3.7.1 Bubble entrapment...................................................................... 108

3.7.2 Jetting ......................................................................................... 108

3.7.3 Impact VII (Fr = 111, We = 102, Re = 3928, tc = 1.55) ............ 110

3.7.4 Impact VIII (Fr = 125, We = 116, Re = 4199, tc = 1.47)........... 112

3.7.5 Impact IX (Fr = 138, We = 127, Re = 4380, tc = 1.39) ............. 114

3.7.6 Impact X (Fr = 170, We = 151, Re = 4751, tc = 1.24)............... 116

3.8 Primary bubble entrapment/Post-entrapment jetting transition ................ 120

3.8.1 Impact XI (Fr = 174, We = 158, Re = 4891, tc = 1.23) ............. 121

3.9 Post-entrapment jetting regime................................................................. 123

3.9.1 Impact XII (Fr = 182, We = 161, Re = 4899, tc = 1.20) ............ 124

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3.9.2 Impact XIII (Fr = 211, We = 187, Re = 5279, tc = 1.11)........... 126

3.9.3 Impact XIV (Fr = 235, We = 207, Re = 5797, tc = 1.06)........... 128

3.9.4 Impact XV (Fr = 275, We = 258, Re = 6294, tc = 0.99) ............ 130

3.9.5 Impact XVI (Fr = 454, We = 403, Re = 7768, tc = 0.76)........... 132

3.9.6 Jetting ......................................................................................... 134

3.10 Total coalescence regime.......................................................................... 137

3.11 Primary microbubble formation regime.................................................... 137

3.11.1 Film draining (Slow) .................................................................. 138

3.11.2 Impact XVII (Fr = 2, We = 2, Re = 576, tc = 11.62 ms) ............ 139

3.11.3 Film draining (Fast) ................................................................... 141

3.11.4 Impact XIX (Fr = 5.5, We = 7, Re = 1042, tc = 7.45 ms) .......... 142

3.11.5 Impact XX (Fr = 9, We = 11, Re = 1300, tc = 5.64 ms)............. 144

3.12 Quantitative Drop Splash Map ................................................................. 146

3.13 Summary and Conclusion......................................................................... 148

CHAPTER 4 - PIV STUDY OF CAVITY FORMATION AND COLLAPSE ..... 149

4.1 Introduction............................................................................................... 149

4.2 PIV of Cavity Formation and Collapse..................................................... 149

4.2.1 PIV Impact I (Fr = 56, We = 33, Re = 2010, tc = 1.96) ............ 150

4.2.2 PIV Impact II (Fr = 129, We = 78, Re = 3089, tc = 1.30) ......... 156

4.2.3 PIV Impact III (Fr = 297, We = 170, Re = 4509, tc = 0.84)...... 162

4.2.4 PIV Impact IV (Fr = 452, We = 249, Re = 5421, tc = 0.67) ...... 169

4.3 Cavity Outlines ......................................................................................... 176

4.4 Stationary Line.......................................................................................... 181

4.5 Cavity Formation and Collapse Flow Model............................................ 185

4.5.1 Expansion and wave swell growth.............................................. 185

4.5.2 Peak wave swell height............................................................... 189

4.5.3 Wave swell drainage................................................................... 191

4.5.4 Cavity base stagnation................................................................ 194

4.5.5 Vortex formation......................................................................... 196

4.5.6 Flow convergence along centreline............................................ 197

4.6 Summary................................................................................................... 200

CHAPTER 5 - JETTING........................................................................................... 201

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5.1 Introduction............................................................................................... 201

