Series Editor's Preface ...................................... xiii
Preface ........................................................ xv
Acknowledgments ............................................. xviii
1 Digital Microfluidics in Today's Microfluidics ............... 1
1.1 The Development of Microfluidics ........................ 1
1.2 The Advantages of Digital and Droplet Microfluidics
Compared to Conventional Microflows ..................... 2
1.2.1 From Microflows to Microdrops .................... 2
1.2.2 Microdrops: Comparison Between Digital and
Droplet Microfluidics ............................ 2
1.3 The Respective Place of Digital and Droplet
Microfluidics in Today's Microfluidics .................. 4
1.4 Summary ................................................. 5
References ................................................... 5
2 Theory of Wetting ............................................ 7
2.1 Introduction ............................................ 7
2.2 Interfaces and Surface Tension .......................... 9
2.2.1 The Notion of Interface .......................... 9
2.2.2 Surface Tension ................................. 12
2.3 Laplace Law and Applications ........................... 18
2.3.1 Laplace's Law ................................... 18
2.3.2 Examples of Application of Laplace's Law ........ 23
2.4 Wetting—Partial or Total Wetting ....................... 34
2.5 Contact Angle—Young's Law .............................. 36
2.5.1 Young's Law ..................................... 36
2.5.2 Nano-bubbles on Hydrophobic Walls, Line
Tension and the Modified Young's Law ............ 38
2.6 Work of Adhesion, Work of Cohesion, and the Young-
Dupré Equation ......................................... 40
2.6.1 Work of Adhesion ................................ 40
2.6.2 Work of Cohesion ................................ 41
2.6.3 Young-Dupré Equation ............................ 42
2.7 Capillary Force, Force on a Triple Line ................ 42
2.7.1 Introduction .................................... 42
2.7.2 Capillary Force Between Two Parallel Plates ..... 43
2.7.3 Capillary Rise in a Tube ........................ 44
2.7.4 Capillary Rise Between Two Parallel Vertical
Plates .......................................... 47
2.7.5 Capillary Rise in a Pipette ..................... 49
2.7.6 Force on a Triple Line .......................... 51
2.7.7 Examples of Capillary Forces in Microsystems .... 52
2.8 Measuring Surface Tension of Liquids ................... 53
2.8.1 Using Pressure (Bubble Pressure Method) ......... 53
2.8.2 Using the Capillary Rise on a Plate—Wilhelmy
Plate ........................................... 55
2.8.3 Using Gravity: The Pendant Drop Method .......... 55
2.8.4 Using Shear Stress in a Microflow ............... 59
2.9 Surface Tension of Solids .............................. 61
2.9.1 Introduction .................................... 61
2.9.2 Surface Free Energy ............................. 62
2.9.3 Critical Surface Tension and Surface Free
Energy .......................................... 64
2.10 Minimization of the Surface Energy and Minimal
Energy Surfaces ........................................ 68
2.10.1 Minimal Surfaces ................................ 68
2.10.2 Minimization of the Surface Energy .............. 69
2.11 Summary ................................................ 70
References .................................................. 71
3 The Physics of Droplets ..................................... 75
3.1 Introduction ........................................... 75
3.2 The Shape of Micro-drops ............................... 75
3.2.1 Sessile Droplets ................................ 75
3.2.2 Droplets Constrained Between Two Plates ......... 83
3.2.3 Droplet At a Liquid Interface—Neumann's
Construction .................................... 89
3.2.4 Droplet in a Corner ............................. 91
3.2.5 Droplet in a Groove ............................. 97
3.2.6 Droplet in a Micro-well ......................... 99
3.2.7 Droplet on Striped Surface Domains ............. 101
3.2.8 Droplet Pierced by a Micro-wire (catena) ....... 105
3.3 Drops on Inhomogeneous Surfaces ....................... 106
3.3.1 Wenzel's Law ................................... 108
3.3.2 Cassie-Baxter Law .............................. 110
3.3.3 Contact on Fabricated Surfaces:
The Transition Between the Wenzel and Cassie
Laws ........................................... 112
3.4 Drops Moving by Capillarity ........................... 124
3.4.1 Drop Moving Over a Transition of Wettability ... 124
3.4.2 Drop Moving Uphill ............................. 126
3.4.3 Drop Moving up a Step .......................... 128
3.4.4 Drop Moving Over a Gradient of Surface
Concentration of Surfactant .................... 128
3.4.5 Conclusion ..................................... 129
3.5 Contact Angle Hysteresis .............................. 130
3.6 Droplet Pinning ....................................... 133
3.6.1 Droplet Pinning on a Surface Defect ............ 133
3.6.2 Droplet Pinning at a Wettability Separation
Line ........................................... 134
3.6.3 Droplet Pinning on an Edge ..................... 135
