Bubble Dynamics and Shock Waves (eBook)

Preface 6
Contents 9
Part I: Bubble Dynamics and Shock Wave 
11 
Shock 
12 
Introduction 12
Experiments 14
Early Experiments 14
Light Emission 15
Jetting from Stable Gas Bubbles 15
Simulations of a Shock Wave and a Gas Bubble Interaction 16
Injection into Boundaries 20
Jetting from Liquid Menisci 21
Bubble-Bubble Interaction 22
Gas-Bubble Cavitation Interaction 23
Cavitation Bubble - Cavitation Bubble Interaction 24
Cavitation Bubble-Shockwave Interaction 26
Molecular Dynamics Simulations 33
Concluding Remarks 36
References 36
Pulsating Bubbles Near Boundaries 41
Physical and Mathematical Modelling 41
Experimental Studies on Bubbles Near Boundaries 43
Fundamental Physics 44
Dimensionless Parameters 44
Equations of Motion 46
Global Properties: Kelvin Impulse 47
Global Properties: Kinetic and Potential Energy 48
Incompressible Bubble Dynamics 51
Introduction 51
Recent Developments with the Boundary Integral Method: Incompressible Bubble Dynamics 52
Toroidal Bubbles 57
Numerical Results 58
Comparison with Rigid Boundary Results 59
Further Developments in the Boundary Integral Method: Weakly Compressible Bubble Dynamics 60
Introduction 60
Mathematical Formulation 62
Matched Asymptotic Expansion 63
The Theoretical Basis for the Computational Model: Second Order Theory 66
Comparisons with Previous Studies 67
Analysis of Bubble Behaviour When Subjected to a Weak Acoustic Wave 68
Bubble Behaviour When Subjected to a Strong Acoustic Wave 69
Summary and Conclusions 69
References 71
ShockWave Emission by Laser Generated Bubbles 74
Introduction 75
Laser Induced Breakdown in Liquids 80
Shock Wave Emission at Breakdown 82
Bubble Formation and Subsequent Dynamics 89
Shock Wave Emission at Bubble Collapse 93
Applications and Future Perspectives 100
References 104
Part II: Shock Wave Propagation in Bubbly 
111 
Nonlinear Wave Propagation in Bubbly 
112 
Introduction 112
Formulation of the Model 114
Average Description of Waves in Bubbly Liquids 114
Forces Exerting on Bubbles 115
Dissipation Effects on Wave Propagation 116
Linear Dispersion Relation 116
Plane Waves in Uniform Bubbly Liquids 117
Governing Equations of Two-Fluid Model 118
Method of Multiple Scales 120
Korteweg–de Vries–Burgers Equation 123
Parameter Scaling 123
Linear Propagation in a Near Field 124
Nonlinear Propagation in a Far Field 126
Nonlinear Schr¨odinger Equation 128
Parameter Scaling 129
Quasi-Monochromatic Wave Train 129
Slow Variation of Wave Train 132
NLS Equation and Nonlinear Propagation of Envelope Wave 133
Sound Beam in Nonuniform Bubbly Liquid 136
Khokhlov–Zabolotskaya–Kuznetsov Equation 137
Parameter Scaling 137
Method of Multiple Scales 137
Nonuniform Bubble Distribution 138
Generalized KZK Equation 139
Comparison between Mixture and Two-Fluid Models 140
Basic Equations of Mixture Model 140
KdVB Equation 140
NLS Equation 142
Conclusion 142
References 143
Shock Propagation in Polydisperse Bubbly Liquids 146
Introduction 146
Modelling of Continuum Bubbly Flows 148
Mixture-Averaged Conservation Laws 148
Single-Bubble-Dynamic Equations 150
Acoustics of Polydisperse Bubbly Liquids 152
Simulation of Averaged Shock Dynamics 157
Numerical Method 157
Steady Shock Relations 158
One-Dimensional Shock Propagation 161
Shocks in a Mixture-Filled Deformable Tube 165
Quasi-One-Dimensional Conservation Laws 165
FSI Shock Theory 166
Water-Hammer Experiments 168
Concluding Remarks 174
References 175
Direct Numerical Simulation of Shock Propagation in Bubbly Liquids 181
Introduction 181
Direct Numerical Simulations of Bubbly Flows 183
Numerical Method 187
Simulations of Single Bubbles 193
Simulations of 1D Shocks 194