5.2 Pre-Entrapment Jetting ............................................................................. 201

5.2.1 Jet Drop Characteristics ............................................................ 205

5.2.2 Mechanisms of jet formation ...................................................... 209

5.3 Primary Bubble Entrapment Jetting.......................................................... 214

5.3.1 Drop Characteristics .................................................................. 221

5.3.2 Mechanisms of jet formation ...................................................... 224

5.4 Downward Jets During Primary Bubble Entrapment ............................... 229

5.4.1 Downward jet break-up .............................................................. 233

5.4.2 Entrapped drop behaviour.......................................................... 234

5.5 Post-Entrapment Jetting............................................................................ 237

5.5.1 Jet and secondary drop characteristics...................................... 239

5.5.2 Mechanism of jet formation........................................................ 241

5.6 Summary................................................................................................... 242

CHAPTER 6 - BUBBLE ENTRAPMENT............................................................... 243

6.1 Introduction............................................................................................... 243

6.2 Bubbles from Initial Impact ...................................................................... 244

6.2.1 Thoroddsen bubbles.................................................................... 244

6.3 Bubbles Formed During Cavity Collapse................................................. 246

6.3.1 Primary bubble entrapment........................................................ 246

6.3.2 Multiple bubble primary bubble entrapment.............................. 249

6.3.3 Secondary Bubble Entrapment ................................................... 256

6.4 Microbubbles from thin film thinning ...................................................... 260

6.4.1 Microbubbles from rapid film thinning (Mesler type)................ 260

6.4.2 Microbubbles from slow film drainage ...................................... 264

6.5 Air Film Formation and Rupture .............................................................. 267

6.5.1 Mechanism of formation............................................................. 267

6.5.2 Limits on microbubble formation ............................................... 268

6.5.3 Estimating quantity of air entrapped.......................................... 269

6.6 Summary................................................................................................... 271

CHAPTER 7 - SUMMARY AND CONCLUSION ................................................. 273

7.1 Splashing Morphology.............................................................................. 273

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7.2 Cavity Behaviour ...................................................................................... 274

7.3 Jetting........................................................................................................ 275

7.4 Bubble Entrapment ................................................................................... 275

7.5 Conclusion ................................................................................................ 275

7.6 Future Work.............................................................................................. 276

REFERENCES............................................................................................................ 278

APPENDIX A – MATLAB CODE............................................................................ 287

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LIST OF SYMBOLS Symbol Definition Units

A Wave amplitude m

A Surface area m2

AR Aspect ratio -

Bo Bond number ( σρ 2gLBo = ) -

C Constant -

Ca Capillary number ( σμUCa = ) -

c Wave speed m/s

D Drop diameter m

d Drop diameter m

dd Diameter of the impacting drop m

pd Actual particle size m

apd , Airy disk particle diameter m

epd , Effective particle size m

opd , Optimal particle diameter M

kE Kinetic energy J

pE Potential energy J

sE Surface energy J

Fr Froude number ( gLUFr 2= ) - #f Lens f-number -

g Gravitational constant m/s2

H Pool height m

H Pool depth m

H Cylinder height, Cone Height m

poolh Depth of impact pool m

k Wave number -

L Characteristic length scale m

cl Capillary length scale m

M Magnification factor -

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m Mass kg

pm Total mass of particles required kg

poolpn , Number of particles required to see the entire pool -

ipn , Number of particles required per interrogation area -

Oh Ohnesorge number ( σρμ LOh = ) -

P Pressure Pa

iP Internal drop pressure Pa

0P Ambient pressure Pa

p Pressure Pa

dp Dynamic pressure Pa

sr Air sheet radius m

R Radius m

mR Maximum cavity radius m

Re Reynolds number ( μρLU=Re ) -

r Radius m

ir Ratio of drop radii -

1r First radius of curvature m

2r Second radius of curvature m

iV Volume of a PIV interrogation area m3

U Characteristic velocity scale m/s

dU Velocity of the impacting drop m/s

spU , Particle settling velocity m/s

u Velocity m/s

bV Drop return bounce velocity m/s

iV Drop impact velocity m/s

poolV Volume of the pool m3

sV Volume of the air sheet m3

T Wave period 1/s

t Time s

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ct Capillary driven time scale s

gt Gravity driven time scale s

sheett Thickness of the laser light sheet μm

We Weber number ( σρ 2LUWe = ) -

iw Width of PIV interrogation area Pixel

pixelw Width of a pixel on the imaging plane μm

sw Edge width of one element on the image sensor μm

ε Drop eccentricity -

η Wave height m

θ Impact angle º

λ Wavelength m

lλ Wave length of laser m

minλ Minimum gravity-capillary wavelength m

μ Fluid viscosity Ns/m2

poolμ Viscosity of pool fluid Ns/m2

ρ Fluid density kg/m3

dρ Density of the drop fluid kg/m3

pρ Bulk density of particles kg/m3

poolρ Density of the pool fluid kg/m3

σ Surface tension N/m

τ Time s

pτ Particle response time s

ω Wave frequency rad/s

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LIST OF FIGURES Figure 1.1 Map of phenomena associated with liquid-liquid impact (Cole 2007)........ 4

