The manipulation of cells and microparticles within microfluidic systems using external forces is valuable for many microscale analytical and bioanalytical applications. Acoustofluidics is the ultrasound-based external forcing of microparticles with microfluidic systems. It has gained much interest because it allows for the simple label-free separation of microparticles based on their mechanical properties without affecting the microparticles themselves.
Microscale Acoustofluidics provides an introduction to the field providing the background to the fundamental physics including chapters on governing equations in microfluidics and perturbation theory and ultrasound resonances, acoustic radiation force on small particles, continuum mechanics for ultrasonic particle manipulation, and piezoelectricity and application to the excitation of acoustic fields for ultrasonic particle manipulation. The book also provides information on the design and characterization of ultrasonic particle manipulation devices as well as applications in acoustic trapping and immunoassays.
Written by leading experts in the field, the book will appeal to postgraduate students and researchers interested in microfluidics and lab-on-a-chip applications.

Over the last fifteen years acoustophoresis, i.e. the manipulation of particles by means of acoustic forces, in microfluidic structures has taken giant leaps forward. Much insight and improved understanding of these complex systems have been gained in all aspects, ranging from basic theory to modeling, design and fabrication. As a consequence, the number of appli-cations in which the possibility of non-contact handling of cells and particles in a gentle way is also increasing rapidly.
The origin of this book began at a summer school on acoustofluidics in Udine, Italy in 2010. The information presented was overwhelming, and voices were raised to try to compile this wealth of specialized knowledge in a comprehensive manner for the broader scientific community.
This eventually became a series of tutorial review papers published in the journal Lab on a Chip between 2011 and 2013, in which 23 separate papers covered different aspects of acoustofluidics, starting with Lab Chip, 2011, 11, 3579. This tutorial series serves as the foundation for this book. Since then, updates of recent developments and additional chapters have been written to provide a more comprehensive, broader and up to date overview of the field of microscale acoustofluidics.
It is our hope that the presented material can serve as a valuable source of information in your scientific or educational work.
Andreas Lens h of and Thomas Laurell
Lund

