The Physics of Microdroplets

Preface xviii
 
Acknowledgements xxi
 
Introduction 1
 
1. Fundamentals of Capillarity 5
 
1.1 Abstract 5
 
1.2 Interfaces and Surface Tension 5
 
1.3 Laplace's Law and Applications 12
 
1.4 Measuring the Surface Tension of Liquids 49
 
1.5 Minimization of the Surface Energy 61
 
1.6 References 62
 
2. Minimal Energy and Stability Rubrics 67
 
2.1 Abstract 67
 
2.2 Spherical Shapes as Energy Minimizers 68
 
2.3 Symmetrization and the Rouloids 73
 
2.4 Increasing Pressure and Stability 77
 
2.5 The Double-Bubble Instability 81
 
2.6 Conclusion 84
 
2.7 References 84
 
3. Droplets: Shape, Surface and Volume 85
 
3.1 Abstract 85
 
3.2 The Shape of Micro-drops 86
 
3.3 Electric Bonds Number 87
 
3.4 Shape, Surface Area and Volume of Sessile Droplets 87
 
3.5 Conclusion 105
 
3.6 References 105
 
4. Sessile Droplets 107
 
4.1 Abstract 107
 
4.2 Droplet Self-motion Under the Effect of a Contrast or Gradient of Wettability 107
 
4.3 Contact Angle Hysteresis 114
 
4.4 Pinning and Canthotaris 117
 
4.5 Sessile Droplet on a Non-ideally Planar Surface 124
 
4.6 Droplet on Textured or Patterned Substrates 125
 
4.7 References 142
 
5. Droplets Between Two Non-parallel Planes: from Tapered Planes to Wedges 145
 
5.1 Abstract 145
 
5.2 Droplet Self-motion Between Two Non-parallel Planes 145
 
5.3 Droplet in a Corner 154
 
5.4 Conclusion 160
 
5.5 References 161
 
6. Microdrops in Microchannels and Microchambers 163
 
6.1 Abstract 163
 
6.2 Droplets in Micro-wells 163
 
6.3 Droplets in Microchannels 168
 
6.4 Conclusion 180
 
6.5 References 181
 
7. Capillary Effects: Capillary Rise, Capillary Pumping, and Capillary Valve 185
 
7.1 Abstract 185
 
7.2

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.