Figure 1.2 Diagram of the forces acting on an interface. Carats signify properties

of the lower fluid.......................................................................................... 6

Figure 1.3 The coalescence cascade (Liow 2001)....................................................... 12

Figure 1.4 Trajectory trace of drops in the coalescence cascade (Honey and

Kavehpour 2006) ....................................................................................... 14

Figure 1.5 Comparison between analytical model and experimental results for the

coalescence cascade hmax*

being the maximum height obtained during

each stage (normalised by capillary length) and R1* the drop radius

(normalised by capillary length). Minimum jump height is achieved at

approximately R1* = 0.4 (Honey and Kavehpour 2006) ............................ 15

Figure 1.6 Rupturing of the air film between (Sigler and Mesler 1990)..................... 16

Figure 1.7 Thin film rupture at different stages of cavity development for three

different impacts (Thoroddsen et al. 2003)................................................ 17

Figure 1.8 Formation of Thoroddsen Bubbles via air sheet contraction

(Thoroddsen et al. 2003)............................................................................ 18

Figure 1.9 Vortex ring formed by a 2.8mm drop falling 38.4 mm (Peck and

Sigurdson 1994) ......................................................................................... 21

Figure 1.10 Relationship between drop eccentricity and vortex ring penetration

depth (Chapman and Critchlow 1967)....................................................... 22

Figure 1.11 Vortex ring diameter (D) as a function of penetration depth (L) (Durst

1996) .......................................................................................................... 22

Figure 1.12 Thin high-speed jet with no bubble entrapment (Liow 2001) ................... 24

Figure 1.13 Pixel outline of cavity with solution to Crapper wave (Liow 2001).......... 25

Figure 1.14 The downward jet associated with bubble entrapment (Elmore et al.

2001). Arrow indicates the “downwards” direction of the jet ................... 26

Figure 1.15 Relationship between upward and downward jet velocity

(Fedorchenko and Wang 2004).................................................................. 27

Figure 1.16 Crown formation due in milk (Edgerton and Killian 1979) ...................... 28

Figure 1.17 Numerical simulations showing the formation of a high speed jet or

ejecta sheet at the drop-pool interface during initial impact (Weiss and

Yarin 1999) ................................................................................................ 29

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Figure 1.18 Ejecta sheet from impact (Thoroddsen 2002)............................................ 29

Figure 1.19 Development of crown formation: (A) No crown formation (B) Partial

crown formation (C) Fully developed crown formation (Liow 2001)....... 30

Figure 1.20 Variation of jet height with Froude number (Fedorchenko and Wang

2004) .......................................................................................................... 31

Figure 1.21 Time sequence of thick jet formation (Rein 1996) .................................... 32

Figure 1.22 Secondary bubble entrapment (Liow 2001)............................................... 33

Figure 1.23 Surface bubble on surface due to high velocity impact (Franz 1959) ....... 34

Figure 1.24 Various spreading morphologies for oblique impacts (Leneweit et al.

2005) .......................................................................................................... 36

Figure 1.25 Crown formation in thin liquid film (Rioboo et al. 2003) ......................... 37

Figure 1.26 Three forms of possible impact.................................................................. 38

Figure 1.27 Bubble entrapment for varying viscosity fluids (Prosperetti and Oguz

1993) .......................................................................................................... 40

Figure 1.28 A 2.7 mm drop impacting at 2.17 m/s on a thin film (Vander-Wal et al.

