CHAPTER 1 Introduction: 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 ............................... 3
1.3 The respective place of digital and droplet microfluidics
in today's microfluidics ................................... 5
1.4 Summary .................................................... 6
References ................................................. 6
CHAPTER 2 Theory of Wetting .................................... 7
2.1 Introduction ............................................... 8
2.2 Interfaces and surface tension ............................ 11
2.2.1 The notion of interface ............................ 11
2.2.2 Surface tension .................................... 14
2.3 Laplace's law and applications ............................ 20
2.3.1 Laplace's law ...................................... 20
2.3.2 Examples of application of Laplace's law ........... 24
2.4 Wetting—partial or total wetting .......................... 36
2.5 Contact angle—Young's law ................................. 38
2.5.1 Young's law ........................................ 38
2.5.2 Nanobubbles on hydrophobic walls, line tension,
and the modified Young's law ....................... 39
2.6 Work of adhesion, work of cohesion, and the Young-
Dupré's equation .......................................... 41
2.6.1 Work of adhesion ................................... 41
2.6.2 Work of cohesion ................................... 42
2.6.3 Young-Dupré's equation ............................. 42
2.7 Capillary force, force on a triple line ................... 43
2.7.1 Introduction ....................................... 43
2.7.2 Capillary force between two parallel plates ........ 43
2.7.3 Capillary rise in a tube ........................... 45
2.7.4 Capillary rise between two parallel vertical
plates ............................................. 48
2.7.5 Capillary rise in a pipette ........................ 50
2.7.6 Force on a triple line ............................. 52
2.7.7 Examples of capillary forces in microsystems ....... 53
2.8 Measuring surface tension of liquids ...................... 53
2.8.1 Using pressure (bubble pressure method) ............ 54
2.8.2 Using the capillary rise on a plate-Wilhelmy
plate .............................................. 55
2.8.3 Using gravity: the pendant drop method ............. 57
2.8.4 Using shear stress in a microflow .................. 60
2.9 Surface tension of solids ................................. 62
2.9.1 Introduction ....................................... 62
2.9.2 Surface free energy ................................ 62
2.9.3 CST and SFE ........................................ 64
2.10 Minimization of the surface energy and minimal energy
surface ................................................... 68
2.10.1 Minimal surfaces ................................... 68
2.10.2 Minimization of the surface energy ................. 69
2.11 Summary ................................................... 70
References ................................................ 71
CHAPTER 3 The Physics of Droplets ............................. 75
3.1 Introduction .............................................. 77
3.2 The shape of microdrops ................................... 77
3.2.1 Sessile droplets ................................... 77
3.2.2 Droplets constrained between two plates ............ 85
3.2.3 Droplet at a liquid interface-Neumann's
construction ....................................... 90
3.2.4 Droplet in a corner ................................ 92
3.2.5 Droplet in a groove ................................ 98
3.2.6 Droplet in a microwell ............................ 100
3.2.7 Droplet on striped surface domains ................ 102
3.2.8 Droplet pierced by a micro wire (catena) .......... 107
3.3 Drops on inhomogeneous surfaces .......................... 108
3.3.1 Wenzel's law ...................................... 109
3.3.2 Cassie-Baxter's law ............................... 110
3.3.3 Contact on fabricated surfaces: the transition
between the Wenzel and Cassie laws ................ 113
3.4 Drops moving by capillarity .............................. 124
3.4.1 Drop moving over a transition of wettability ...... 125
3.4.2 Drop moving uphill ................................ 127
3.4.3 Drop moving up a step ............................. 128
3.4.4 Drop moving over a gradient of surface
concentration of surfactant ....................... 129
3.4.5 Conclusion ........................................ 129
3.5 Contact angle hysteresis ................................. 130
3.6 Droplet pinning .......................................... 134
3.6.1 Droplet pinning on a surface defect ............... 134
3.6.2 Droplet pinning at a wettability separation line .. 135
3.6.3 Droplet pinning on an edge ........................ 136
3.7 The effect of surfactants ................................ 137