Multidimensional Systems 201
Extensions 201
Conclusions 202
References 203
Part III: Shocks in Cavitating Flows 206
Shocks in Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows 207
Introduction 207
Model Equations for Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows 209
Evolution Equations for the Flow Speed and Bubble Radius 212
The Pressure-Void Fraction-Dilation Relation 214
Stationary and Propagating Shock Waves in Quasi-One-Dimensional Bubbly Cavitating Nozzle Flows 215
Steady-State Solutions and Stationary Shocks 216
Temporal Stability of Steady-State Shock Solutions 217
Unsteady Solutions and Propagating Shock Waves 220
Conclusions and Future Perspectives 228
References 235
Shocks in Cavitating Flows 237
Modeling and Simulation of Shocks in Compressible Two-Phase Flows 237
Numerical Methods for Compressible Two-Phase Flows 239
Two-Fluid Model with Sharp Interface Treatment 239
Single-Fluid Model Using Local Thermodynamic Equilibrium Assumptions 241
Investigations Using the Two-Fluid Model 242
Investigations Using the Single-Fluid Model 247
Summary and Future Perspective 256
References 257
Part IV: Applications in Medical and Earth 
259 
Encapsulated Bubble Dynamics in Imaging and Therapy 260
Introduction 260
Shell Models for Microbubble Contrast Agents 262
Effect of a Boundary on the Dynamics of Contrast Microbubbles 269
Contrast Imaging Methods 275
Single-Pulse Excitation Strategies 277
Multi-pulse Excitation Strategies 279
Sonoporation and Drug Delivery 282
Mechanisms of Drug Delivery 282
Drug Delivery Applications 284
References 284
Shock 
291 
Introduction 291
Different Types of Shock Wave Lithotripters 292
Technologies for Shock Wave Generation and Focusing 293
Pressure Waveforms Produced by Different Types of 
294 
Comparison of Different Types of Lithotripters 297
Kidney Stones and Their Physical Properties 298
Shock Wave-Stone Interaction 300
Fundamental Acoustics of Wave Reflection and Refraction at 
300 
Transient Shock Wave-Stone Interaction 302
Basic Concepts of Fracture Mechanics 306
Mechanisms of Stone Comminution in SWL 309
Mechanisms of Tissue Injury 321
Emerging Technologies in SWL 322
Broad Focal Width and Low Peak Pressure Lithoripters 322
New Acoustic Lens for Electromagnetic Shock Wave 
322 
Other Promising Technologies 325
Summary and Future Perspectives 327
Summary 327
Future Perspectives and iLithotripter 328
References 329
Sterilization of Ships’ Ballast Water 339
Introduction 339
Marine Bacterial Cells Exposed to High-Pressure Shock Waves 342
Experimental Method 342
Numerical Prediction of Shock Wave Propagation in Target 
344 
Effects of High-Pressure Shock Waves on Marine Bacterial 
347 
Inactivation of Marine Bacterial Cells Using Microbubble Dynamics 351
Characteristics of Microbubbles and Concept of Shock Wave–Microbubble Sterilization 351
Observation of Shock Wave Interaction with Microbubbles in 
353 
Inactivation of Marine Bacterial Cells in Water Circulation Channel 356
Future Perspectives 359
References 360
Bubbly Magma State Dynamics at Explosive Character of Decompression 363
Introduction 364
Common Sings: Pre-eruption State, Wave Character of a Decompression and Bubbly Structure of Flow 364
Formation of Nucleation Zone and Dynamics of Initial Magma State 372
Dynamics of Saturation of the Cavitation Zone with Nuclei 373
Cavitation Bubble with Constant Gas Mass 374
Crystallites Role in a Magma State 380
Gas Phase Nucleation and Crystallization in Magma Flow 380
Homogeneous-Heterogeneous Nucleation: Features of Wave Field Structure and of Some Characteristics of the Magma State 382
Crystal Clusters in the Cavitating Magma 
385 
Conclusions 388
References 390
Author Index 393