2006) .......................................................................................................... 41

Figure 1.29 Apex drop formation from a secondary drop Fr = 9.5, We = 6.9 (Liow

2001) .......................................................................................................... 42

Figure 1.30 Video and acoustic traces of the primary bubble entrapment process

(Pumphrey and Crum 1989)....................................................................... 43

Figure 1.31 Drop size and velocity distribution from bursting bubbles (Spiel 1995)... 44

Figure 2.1 Liquid dropping arm .................................................................................. 50

Figure 2.2 Sketch of impact tank and overflow tank...................................................... 51

Figure 2.3 PIV laser on mount with light arm............................................................. 55

Figure 2.4 Output power of the Nd:YAG laser for various pulse delays at

different supply amperages ........................................................................ 55

Figure 2.5 Schematic drawing of experimental apparatus .......................................... 56

Figure 2.6 Experimental setup for high speed video................................................... 57

Figure 2.7 Schematic of down cavity lighting configuration...................................... 59

Figure 2.8 Experimental setup of the camera in the down cavity configuration......... 59

Figure 2.9 An example of a calibration shot. (Left) Camera below surface (Right)

Camera above surface ................................................................................ 60

Figure 2.10 Timing diagram for HFR-PIV system ....................................................... 62

Figure 2.11 Schematic of the apparatus for 2D-PIV ..................................................... 64

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Figure 2.12 Experimental setup for 2D PIV.................................................................. 65

Figure 2.13 Screenshot of the drop size and velocity calculator................................... 73

Figure 2.14 Raw PIV image of a cavity collapsing....................................................... 75

Figure 2.15 Mask used to exclude the free surface and cavity from correlation .......... 76

Figure 2.16 Masked raw image ..................................................................................... 76

Figure 2.17 Raw cross-correlation image...................................................................... 77

Figure 2.18 Vector map after moving-average has been applied.................................. 78

Figure 2.19 Final post-processed velocity field ............................................................ 78

Figure 2.20 Scalar velocity map.................................................................................... 79

Figure 2.21 Vorticity map ............................................................................................. 79

Figure 3.1 Information contained in each image......................................................... 82

Figure 3.2 Drop plash map showing all of the flow features and regimes found in

liquid-liquid impacts .................................................................................. 83

Figure 3.3 Below surface images for 26G-01-20mm (4000 FPS) .............................. 86

Figure 3.4 Larger view of the bubble formed below the cavity (A1-C1) ................... 86

Figure 3.5 Above surface images for 26G-01-20mm (5000 FPS) .............................. 87

Figure 3.6 Below surface images for 26g-04-40mm (3000 FPS) ............................... 88

Figure 3.7 Above surface images for 26g-04-40mm (5000 FPS) ............................... 89

Figure 3.8 Down cavity image sequence for a drop falling in the primary vortex

ring regime at 8000 FPS (Estimated parameters We = 60, Fr = 106, Re

= 2684, tc = 1.41) ....................................................................................... 90

Figure 3.9 Image sequence of the initial vortex ring development (Frames 255-

261) ............................................................................................................ 92


Figure 3.11 Above surface images for 26g-04-60mm (5000 FPS) ............................... 96


Figure 3.13 Above surface images for 26g-04-70mm (5000 FPS) ............................. 100

Figure 3.14 Below surface images for 26G-01-80mm (4000 FPS) ............................ 101

Figure 3.15 Above surface images for 26G-01-80mm (5000 FPS) ............................ 102

Figure 3.16 Below surface images for 26G-01-100mm (4000 FPS) .......................... 103

Figure 3.17 Above surface images for 26G-01-100mm (5000 FPS) .......................... 104

Figure 3.18 Enlarged images from Impact IV .............................................................. 105

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Figure 3.19 Down cavity images for a drop falling in the pre-entrapment jetting

regime at 8000 FPS (Estimated parameters We = 83, Fr = 149, Re =

3144, tc = 1.18)......................................................................................... 106





Figure 3.24 Below surface images for 26g-04-160mm (3000 FPS) ........................... 114

Figure 3.25 Above surface images for 26g-04-160mm (5000 FPS) ........................... 115


Figure 3.27 Above surface images for 26g-01-200 (5000 FPS) ................................. 117

