The Physics of Microdroplets (PDF)

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 Capillary Rise 185 7.3 Capillary Pumping 198 7.4 Capillary Valves 205 7.5 Conclusions 209 7.6 References 210 8. Open Microfluidics 213 8.1 Abstract 213 8.2 Droplet Pierced by a Wire 214 8.3 Liquid Spreading Between Solid Structures - Spontaneous Capillary Flow 218 8.4 Liquid Wetting Fibers 241 8.5 Conclusions 250 8.6 References 250 8.7 Appendix: Calculation of the Laplace Pressure for a Droplet on a Horizontal Cylindrical Wire

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.

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