3.7 The Effect of Surfactants ............................. 135
3.7.1 Introduction ................................... 135
3.7.2 From Partial Wetting to Total Wetting .......... 137
3.8 Marangoni Convection .................................. 137
3.8.1 Introduction ................................... 137
3.8.2 Marangoni Convection Due to Thermal
Non-uniformity ................................. 139
3.8.3 Marangoni Convection Due to Concentration
Gradient ....................................... 141
3.8.4 Marangoni Convection Due to an Electric
Field .......................................... 142
3.9 Evaporation ........................................... 143
3.9.1 Evaporation of Sessile Droplets ................ 144
3.9.2 Evaporation Rings .............................. 151
3.9.3 Evaporation Stains ............................. 151
3.9.4 Marangoni Convection During Evaporation ........ 153
3.9.5 The Use of Droplet Evaporation in
Biotechnology, Biology, and Nanoassembly ....... 154
3.10 Summary ............................................... 156
References ................................................. 157
4 Electrowetting Theory ...................................... 161
4.1 Introduction .......................................... 161
4.2 Theoretical Background ................................ 163
4.2.1 Thermodynamic Approach ......................... 163
4.2.2 Energy Minimization Approach ................... 167
4.2.3 Electromechanical Approach ..................... 172
4.3 Lippmann-Young Law and the Electrocapillary
Equivalence ........................................... 176
4.4 Saturation ............................................ 178
4.4.1 Saturation of the Electrowetting Effect ........ 178
4.4.2 Possible Explanations for the Saturation
Effect ......................................... 180
4.4.3 Modified Lippmann-Young Law .................... 190
4.5 Hysteresis ............................................ 193
4.5.1 Introduction ................................... 193
4.5.2 Hysteresis and Minimum Actuation Potential ..... 194
4.6 Working Range of EWOD Devices ......................... 202
4.6.1 Maximum Potential .............................. 202
4.6.2 Working Range .................................. 203
4.6.3 Conclusion ..................................... 205
4.7 Materials and Substrates .............................. 206
4.7.1 Capacitance .................................... 206
4.7.2 Dielectric Breakdown ........................... 208
4.7.3 Materials ...................................... 211
4.7.4 Existing Substrates and Their
Characteristics ................................ 213
4.8 Discussion: Special Substrates and New Concepts ....... 215
4.8.1 Low Voltages ................................... 215
4.8.2 Electrowetting Forces .......................... 216
4.8.3 Superhydrophobic Microfabricated Substrates .... 216
4.8.4 Superhydrophobic Droplets ...................... 219
4.9 Summary ............................................... 221
References ................................................. 222
5 EWOD Microsystems .......................................... 225
5.1 Introduction .......................................... 225
5.2 Open and Covered EWOD Microsystems .................... 225
5.2.1 Open EWOD Microsystems ......................... 226
5.2.2 Covered EWOD Microsystems ...................... 229
5.3 Droplet Motion ........................................ 230
5.3.1 Principle of Droplet Motion—Quasi-static
Aspects and Departure From Equilibrium ......... 231
5.3.2 Dynamic Aspect—Velocity of Motion .............. 232
5.3.3 Shape of the Electrodes: Crenellated
Electrodes ..................................... 240
5.3.4 Motion from a Covered to an Open EWOD System ... 250
5.3.5 Effect of a Catena ............................. 257
5.4 Division of Droplets .................................. 258
5.4.1 Theoretical Approach ........................... 259
5.4.2 Droplet Division in Open EWOD Systems .......... 260
5.4.3 Droplet Division in Covered EWOD Systems ....... 261
5.4.4 Experimental Results ........................... 263
5.4.5 Droplet Dispensing ............................. 263
5.4.6 Influence of the Cutting Electrode on Drop
Volume and Reproducibility ..................... 268
5.4.7 Centering Electrode and Shape of Reservoir
Electrode ...................................... 271
5.5 Droplet Merging and Mixing ............................ 276
5.5.1 The Difficulty of Mixing in Covered EWOD
Microsystems ................................... 277
5.5.2 Mixing in Open EWOD Systems .................... 279
5.6 Dilution .............................................. 281
5.6.1 Dilution of Solutes ............................ 281
5.6.2 Dilution of Discrete Particles ................. 283
5.7 Magnetic Beads in EWOD Microsystems ................... 284
5.8 Architecture of EWOD Microsystems ..................... 286
5.8.1 General Architecture ........................... 286
5.8.2 Multiplexing ................................... 286
5.9 Other EWOD Microsystems ............................... 287
5.9.1 Electrowetting Conveyor System ................. 289
5.9.2 Extension of the Electrowetting Concept:
Electrowetting Filament and Open