Figure 3.28 Down cavity images of a drop impact in the primary bubble

entrapment regime (8 000 FPS) (Estimated parameters We = 110, Fr =

201, Re = 3596, tc = 1.01) ........................................................................ 119













Figure 3.41 Down cavity images of a drop impact in the post-entrapment jetting

entrapment regime (8 000 FPS) (Estimated parameters We = 372, Fr =

654, Re = 6669, tc = 0.57) ........................................................................ 136

Figure 3.42 Enlarged view of Figure 3.43 (B5)............................................................ 138

Figure 3.43 Below surface images showing rupture of thin film supporting a

floating drop (3000 FPS) ......................................................................... 139

Figure 3.44 Above surface images showing rupture of thin film supporting a

floating drop (5000 FPS) ......................................................................... 140

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Figure 3.45 Below surface images showing the film thinning due to a rapid

expansion (3000 FPS) .............................................................................. 142

Figure 3.46 Above surface images showing the film thinning due to a rapid

expansion (5000 FPS) .............................................................................. 143

Figure 3.47 Below surface image sequence film rupture and vortex ring

development (2 500 FPS)......................................................................... 144

Figure 3.48 Above surface image sequence film rupture and vortex ring

development (3 000 FPS)......................................................................... 145

Figure 3.49 Quantitative drop splash map................................................................... 146

Figure 4.1 Image sequence of impact PIV-I showing velocity vectors (Reference

vector 0.25 m/s) ....................................................................................... 154

Figure 4.2 Vorticity development 24 ms after initial impact (sec-1) ......................... 155

Figure 4.3 Velocity magnitude 24 ms after initial impact (m/s) ............................... 155

Figure 4.4 Image sequence of impact PIV-II showing velocity vectors (Reference

vector 0.5 m/s) ......................................................................................... 161

Figure 4.5 Comparison between the PIV results and dyed drop images................... 161

Figure 4.6 Image sequence of impact PIV-III showing velocity vectors

(Reference vector 0.5 m/s)....................................................................... 167

Figure 4.7 Vortex formation mid way down the cavity ............................................ 168

Figure 4.8 Image sequence of impact PIV-IV showing velocity vectors

(Reference vector 0.5 m/s)....................................................................... 175

Figure 4.9 Cavity outlines for CO-I (Fr = 111, We = 66, Re = 2849, tc = 1.40)....... 176

Figure 4.10 Cavity outlines for CO-II (Fr = 174, We = 100, Re = 3463, tc = 1.10) ... 177

Figure 4.11 Cavity outlines for CO-III (Fr = 219, We = 121, Re = 3778, tc = 0.97) .. 177

Figure 4.12 Cavity outlines for CO-IV (Fr = 325, We = 180, Re = 4600, tc = 0.80) .. 178

Figure 4.13 Cavity outlines for CO-V (Fr = 423, We = 242, Re = 5386, tc = 0.71) ... 178

Figure 4.14 Cavity outlines for (Fr = 654, We = 372, Re = 6669, tc = 0.57) .............. 179

Figure 4.15 Variation of dimensionless width of stationary line versus impact

Froude number ......................................................................................... 181

Figure 4.16 Variation of dimensionless maximum cavity depth versus impact Fr

number ..................................................................................................... 182

Figure 4.17 Variation of stationary line depth with impact velocity. Solid lines are

the mean distances ................................................................................... 184

Figure 4.18 Flow field during cavity expansion.......................................................... 186

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Figure 4.19 Vorticity map during cavity expansion (sec-1)......................................... 186

Figure 4.20 Velocity magnitude during cavity expansion (m/s) (298) ....................... 186

Figure 4.21 Flow regions during cavity expansion ..................................................... 188

Figure 4.22 Flow field during wave swell stagnation ................................................. 190

Figure 4.23 Vorticity map during wave swell stagnation (sec-1) ................................ 190

Figure 4.24 Velocity magnitude during wave swell stagnation (m/s) (301) ............... 190

Figure 4.25 Flow regions at peak wave swell height .................................................. 191

Figure 4.26 Flow field during wave swell drainage.................................................... 192

Figure 4.27 Vorticity map during wave swell drainage (sec-1) ................................... 192