3.7.1 Introduction ...................................... 137
3.7.2 From partial wetting to total wetting ............. 138
3.8 Marangoni convection ..................................... 138
3.8.1 Marangoni convection due to thermal
nonuniformity ..................................... 139
3.8.2 Marangoni convection due to concentration
gradient .......................................... 142
3.8.3 Marangoni convection due to an electric field ..... 143
3.9 Evaporation .............................................. 144
3.9.1 Evaporation of sessile droplets ................... 144
3.9.2 Evaporation rings ................................. 151
3.9.3 Evaporation stains ................................ 152
3.9.4 Marangoni convection during evaporation ........... 152
3.9.5 The use of droplet evaporation in biotechnology,
biology, and nanoassembly ......................... 153
3.10 Summary .................................................. 157
References ............................................... 157
CHAPTER 4 Electrowetting Theory .............................. 161
4.1 Introduction ............................................. 162
4.2 Theoretical background ................................... 164
4.2.1 Thermodynamic approach ............................ 164
4.2.2 Energy minimization approach ...................... 169
4.2.3 Electromechanical approach ........................ 172
4.3 Lippmann-Young's law and the electrocapillary
equivalence .............................................. 176
4.4 Saturation ............................................... 179
4.4.1 Saturation of the electrowetting effect ........... 179
4.4.2 Possible explanations for the saturation effect ... 180
4.4.3 Modified Lippmann-Young's law ..................... 189
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 ..................................... 204
4.6.3 Conclusion ........................................ 206
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 .......... 214
4.8.1 Low voltages ...................................... 216
4.8.2 Electrowetting forces ............................. 216
4.8.3 Superhydrophobic microfabricated substrates ....... 217
4.8.4 Superhydrophobic droplets ......................... 220
4.9 Summary .................................................. 222
References ............................................... 222
CHAPTER 5 EWOD Microsystems .................................. 225
5.1 Introduction ............................................. 226
5.2 Open and covered EWOD microsystems ....................... 228
5.2.1 Open EWOD microsystems ............................ 228
5.2.2 Covered EWOD microsystems ......................... 231
5.3 Droplet motion ........................................... 232
5.3.1 Principle of droplet motion-quasi-static aspects
and departure from equilibrium .................... 232
5.3.2 Dynamic aspect-velocity of motion ................. 234
5.3.3 Shape of the electrodes: crenellated electrodes ... 242
5.3.4 Motion from a covered to an open EWOD system ...... 253
5.3.5 Effect of a catena ................................ 259
5.4 Division of droplets ..................................... 260
5.4.1 Theoretical approach .............................. 260
5.4.2 Droplet division in open EWOD systems ............. 261
5.4.3 Droplet division in covered EWOD systems .......... 263
5.4.4 Experimental results .............................. 269
5.4.5 Droplet dispensing ................................ 271
5.4.6 Influence of the cutting electrode on drop
volume and reproducibility ........................ 275
5.4.7 Centering electrode and shape of reservoir
electrode ......................................... 278
5.5 Droplet merging and mixing ............................... 284
5.5.1 The difficulty of mixing in covered EWOD
microsystems ...................................... 284
5.5.2 Mixing in open EWOD systems ....................... 288
5.6 Dilution ................................................. 289
5.6.1 Dilution of solutes ............................... 289
5.6.2 Dilution of discrete particles .................... 291
5.7 Magnetic beads in EWOD microsystems ...................... 292
5.8 Architecture of EWOD microsystems ........................ 294
5.8.1 General architecture .............................. 294
5.8.2 Multiplexing ...................................... 295
5.9 Other EWOD microsystems .................................. 296
5.9.1 Electrowetting conveyor system .................... 296
5.9.2 Extension of the electrowetting concept:
electrowetting filament and open microfluidics .... 297
5.10 Summary .................................................. 298
References ............................................... 299
CHAPTER 6 Introduction to Liquid Dielectrophoresis .......... 303