Microfluidics .................................. 289
5.10 Summary ............................................... 290
References ................................................. 291
6 Biological Applications of EWOD ............................ 295
6.1 Introduction .......................................... 295
6.2 Biological Liquids and Physiological Samples
Compatible with EWOD Devices .......................... 295
6.2.1 Physiological Liquids .......................... 296
6.2.2 Proteins and Biofouling ........................ 297
6.2.3 Cells .......................................... 297
6.2.4 Conclusion ..................................... 298
6.3 Sample Collection and Analysis on a Lab-on-a-chip
Platform .............................................. 299
6.4 Polymerase Chain Reaction (PCR) on Digital
Microfluidics Systems ................................. 301
6.4.1 Introduction ................................... 301
6.4.2 Architecture of a PCR-EWOD Microsystem ......... 302
6.4.3 Thermal Analysis ............................... 303
6.4.4 Experimental Realization of PCR and Results .... 306
6.5 DNA Repair Microprocessor ............................. 310
6.6 Protein Analysis Coupled with Mass Spectrometry ....... 314
6.7 Cell-on-a-chip Microsystems: Example of a Cell
Concentrator .......................................... 317
6.8 Summary ............................................... 319
References ................................................. 319
7 Chemical Applications ...................................... 321
7.1 Introduction .......................................... 321
7.1.1 Continuous Flow Systems ........................ 321
7.1.2 Digital Microfluidic ........................... 323
7.2 Non Aqueous Solvents on EWOD Chips .................... 326
7.2.1 Volatile Organic Solvents (VOS) ................ 326
7.2.2 Displacement of Ionic Liquids .................. 331
7.3 Chemical Synthesis in Droplets in EWOD-based
Systems ............................................... 340
7.3.1 Synthesis in Aqueous Media ..................... 340
7.3.2 Synthesis in Volatile Organic Solvents ......... 342
7.3.3 Synthesis in Ionic Liquids ..................... 343
7.4 Conclusions and Perspectives .......................... 348
References ................................................. 349
8 Acoustic Methods for Manipulating Droplets ................. 353
8.1 Introduction .......................................... 353
8.2 Digital Microfluidics ................................. 355
8.2.1 Acoustic Streaming ............................. 356
8.2.2 Internal Streaming ............................. 363
8.2.3 Droplet Actuation .............................. 366
8.3 Example 1: Acoustic Mixing ............................ 368
8.4 Example 2: Acoustic Droplet Actuation ................. 370
8.5 Applications .......................................... 372
8.5.1 Micro-array Hybridization (Biological
Application) ................................... 372
8.5.2 Polymerase Chain Reaction ...................... 376
8.5.3 Cell Adhesion .................................. 380
8.6 Summary ............................................... 384
Acknowledgements ........................................... 386
References ................................................. 387
9 Introduction to Droplet Microfluidics and Multiphase
Microflows ................................................. 389
9.1 Introduction .......................................... 389
9.2 Two-phase Flows: Plugs in Microchannels ............... 390
9.2.1 Interface and Meniscus ......................... 390
9.2.2 Dynamic Contact Angle .......................... 390
9.2.3 Plugs Moving Inside a Capillary ................ 393
9.2.4 Hysteresis of Static Contact Angle ............. 398
9.2.5 Example of Three-phase Flow in
a Microchannel ................................. 398
9.3 Two-phase Flows: Flowing Fluids Separated by an
Interface ............................................. 401
9.3.1 Introduction ................................... 401
9.3.2 Model .......................................... 401
9.3.3 Experimental Results ........................... 407
9.3.4 Discussion and Conclusions ..................... 408
9.4 Droplets in Two-phase Flows ........................... 410
9.4.1 Flow Focusing Devices (FFD) and T-junctions .... 410
9.4.2 Encapsulation .................................. 424
9.5 Summary ............................................... 424
References ................................................. 426
10 Epilog ..................................................... 429
10.1 Increasing the Domain of EWOD Applicability ........... 429
10.2 Interconnecting the Different Microfluidic
Toolboxes ............................................. 429
10.3 Miniaturization: Nano-EWOD ............................ 431
10.4 Other Applications Specific to Digital
Microfluidics ......................................... 432
10.5 Summary ............................................... 433
References ................................................. 433
Index ......................................................... 435
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