The Physics of Microdroplets

Microdrops and interfaces are now a common feature in most fluidic microsystems, from biology, to biotechnology, materials science, 3D -microelectronics, optofluidics, and mechatronics. On the other hand, the behaviour of droplets and interfaces in today's microsystems is complicated and involves complex 3D geometrical considerations. From a numerical standpoint, the treatment of interfaces separating different immiscible phases is difficult. This book aims to give the reader the theoretical and numerical tools to understand, explain, calculate and predict the often non intuitive, observed behaviour of droplets in microsystems. After a chapter dedicated to the general theory of wetting, the book successively · presents the theory of 3D liquid interfaces, · gives the formulas for volume and surface of sessile and pancake droplets, · analyses the behaviour of sessile droplets, · analyses the behaviour of droplets between tapered plates and in wedges, · presents the behaviour of droplets in microchannels · investigates the effect of capillarity with the analysis of capillary rise, · treats the onset of spontaneous capillary flow in open microfluidic systems, · analyses the interaction between droplets, like engulfment, · presents the theory and application of electrowetting, · presents the state of the art for the approach of 3D-microelectronics using capillary alignment.

Jean Berthier is a Scientist at the CEA/LETI and teaches at the University of Grenoble, France. He is presently involved in the development of microdevices for liquid-liquid extraction (LLE), flow focusing devices (FFD) for bio-encapsulation of live cells, microfluidic resonators for high sensitivity biodetection and numerical methods for the prediction of droplets and interfaces behavior in microsystems. He is the first author of the book Microfluidics for Biotechnology published in 2005 with a second edition in 2010. He is also the author of the book Microdrops and Digital Microfluidics, published in 2008.

Kenneth A. Brakke is Professor of Mathematics and Computer Science at Susquehanna University in Pennsylvania. He received his PhD in mathematics from Princeton University in the field of geometric measure theory. Since 1988, he has written and maintained his freely available Surface Evolver software, which shows computer models of liquid surfaces.

Preface	p. xviii
Acknowledgements	p. xxi
Introduction	p. 1
Fundamentals of Capillarity	p. 5
Abstract	p. 5
Interfaces and Surface Tension	p. 5
LaplaceâÇÖs Law and Applications	p. 12
Measuring the Surface Tension of Liquids	p. 49
Minimization of the Surface Energy	p. 61
References	p. 62
Minimal Energy and Stability Rubrics	p. 67
Abstract	p. 67
Spherical Shapes as Energy Minimizers	p. 68
Symmetrization and the Rouloids	p. 73
Increasing Pressure and Stability	p. 77
The Double-Bubble Instability	p. 81
Conclusion	p. 84
References	p. 84
Droplets: Shape, Surface and Volume	p. 85
Abstract	p. 85
The Shape of Micro-drops	p. 86
Electric Bonds Number	p. 87
Shape, Surface Area and Volume of Sessile Droplets	p. 87
Conclusion	p. 105
References	p. 105
Sessile Droplets	p. 107
Abstract	p. 107
Droplet Self-motion Under the Effect of a Contrast or Gradient of Wettability	p. 107
Contact Angle Hysteresis	p. 114
Pinning and Canthotaris	p. 117
Sessile Droplet on a Non-ideally Planar Surface	p. 124
Droplet on Textured or Patterned Substrates	p. 125
References	p. 142
Droplets Between Two Non-parallel Planes: from Tapered Planes to Wedges	p. 145
Abstract	p. 145
Droplet Self-motion Between Two Non-parallel Planes	p. 145
Droplet in a Corner	p. 154
Conclusion	p. 160
References	p. 161
Microdrops in Microchannels and Microchambers	p. 163
Abstract	p. 163
Droplets in Micro-wells	p. 163
Droplets in Microchannels	p. 168
Conclusion	p. 180
References	p. 181
Capillary Effects: Capillary Rise, Capillary Pumping, and Capillary Valve	p. 185
Abstract	p. 185
Capillary Rise	p. 185
Capillary Pumping	p. 198
Capillary Valves	p. 205
Conclusions	p. 209
References	p. 210
Open Microfluidics	p. 213
Abstract	p. 213
Droplet Pierced by a Wire	p. 214
Liquid Spreading Between Solid Structures âÇô Spontaneous Capillary Flow	p. 218
Liquid Wetting Fibers	p. 241
Conclusions	p. 250
References	p. 250
Appendix: Calculation of the Laplace Pressure for a Droplet on a Horizontal Cylindrical Wire	p. 251
Droplets, particles and Interfaces	p. 253
Abstract	p. 253
NeumannâÇÖs Construction for liquid Droplets	p. 253
The Difference Between Liquid Droplets and Rigid Spheres at an Interface	p. 254
Liquid Droplet Deposited at a Liquid Surface	p. 256
Immiscible Droplets in Contact and Engulfment	p. 261
Non-deformable (Rigid) Sphere at an Interface	p. 265
Droplet Evaporation and Capillary Assembly	p. 278
Conclusion	p. 291
References	p. 292
Digital Microfluidics	p. 295
Introduction	p. 295
Electrowetting and EWOD	p. 295
Droplet Manipulation with EWOD	p. 306
Examples of EWOD in Biotechnology âÇô Cell Manipulation	p. 335
Examples of Electrowetting for Optics-Tunable Lenses and Electro fluidic Display	p. 337
Conclusion	p. 338
References	p. 339
Capillary Self-assembly for 3D Microelectronics	p. 343
Abstract	p. 343
Ideal Case: Total Pinning on the Chip and Pad Edges	p. 344
Real Case: Spreading and Wetting	p. 355
The Importance of Pinning and Confinement	p. 358
Conclusion	p. 359
Appendix A: Shift Energy and Restoring Force	p. 360
Appendix B: Twist Energy and Restoring Torque	p. 362
Appendix C: Lift Energy and Restoring Force	p. 364
References	p. 365
Epilogue	p. 369
Index	p. 369
Table of Contents provided by Publisher. All Rights Reserved.

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The Physics of Microdroplets

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