Chapter 1 Governing Equations in Microfluidics 1

Henrik Bruus

1.1 Introduction 1

1.2 The Basic Continuum Fields 2

1.3 Mathematical Notation 3

1.4 Governing Equations 5

      1.4.1 The Continuity Equation 5

      1.4.2 The Navier-Stokes Equation 7

      1.4.3 The Heat-transfer Equation 9

1.5 Flow Solutions 11

      1.5.1 Hydrostatic Pressure 11

      1.5.2 The Reynolds Number and the Stokes Equation 12

      1.5.3 Poiseuille Flow 13

      1.5.4 Flow Rate 16

1.6 Equivalent Circuit Modeling 16

      1.6.1 Hydraulic Resistance 17

      1.6.2 Hydraulic Compliance 18

      1.6.3 Hydraulic Inductance 20

1.7 Scaling Laws in Microfluidics 20

      1.7.1 Flow Rate 21

      1.7.2 Characteristic Dimensionless Numbers 22

      1.7.3 Entrance Length 24

      1.7.4 Inertial Time Scale 25

References 27

Chapter 2 Perturbation Theory and Ultrasound Resonances 29

Henrik Bruus

2.1 Introduction 29

2.2 First-order Perturbation Theory, the Acoustic Wave Equation 30

2.3 Second-order Perturbation Theory and Acoustic Streaming 32

2.4 Basics of Acoustic Resonances in Viscous Liquids 35

2.5 Acoustic Eigenmodes 38

      2.5.1 Boundary Conditions 38

      2.5.2 An Ideal Water-filled Rectangular Channel 39

      2.5.3 Viscous and Radiative Losses in the Rectangular Channel 40

2.6 Geometrical Effects and FEM Simulations 42

      2.6.1 Finite Element Method (FEM) Simulations 42

      2.6.2 Symmetry Breaking in Acoustic Resonances 43

References 45

Chapter 3 Continuum Mechanics for Ultrasonic Particle Manipulation 46

Jürg Dual and Thomas Schwarz

3.1 Introduction 46

3.2 Linear Elastodynamics 47

3.3 Deformations of Structures 51

3.4 Fluid Structure Interaction at the Device Level 56

      3.4.1 Acoustic Radiation from a Vibrating Surface 56

      3.4.2 Acoustic Radiation from a Plate Vibrating Harmonically 58

      3.4.3 Vibrations of Devices for Particle Manipulation 59

3.5 Example of a Mechanical Model of an Ultrasonic Cavity used for Particle Manipulation 61

3.6 Conclusions 63

References 64

Chapter 4 Acoustic Radiation Force on Small Particles 65

Henrik Bruus

4.1 Introduction 65

4.2 The Acoustic Radiation Force 66

4.3 Scattering Theory 67

      4.3.1 Scattering and the Radiation Force 68

      4.3.2 The Near-field Potential 70

      4.3.3 The Monopole Coefficient f1 71

      4.3.4 The Dipole Coefficient f2 71

      4.3.5 The Resulting Radiation Force for a Standing Plane Wave 72

4.4 Acoustophoretic Particle Tracks 74

4.5 Energy Density as a Function of the Applied Piezo Voltage 77

4.6 Viscous Corrections to the Radiation Force 78

References 79

Chapter 5 Piezo electricity and Application to the Excitation of Acoustic Fields for Ultrasonic Particle Manipulation 81

Jürg Dual and Dirk Möller

5.1 Introduction 81

5.2 Basic Equations 82

5.3 Vibration of a Free Piezoelectric Element Excited by an Applied Electrical Voltage 85

5.4 Piezoelectric Transducers Used to Excite Mechanical Vibrations in a Structure 87

5.5 FEM Model Example of an Ultrasonic Cavity used for Particle Manipulation 95

5.6 Conclusions 98

References 98

Chapter 6 Building Microfluidic Acoustic Resonators 100

Andreas Lenshof, Mikael Evander, Thomas Laurel, and Johan Nilsson

6.1 Introduction 100

6.2 Choice of Material 103

6.3 Design Configurations 106

      6.3.1 Layered Resonators 106

      6.3.2 Transversal Resonators 107

      6.3.3 SAW Devices 108

      6.3.4 Flow Splitter Design 109

      6.3.5 1D and 2D Acoustic Focusing in Continuous Flow 110

      6.3.6 Acoustic Traps 111

      6.3.7 Capillaries 114

6.4 Actuation 116

      6.4.1 Transducer Coupling 116

      6.4.2 Coupled Resonance Modes 118

      6.4.3 Electrode and Transducer Modifications 119

      6.4.4 Focused Transducers 121

6.5 Conclusions 123

References 124

Chapter 7 Modelling and Applications of Planar Resonant Devices for Acoustic Particle Manipulation 127

