Physics of Microdroplets

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 xviii Acknowledgements xxiIntroduction 11. Fundamentals of Capillarity 51.1 Abstract 51.2 Interfaces and Surface Tension 51.3 Laplace’s Law and Applications 121.4 Measuring the Surface Tension of Liquids 491.5 Minimization of the Surface Energy 611.6 References 622. Minimal Energy and Stability Rubrics 672.1 Abstract 672.2 Spherical Shapes as Energy Minimizers 682.3 Symmetrization and the Rouloids 732.4 Increasing Pressure and Stability 772.5 The Double-Bubble Instability 812.6 Conclusion 842.7 References 843. Droplets: Shape, Surface and Volume 853.1 Abstract 853.2 The Shape of Micro-drops 863.3 Electric Bonds Number 873.4 Shape, Surface Area and Volume of Sessile Droplets 873.5 Conclusion 1053.6 References 1054. Sessile Droplets 1074.1 Abstract 1074.2 Droplet Self-motion Under the Effect of a Contrast or Gradient of Wettability 1074.3 Contact Angle Hysteresis 1144.4 Pinning and Canthotaris 1174.5 Sessile Droplet on a Non-ideally Planar Surface 1244.6 Droplet on Textured or Patterned Substrates 1254.7 References 1425. Droplets Between Two Non-parallel Planes: from Tapered Planes to Wedges 1455.1 Abstract 1455.2 Droplet Self-motion Between Two Non-parallel Planes 1455.3 Droplet in a Corner 1545.4 Conclusion 1605.5 References 1616. Microdrops in Microchannels and Microchambers 1636.1 Abstract 1636.2 Droplets in Micro-wells 1636.3 Droplets in Microchannels 1686.4 Conclusion 1806.5 References 1817. Capillary Effects: Capillary Rise, Capillary Pumping, and Capillary Valve 1857.1 Abstract 1857.2 Capillary Rise 1857.3 Capillary Pumping 1987.4 Capillary Valves 2057.5 Conclusions 2097.6 References 2108. Open Microfluidics 2138.1 Abstract 2138.2 Droplet Pierced by a Wire 2148.3 Liquid Spreading Between Solid Structures – Spontaneous Capillary Flow 2188.4 Liquid Wetting Fibers 2418.5 Conclusions 2508.6 References 2508.7 Appendix: Calculation of the Laplace Pressure for a Droplet on a Horizontal Cylindrical Wire 2519. Droplets, particles and Interfaces 2539.1 Abstract 2539.2 Neumann’s Construction for liquid Droplets 2539.3 The Difference Between Liquid Droplets and Rigid Spheres at an Interface 2549.4 Liquid Droplet Deposited at a Liquid Surface 2569.5 Immiscible Droplets in Contact and Engulfment 2619.6 Non-deformable (Rigid) Sphere at an Interface 2659.7 Droplet Evaporation and Capillary Assembly 2789.8 Conclusion 2919.9 References 29210. Digital Microfluidics 29510.1 Introduction 29510.2 Electrowetting and EWOD 29510.3 Droplet Manipulation with EWOD 30610.4 Examples of EWOD in Biotechnology – Cell Manipulation 33510.5 Examples of Electrowetting for Optics-Tunable Lenses and Electro fluidic Display 33710.6 Conclusion 33810.7 References 33911. Capillary Self-assembly for 3D Microelectronics 34311.1 Abstract 34311.2 Ideal Case: Total Pinning on the Chip and Pad Edges 34411.3 Real Case: Spreading and Wetting 35511.4 The Importance of Pinning and Confinement 35811.5 Conclusion 35911.6 Appendix A: Shift Energy and Restoring Force 36011.7 Appendix B: Twist Energy and Restoring Torque 36211.8 Appendix C: Lift Energy and Restoring Force 36411.9 References 36512. Epilogue 369Index 369