Figure 4.28 Velocity magnitude during wave swell drainage (m/s) (302)................ 192

Figure 4.29 Direction of the flow draining from the wave swell ................................ 193

Figure 4.30 Flow field during cavity base stagnation and collapse initiation............. 194

Figure 4.31 Vorticity map during cavity base stagnation and collapse start (sec-1).... 195

Figure 4.32 Velocity magnitude during base stagnation and collapse initiation

(m/s) (304) .............................................................................................. 195

Figure 4.33 Flow direction around cavity as the base of the cavity stagnates ............ 195

Figure 4.34 Flow field during flow reversal and collapse........................................... 196

Figure 4.35 Vorticity map during flow reversal and collapse (sec-1) .......................... 196

Figure 4.36 Contours of velocity magnitude during flow reversal and collapse

(m/s) 08)................................................................................................... 197

Figure 4.37 Vortex formation around the collapsing cavity ....................................... 197

Figure 4.38 Flow field during downward convergence .............................................. 198

Figure 4.39 Flow field during parallel flow convergence ........................................... 198

Figure 4.40 Flow field during upward convergence ................................................... 198

Figure 4.41 Flow convergence conditions .................................................................. 198

Figure 5.1 Below surface images from the pre-entrapment jetting regime (6 000

FPS & 33g Needles)................................................................................. 202

Figure 5.2 Above surface images for jets formed in pre-entrapment jetting regime

(5 000 FPS) .............................................................................................. 204

Figure 5.3 Diameter of the first drop exiting the cavity for different impact

Froude numbers ....................................................................................... 206

Figure 5.4 Velocity of the first drop exiting the cavity for different impact Froude

numbers.................................................................................................... 207

Figure 5.5 Number of drops produced from each pre-entrapment jetting event....... 207

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Figure 5.6 Drop velocity versus diameter of the first drops that exit the cavity ....... 208

Figure 5.7 Retraction of the cavity base for pre-entrapment jetting (Fr = 154, We

= 91, Re = 3338, tc = 1.18) (40 000 FPS) ................................................ 209

Figure 5.8 Cavity tip displacement over time ........................................................... 210

Figure 5.9 Graph of cavity tip velocity versus time .................................................. 210

Figure 5.10 Process of cavity retraction leading to jetting in the pre-entrapment

jetting regime. (a) Cavity driven inward by the inertia of the flow

around cavity while the downward displacement of the cavity balances

the upward surface tension force. (b) Cavity stops growing downward

allowing surface tension to pull the cavity upward which in turn allows

the flow to converge along the centreline. (c) Parallel flow converging

forms a stagnation point that it turn forms a high pressure point that

drives a high-speed jet upward. ............................................................... 212

Figure 5.11 Contours of velocity magnitude as the flow converges along the

centreline (m/s) (a) PIV Impact II (Umax = 1.08 m/s) (b) PIV Impact III

(Umax = 1.69 m/s) (c) PIV Impact IV (Umax = 1.93 m/s) .......................... 213

Figure 5.12 Above surface images for PBE-I (Fr = 149, We = 83, Re = 3144, tc =

1.18) (10 000 FPS).................................................................................. 215

Figure 5.13 Above surface images for PBE-II (Fr = 168, We = 92, Re = 3291, tc =

1.11) (10 000 FPS).................................................................................. 216

Figure 5.14 Above surface images for PBE-III (Fr = 219, We = 123, Re = 3823, tc

= 0.96) (10 000 FPS)................................................................................ 217

Figure 5.15 Above surface images PBE-IV (Fr = 270, We = 150, Re = 4223, tc =

0.88) (10 000 FPS)................................................................................... 217

Figure 5.16 Above surface images for PBE-V (Fr = 318, We = 180, Re = 4580, tc =

0.81) (10 000 FPS)................................................................................... 218

Figure 5.17 Above surface images for PBE-VI (Fr = 342, We = 192, Re = 4781, tc

= 0.78) (10 000 FPS)................................................................................ 219

Figure 5.18 Above surface images for PBE-VI (Fr = 360, We = 202, Re = 4907, tc

= 0.76) (10 000 FPS)................................................................................ 219

Figure 5.19 Drop diameter vs impact Froude number for first drops exiting the

cavity in the primary bubble entrapment regime ..................................... 222