Peter Glynne-Jones, Rosemary J. Boltryk, and Martyn Hill

7.1 Introduction 127

7.2 Acoustic Radiation Forces 127

7.3 Generating the Required Acoustic Field 128

7.4 Modelling of Planar Resonators 128

7.5 Resonator Configurations 131

      7.5.1 Half-Wave Devices 133

      7.5.2 Quarter-Wave Resonators 137

      7.5.3 Thin-Reflector Resonators 138

7.6 Position Control in Resonators 138

7.7 Applications 141

      7.7.1 Filtration, Washing and Separation 141

      7.7.2 Sensing and Detection 142

      7.7.3 Cell-Interaction Studies and Sonoporation 143

7.8 Conclusions 144

References 144

Chapter 8 Applications in Continuous Flow Acoustophoresis 148

Andreas Lenshof, Per Augustsson, and Thomas Laurell

8.1 Introduction 148

8.2 Concentration 150

8.3 Clarification 152

8.4 Acoustic Particle Sorting and Cytometry Applications 154

8.5 Medium Exchange of Cells and Microparticles 157

      8.5.1 Transport Mechanisms 158

      8.5.2 Acoustic Forces in Stratified Liquids 163

      8.5.3 Devices for Buffer Exchange 163

8.6 Separation by Acoustophysical Properties 167

      8.6.1 Free Flow Acoustophoresis (FFA) 168

      8.6.2 FFA Devices 169

      8.6.3 Pre-Alignment and Fractionation 172

      8.6.4 Bi-Directional Fractionation 174

      8.6.5 Altering the Acoustic Properties of the Medium 176

8.7 Cells Bound to Beads 176

      8.7.1 Positive Contrast Particles 176

      8.7.2 Negative Contrast Particles 177

8.8 Frequency Switching 177

8.9 Acoustic Radiation Forces in Stratified Liquids 179

8.10 Considerations 181

      8.10.1 Variations of the Acoustic Field 181

      8.10.2 Temperature Aspects 182

      8.10.3 Cell Analysis Following Acoustofluidic Handling 182

      8.10.4 Measuring Separation Performance 183

      8.10.5 Size Limitations 184

References 185

Chapter 9 Applications in Acoustic Trapping 189

Mikael Evander and Johan Nilsson

9.1 Introduction 189

9.2 Theory 190

9.3 Methods for Acoustic Trapping 193

9.4 Applications in Acoustic Trapping 196

      9.4.1 Particle Studies 196

      9.4.2 Bioassays on Trapped Microparticles 199

9.5 Cell Population Studies 201

      9.5.1 Enrichment/Washing of Cells 204

      9.5.2 Size Sorting and Separations 208

9.6 Conclusion 208

References 208

Chapter 10 Ultrasonic Micro robotics in Cavities：Devices and Numerical Simulation 212

Jürg Dual, Philipp Hahn, Andreas Lamprecht, Ivo Leibacher, Dirk Möller, Thomas Schwarz, and Jingtao Wang