6.1 Introduction ............................................. 303
6.2 DEP and the manipulation of particles .................... 304
6.2.1 Theoretical basis-the dielectrophoretic force ..... 304
6.2.2 The Clausius-Mossoti's factor ..................... 306
6.2.3 The crossover frequency ........................... 308
6.2.4 Conclusions ....................................... 308
6.3 Liquid dielectrophoresis ................................. 309
Ј 6.3.1 Introduction-experimental approach ............. 309
6.3.2 Basis of LDEP ..................................... 311
6.3.3 LDEP modeling ..................................... 314
6.3.4 LDEP and EWOD-critical frequency .................. 317
6.3.5 LDEP devices for water nanodroplet formation ...... 318
6.3.6 Applications to single DNA molecule isolation ..... 321
6.4 Conclusions .............................................. 322
References ............................................... 323
CHAPTER 7 Electrowetting on Curved Surfaces .................. 325
7.1 Introduction ............................................. 325
7.2 Theory of curved electrowetting .......................... 325
7.2.1 EWOD on a spherical surface ....................... 327
7.2.2 EWOD on a cylindrical surface ..................... 329
7.2.3 Conclusions ....................................... 330
7.3 Electrowetting on a wavy surface ......................... 330
7.4 Electrowetting on a rod .................................. 332
7.4.1 Introduction ...................................... 332
7.4.2 Electrowetting on a wire .......................... 334
7.5 Electrowetting on a sphere ............................... 335
7.6 Conclusion ............................................... 336
References ............................................... 337
CHAPTER 8 Biological Applications of EWOD ..................... 339
8.1 Introduction ............................................. 340
8.2 Biological liquids and physiological samples compatible
with EWOD devices ........................................ 340
8.2.1 Physiological liquids ............................. 340
8.2.2 Proteins and biofouling ........................... 342
8.2.3 Cells ............................................. 342
8.2.4 Conclusion ........................................ 344
8.3 Sample collection and analysis on an LOC platform ........ 344
8.4 PCR on DMF systems ....................................... 346
8.4.1 Introduction ...................................... 346
8.4.2 Architecture of a PCR-EWOD microsystem ............ 347
8.4.3 Thermal analysis .................................. 348
8.4.4 Experimental realization of PCR and results ....... 352
8.4.1 DNA repair microprocessor ......................... 357
8.6 Protein analysis coupled with mass spectrometry .......... 360
8.7 Cell-on-a-chip microsystems: example of a cell
concentrator ............................................. 362
8.8 Summary .................................................. 364
References ............................................... 365
CHAPTER 9 Cell Manipulations in EWD .......................... 367
9.1 Introduction ............................................. 367
9.2 Cells in EWOD devices .................................... 368
9.2.1 Motion of droplets laden with cells ............... 368
9.2.2 Viability ......................................... 370
9.3 DMF for cell-based arrays ................................ 370
9.4 Virtual micro wells ...................................... 371
9.4.1 Introduction ...................................... 371
9.4.2 Theoretical approach .............................. 372
9.4.3 Cancer cell culture in an EWOD microdevice ........ 376
9.4.4 Electrowetting device for dried blood spot
analysis .......................................... 378
9.5 Hydrogel disks for DMF ................................... 379
9.6 Concentration of immune cells in blood ................... 383
9.7 Conclusion ............................................... 384
Acknowledgment ........................................... 384
References ............................................... 385
CHAPTER 10 Chemical Applications .............................. 387
10.1 Introduction ............................................. 388
10.1.1 Continuous flow systems ........................... 388
10.1.2 Digital microfluidic .............................. 390
10.2 Nonaqueous solvents on EWOD chips ........................ 393
10.2.1 Volatile organic solvents ......................... 393
10.2.2 Displacement of ionic liquids ..................... 398
10.3 Chemical synthesis in droplets in EWOD-based systems ..... 407
10.3.1 Synthesis in aqueous media ........................ 407
10.3.2 Synthesis in VOSs ................................. 409
10.3.3 Synthesis in ionic liquids ........................ 410