Figure 5.20 Drop velocity vs impact Froude number for first drops exiting the

cavity in the primary bubble entrapment regime ..................................... 222

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Figure 5.21 No. of drops formed for selected impact in Prim. Bubble Entrapment ... 223

Figure 5.22 Velocity/size characteristics for all the drops formed in primary bubble

entrapment regime ................................................................................... 223

Figure 5.23 Neck rupture for 33g-08-220mm (Fr = 225, We = 128, Re = 3917, tc =

0.97) (81595 FPS).................................................................................... 224

Figure 5.24 Velocity time graph for the retracting cavity during primary bubble

entrapment................................................................................................ 224

Figure 5.25 Stem break leaving multiple small bubbles entrapped (Fr = 71, We =

97, Re = 4222 ,tc = 2.13) (3000 FPS)....................................................... 226

Figure 5.26 Image sequence two jets forming (Fr = 279, We = 171, Re = 4599, tc =

0.88) (30 000 FPS)................................................................................... 226

Figure 5.27 Mechanism of primary bubble entrapment jetting (a) Downward

component of the flow pushes the base of the stem downward while

the converging flow pushes the walls of the cavity inward (b)

Converging flow forces the cavity walls to become a thin unstable

cylinder that break-ups (c) Break up of the cavity’s stem allows the

converging flow to meet which forms one or more stagnation point

giving rise to jets in orthogonal directions............................................... 227

Figure 5.28 Upward jet when multiple bubbles form during stem break up (Fr =

71, We = 97, Re = 4222,tc = 2.13) (5000 FPS)........................................ 227

Figure 5.29 Image sequence for the formation of a downward jet (Fr = 203, We =

125, Re = 3938,tc = 1.04) (30 000 FPS)................................................... 231

Figure 5.30 Example of the downward jet penetrating a small distance into the

bubble (Fr = 236, We = 147, Re = 4284,tc = 0.96) (30 000 FPS)............ 233

Figure 5.31 Image sequence showing the movement of the entrapped drop (Fr =

228, We = 140, Re = 4156, tc = 0.98) (30000 FPS)................................. 235

Figure 5.32 Dyed drop image sequence of drop in bubble coalescence (Fr = 138,

We = 127, Re = 4380, tc = 1.39) (3 000 FPS).......................................... 236

Figure 5.33 Thick jet shape moments before secondary drop detachment ................. 239

Figure 5.34 Secondary drop size variation versus impact Froude number for the

26g-04 data set ......................................................................................... 240

Figure 5.35 Maximum jet height in the post-entrapment jetting regime versus

impact Froude number ............................................................................. 240

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Figure 5.36 Mechanism of post-entrapment jetting (a) Converging flow at the base

of cavity drives the cavity walls upward and inward (b) Flow begins to

converge with a strong upward component (c) The converging flow

meets and drives the base of the cavity upward to form thick slow

moving jets............................................................................................... 241

Figure 6.1 Thoroddsen bubble sizes from the impacts from 3.2 mm drops (20g

needles) .................................................................................................... 244

Figure 6.2 Total volume of the Thoroddsen bubbles formed from 3.2 mm drops

(20g needles)............................................................................................ 245

Figure 6.3 A series of impacts showing the shape of the bubble formed from

primary bubble entrapment ...................................................................... 247

Figure 6.4 Plot of entrapped bubble size versus Froude number .............................. 248

Figure 6.5 Below surface images for MBE-I (Fr = 332, We = 194, Re = 4824, tc =

0.8) 250

Figure 6.6 Below surface images for MBE-II (Fr = 332, We = 194, Re = 4824, tc

= 0.8) (40000 FPS).................................................................................. 251

Figure 6.7 Below surface images for MBE-III (Fr = 343, We = 195, Re = 4826, tc

= 0.78) (40000 FPS)............................................................................... 252

Figure 6.8 Below surface images for MBE-IV (Fr = 345, We = 196, Re = 4841, tc

= 0.78) (40000 FPS)............................................................................... 253

Figure 6.9 Below surface images for MBE-V (Fr = 356, We = 202, Re = 4904, tc

= 0.77) (40000 FPS)................................................................................ 254

Figure 6.10 Secondary bubble size versus impact Froude number............................. 256