10.1 Introduction 212

10.2 Particle Manipulation in Cavities 214

      10.2.1 Pattern Formation in Micro chambers 214

      10.2.2 Rotation of Micro-particles 220

      10.2.3 Particle Transport 223

      10.2.4 Particle Positioning Combined with a Microgripper 227

10.3 Numerical Techniques for the Time-averaged Acoustic Effects 229

      10.3.1 Perturbation Method 231

      10.3.2 Solving the N-S Equation by FVM 233

      10.3.3 Numerical Examples 234

      10.3.4 Summary of the Numerical Examples 239

10.4 Summary and Conclusions 239

References 239

Chapter 11 Acoustic Manipulation Combined with Other Force Fields 242

Peter Glynne-Jones and Martyn Hill

11.1 Introduction 242

11.2 Gravitational Forces 243

11.3 Hydrodynamic Forces 245

11.4 Forces Induced by Electrical Fields 248

11.5 Magnetic Forces 250

11.6 Optical Forces 252

11.7 Conclusions 253

References 254

Chapter 12 Analysis of Acoustic Streaming by Perturbation Methods 256

Satwindar Singh Sadhal

12.1 Introduction 256

      12.1.1 Oscillatory Flows 259

      12.1.2 Incompressible Flow Approximation 263

12.2 One-and Two-Dimensional Cases 266

      12.2.1 The Quartz Wind 266

      12.2.2 Rayleigh Streaming 268

      12.2.3 Stokes Drift 270

      12.2.4 Streaming between Two Plates 271

12.3 Interaction of Solid Particles and Drops with Ultrasound 276

      12.3.1 Acoustic Levitators 278

12.4 Solid Particles and Drops Placed Between Nodes 279

      12.4.1 Solution 282

      12.4.2 Discussion 286

      12.4.3 Streaming around a Solid Sphere Placed between Nodes 289

      12.4.4 Solid Particle/Liquid Drop at the Velocity Antinode 290

      12.4.5 Solid Sphere at the Velocity Node 294

      12.4.6 Discussion 296

12.5 Bubbles in Acoustic Fields 296

      12.5.1 Transverse Oscillations with Fixed Volume 297

      12.5.2 Radial and Transverse Oscillations of Bubbles 299

      12.5.3 Semi-cylindrical Bubble 302

12.6 Concluding Remarks 305

Acknowledgements 308

Nomenclature 308

Roman Symbols 308

Greek Letters 309

Subscripts, Superscripts and Accents 309

References 310

Chapter 13 Applications of Acoustic Streaming 312

Roy Green, Mathias Ohlin, and Martin Wiklund

13.1 Introduction 312

13.2 A Qualitative Description of Acoustic Streaming Phenomena 313

13.2.1 Inner and Outer Boundary Layer Acoustic Streaming 314

13.2.2 Eckart Streaming 316

13.2.3 Cavitation Micro streaming 317

13.3 Microfluidic Applications of Acoustic Streaming 318

13.3.1 Applications of Rayleigh Streaming 318

13.3.2 Applications of Eckart Streaming 326

13.3.3 Applications of Cavitation Micro streaming 327

13.3.4 Surface Acoustic Wave Induced Streaming Applications 331

13.4 Conclusion 333

References 333

Chapter 14 Theory of Surface Acoustic Wave Devices for Particle Manipulation 337

Michael Gedge and Martyn Hill

14.1 Introduction 337

14.2 Rayleigh Waves 338

14.3 Leaky Rayleigh Waves 344

14.4 Scholte Waves 347

14.5 Interface Waves 347

14.6 Stone ley Waves 349

14.7 Anisotropic Media and Piezoelectric Considerations 349

14.8 Generation of Surface Acoustic Waves 350

14.9 Conclusions 352

References 352

Chapter 15 Lab-on-a-chip Technologies Enabled by Surface Acoustic Waves 354

xiaoyun Ding, Peng Li, Sz-Chin Steven Lin, Zackary S. Stratton, Nitesh Nama, Feng Guo, Daniel Slotcavage, Xiaole Mao, Jinjie Shi, Francesco Costanzo, Thomas Franke, Achim Wixforth, and Tony Jun Huang

15.1 Introduction 354

15.2 Travelling Surface Acoustic Wave (TSAW) Microfluidics 357

      15.2.1 Theory Involved with TSAW 357

      15.2.2 Microfluidic Technologies Enabled by TSAWs 358

      15.2.3 Microfluidic Technologies Enabled by Phono nic Crystal-assisted TSAWS 370

15.3 Standing Surface Acoustic Wave (SSAW) Microfluidics 375

      15.3.1 Theory Involved with SSAW 375

      15.3.2 Microfluidic Technologies Enabled by SSAWs 377

15.4 Conclusions and Perspectives 389

Acknowledgements 391

References 392

Chapter 16 Surface Acoustic Wave Based Microfluidics and Droplet Applications 399

Thomas Franke, Thomas Frommelt, Lothar Schmid, Susanne Braunmüller, Tony Jun Huang, and Achim Wixforth