10.4 Conclusions and perspectives ............................. 415
References ............................................... 416
CHAPTER 11 DMF for Optofluidic Microdevices ................... 421
11.1 Introduction ............................................. 421
11.2 Electrowetting screen display ............................ 422
11.2.1 Principle ......................................... 423
11.2.2 Pixel actuation and dewetting ..................... 424
11.2.1 Virtual confinement and Laplace's barriers ........ 426
11.2.4 Perspectives ...................................... 426
11.3 Tunable lens ............................................. 427
11.3.1 Introduction ...................................... 427
11.3.2 Principle ......................................... 428
11.4 Electrowetting-actuated micromirrors ..................... 433
11.5 Polymer dispersed liquid crystals ........................ 436
11.6 Conclusion ............................................... 437
References ............................................... 431
CHAPTER 12 Droplet on Deformable Surfaces-Elasto-
Capillarity and Electro-Elasto-Capillarity .................... 439
12.1 Introduction ............................................. 439
12.2 Neumann's construction ................................... 440
12.3 Sessile droplet on a deformable substrate ................ 441
12.4 Example of a cantilever .................................. 443
12.5 Elasto-capillarity and capillary origami ................. 445
12.6 Electro-elasto-capillarity ............................... 447
12.7 Droplet at a liquid interface ............................ 448
12.7.1 Introduction: the difference between liquid
droplets and rigid spheres at an interface ........ 449
12.7.2 Behavior of a droplet on an immiscible liquid
surface ........................................... 450
12.7.3 Spreading and engulfment .......................... 452
12.7.4 Engulfment with gravity ........................... 453
12.8 Conclusion ............................................... 455
References ............................................... 455
CHAPTER 13 Acoustic Methods for Manipulating Droplets ......... 457
13.1 Introduction ............................................. 458
13.2 Digital microfluidics .................................... 459
13.2.1 Acoustic streaming ................................ 460
13.2.2 Internal streaming ................................ 468
13.2.3 Droplet actuation ................................. 471
13.3 Example 1: Acoustic mixing ............................... 473
13.4 Example 2: Acoustic droplet actuation .................... 475
13.5 Applications ............................................. 478
13.5.1 Microarray hybridization (biological
application) ...................................... 478
13.5.2 Polymerase chain reaction ......................... 479
13.5.3 Cell adhesion ..................................... 484
13.6 Summary .................................................. 489
Acknowledgments .......................................... 490
References ............................................... 491
CHAPTER 14 Introduction to Droplet Microfluidics and
Multiphase Microflows ......................................... 493
14.1 Introduction ............................................. 494
14.2 Two-phase flows: plugs in microchannels .................. 494
14.2.1 Interface and meniscus ............................ 495
14.2.2 Dynamic contact angle ............................. 495
14.2.3 Plugs moving inside a capillary ................... 498
14.2.5 Example of three-phase flow in a microchannel ..... 503
14.3 Two-phase flows: flowing fluids separated by an
interface ................................................ 505
14.3.1 Introduction ...................................... 505
14.3.2 Model ............................................. 506
14.3.3 Discussion and conclusions ........................ 512
14.4 Droplets in two-phase flows .............................. 514
14.4.1 FFDs and T-junctions .............................. 514
14.4.2 Encapsulation ..................................... 527
14.5 Summary .................................................. 527
References ............................................... 530
CHAPTER 15 Epilog ............................................. 533
15.1 Increasing the domain of EWOD applicability .............. 533
15.2 Interconnecting the different microfluidic toolboxes ..... 534
15.3 Miniaturization: nano-EWOD ............................... 536
15.4 Other applications specific to DMF ....................... 537
15.5 Summary .................................................. 537
References ............................................... 538
Index ......................................................... 539
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