Figure 6.11 An example of secondary bubble entrapment in the post-entrapment

regime (Fr = 721, We = 410, Re = 7003, tc = 0.54) (2000 FPS).............. 257

Figure 6.12 Cavity outlines from the image sequence shown above .......................... 257

Figure 6.13 Down cavity image sequence for 33g-09-660mm (8000 FPS) showing

capillary wave convergence (Estimated impact conditions Fr = 560,

We = 318, Re = 6169, tc = 0.61) .............................................................. 259

Figure 6.14 Air film rupture due to a rapid thinning of the film (Impact conditions

of drop not captured) (27175 FPS) .......................................................... 261

Figure 6.15 An example of the thin film not rupturing during initial impact (Fr =

37, We = 18) (3000 FPS) ......................................................................... 262

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Figure 6.16 Air film rupture due to a rapid thinning of the film (Impact conditions

of drop not captured) (27175 FPS) .......................................................... 263

Figure 6.17 Air film rupture due to less rapid thinning of the film (Impact

conditions of drop not captured) (27175 FPS)........................................ 263

Figure 6.18 Rupture of the air film supporting a floating drop (3000 FPS) ................. 265

Figure 6.19 Second stage in coalescence cascade (3000 FPS).................................... 266

Figure 6.20 Dimensionless parameters of secondary drops as they impact the liquid

surface ...................................................................................................... 268

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LIST OF TABLES Table 1.1 Classification of pool depth ......................................................................... 3

Table 2.1 Viscosity and surface tension for different recorded temperatures

(Munson et al. 1998).................................................................................. 51

Table 2.2 Technical specifications of the Redlake HG-100K cameras ..................... 52

Table 2.3 Maximum resolution possible for a given FPS rate................................... 53

Table 2.4 Technical specifications of the PIV laser................................................... 54

Table 2.5 Expected ranges for various parameters .................................................... 61

Table 2.6 Available particles with their corresponding properties ............................ 67

Table 2.7 Experiments conducted with 33G needles................................................. 70

Table 2.8 Experiments conducted with 26g needles.................................................. 71

Table 2.9 Experiments conducted with 20g needles.................................................. 71

Table 2.10 Repeatability of drops................................................................................... 72

Table 3.1 Impact numbers and corresponding dimensionless numbers..................... 82

Table 3.2 Impact conditions for the drops that fall into the primary microbubble

formation regime...................................................................................... 137

Table 4.1 Impact conditions for PIV results ............................................................ 149

Table 4.2 Impact details of the image sequences used for the cavity outlines ........ 176

Table 4.3 Depth of free surface influence................................................................ 188

Table 4.4 Comparison between experimental cavity collapse times and predicted

values ....................................................................................................... 193

Table 5.1 Impact conditions for images in Figure 5.1 and Figure 5.2 ..................... 201

Table 5.2 Velocity and diameters of drops exiting the cavity ................................. 205

Table 5.3 Impact conditions for the images sequences from the primary bubble

entrapment regime ................................................................................... 214

Table 5.4 Drop characteristics of the drops from the Primary Bubble Entrapment

Regime ..................................................................................................... 220

Table 5.5 Impact conditions for drops falling in the post-entrapment jetting

regime ...................................................................................................... 237

Table 6.1 Impact conditions for the image sequences shown in Figure 6.3 ............ 246

Table 6.2 Impact conditions for multiple bubble entrapment.................................. 249

Table 6.3 Microbubble size and quantity distribution for the 20g-03 data set ........ 264

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Table 6.4 Estimated and measured values of air volume entrapment due to thin

film rupture during expansion.................................................................. 270

Table 6.5 Estimated entrapped air volumes for floating drops ................................ 270

Table 6.6 Entrapped air volume as a percentage of original drop volume for all

bubble entrapment mechanisms............................................................... 271

the splashing morphology of liquid-liquid impacts

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