16.1 Introduction 399

16.2 Acoustic Streaming Effects 400

16.3 Acoustically Induced Mixing 403

16.4 Acoustic Droplet Actuation 405

16.5 PDMS Microfluidics 407

      16.5.1 SAW Excitation on a Piezo substrate and Acoustic Coupling to Standard PDMS Devices

      408

      16.5.2 Pumping in Closed PDMS Channels 410

      16.5.3 Droplet Based Fluidics 412

16.6 Conclusions 417

References 417

Chapter 17 Ultrasound-Enhanced Immunoassays and Particle Sensors 420

Martin Wiklund, Stefan Radel, and Jeremy Hawkes

17.1 Introduction 420

17.2 Ultrasound-Enhanced Bead-Based Immunoassays 421

      17.2.1 Agglutination Assays 422

      17.2.2 Fluorescence Assays 425

17.3 Ultrasound-Enhanced Particle Sensors 427

      17.3.1 The Distinctive Pattern of Clumps in Contact with a Surface 428

      17.3.2 The Need for a Cell Attracting Wall in Microsystems 428

      17.3.3 Device Design 430

      17.3.4 The Cell Attractor Wall 430

      17.3.5 Immuno-Based Selective Cell Capture and Detection by Light 431

      17.3.6 The Next Stage of Developments 434

17.4 Ultrasound-Enhanced Vibrational Spectroscopy 435

      17.4.1 Agglomeration of Crystals for Raman Spectroscopy 436

      17.4.2 Enhancement of Stopped Flow FT-IR ATR Spectroscopy 439

      17.4.3 ATR Probe for Inline Bioprocess Monitoring443

17.5 Conclusions 448

References 448

Chapter 18 Multi-Wavelength Resonators, Applications and Considerations 452

Jeremy J. Hawkes and Stefan Radel

18.1 Introduction 452

18.2 Acoustic Filters 455

      18.2.1 Ultrasonically Enhanced Sedimentation 456

      18.2.2 Enhanced Sedimentation 459

      18.2.3 Influences on Separation Efficiency (UES) 460

      18.2.4 Flow Splitters in the h-Shape Separator 461

18.3 Resonators 462

      18.3.1 Construction 462

      18.3.2 Tools for Development 465

      18.3.3 Models and Measurements 465

      18.3.4 Gel Technique 468

      18.3.5 Control of Acoustic Signal 470

      18.3.6 Dimensions 471

      18.3.7 Thickness Limits and Scale Considerations 472

      18.3.8 Acoustic Contrast 473

18.4 Flow Changes Produced by Scale-up 474

      18.4.1 Non-Turbulent Flow Required 474

      18.4.2 Calculating the Onset of Turbulence 475

      18.4.3 Effect of Scale-upon the Initiation of Turbulence 476

      18.4.4 Heating 476

      18.4.5 Entrance Condition 479

      18.4.6 Flow Expansion and Contraction without Disruption or Dead Volumes 480

18.5 New Design Approaches 482

      18.5.1 Heating Mitigation 482

      18.5.2 Creating a Standing Wave: Selection of a Particular Wall Mode Is Not Always Required 482

      18.5.3 Modelling Resonant Parts 483

      18.5.4 Modelling the Chamber Wall 484

      18.5.5 Experimental Confirmation 486

18.6 Appendix 487

Nomenclature 487

Greek Letters 488

References 488

Chapter 19 Microscopy for Acousto fluidic Micro-Devices 493

Martn Wiklund, Hjalmar Brismar, and Björn Önfelt

19.1 Introduction 493

19.2 Basic Principles of Optical Microscopy 494

      19.2.1 Illumination System 497

19.3 Modes of Optical Microscopy 506

      19.3.1 Bright-Field Microscopy 507

      19.3.2 Fluorescence Microscopy 509

19.4 Implementation of Optical Microscopy in an Acoustofluidic Micro-Device 512

      19.4.1 Design Criteria 512

      19.4.2 Applications of Microscopy to Acoustofluidics 515

19.5 Conclusions 516

Acknowledgements 517

References 517

Chapter 20 Experimental Characterization of Ultrasonic Particle Manipulation Devices 520

Jürg Dual, Philipp Hahn, Ivo Leibacher, Dirk Möller, and Thomas Schwarz

20.1 Introduction 520

20.2 Laser Interferometry 521

      20.2.1 Obtainable Resolution in Interferometry 523

20.3 Frequency Analysis, Admittance Curves and Modal Analysis 524

20.4 Schlieren Imaging of 2D Pressure Fields in Cavities 527

20.5 Measurements 529

      20.5.1 Characterization of a Transducer 529

      20.5.2 Characterization of Manipulation Devices 539

20.6 Conclusions 542

References 543

Chapter 21 Biocompatibility and Cell Viability in Acoustofluidic Resonators 545

Martin Wiklund

21.1 Introduction 545

21.2 Physical Mechanisms of Ultrasound Causing a Bioeffect 547

      21.2.1 Thermal Effects 547

      21.2.2 Cavitation-Based Effects 550

      21.2.3 Effects of Acoustic Radiation Forces 553

      21.2.4 Effects of Acoustic Streaming 554

      21.2.5 Effects Not Caused by Ultrasound 555

21.3 Observed Bio effects on Cells in Ultrasonic Standing Wave Manipulation Devices 555

21.4 Methods for Measuring the Impact of Ultrasound on Cell Viability 558

21.5 Conclusions 561

Acknowledgements 562

References 562

Subject Index 566

Professor Thomas Laurell holds a position as Professor in Medical and Chemical Microsensors and has since 1995 built his research activities around microtechnologies in biomedicine (http://www.elmat.lth.se/forskning/nanobio technology_and_labonachip). Laurell recently started a new applied nanoproteomics laboratory at the Biomedical Centre in Lund, integrating microfluidics and nanobiotechnology developments with medical research. This research is focused on new microchip technologies in the area of biomedicine, biochemistry, nanobiotechnology with a focus on disease biomarkers, diagnostic microsystems and miniaturised sample processing. Laurell also leads the clinically oriented research environment CellCARE, (www.cellcare.lth.se), which targets chip based cell separation utilising ultrasonic standing wave technology (acoustophoresis) as the fundamental mode of separation.

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