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The Physics of Microdroplets

Book Description

The Physics of Microdroplets gives the reader the theoretical and numerical tools to understand, explain, calculate, and predict the often nonintuitive observed behavior of droplets in microsystems.

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 behavior 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.

After a chapter dedicated to the general theory of wetting, this practical book successively details:

  • The theory of 3D liquid interfaces

  • The formulas for volume and surface of sessile and pancake droplets

  • The behavior of sessile droplets

  • The behavior of droplets between tapered plates and in wedges

  • The behavior of droplets in microchannels

  • The effect of capillarity with the analysis of capillary rise

  • The onset of spontaneous capillary flow in open microfluidic systems

  • The interaction between droplets, like engulfment

  • The theory and application of electrowetting

The state of the art for the approach of 3D-microelectronics using capillary alignment

Table of Contents

  1. Cover
  2. Half Title page
  3. Title page
  4. Copyright page
  5. Acknowledgements
  6. Preface
  7. Introduction
    1. From Conventional Single-phase Microfluidics to Droplets and Digital Microfluidics
    2. Domains of Application
    3. Organization of the Book
    4. References
  8. Chapter 1: Fundamentals of Capillarity
    1. 1.1 Abstract
    2. 1.2 Interfaces and Surface Tension
    3. 1.3 Laplace’s Law and Applications
    4. 1.4 Measuring the Surface Tension of Liquids
    5. 1.5 Minimization of the Surface Energy and Minimal Surfaces
    6. 1.6 References
  9. Chapter 2: Minimal Energy and Stability Rubrics
    1. 2.1 Abstract
    2. 2.2 Spherical Shapes as Energy Minimizers
    3. 2.3 Symmetrization and the Rouloids
    4. 2.4 Increasing Pressure and Stability
    5. 2.5 The Double-Bubble Instability
    6. 2.6 Conclusion
    7. 2.7 References
  10. Chapter 3: Droplets: Shape, Surface and Volume
    1. 3.1 Abstract
    2. 3.2 The Shape of Micro-drops
    3. 3.3 Electric Bond Number
    4. 3.4 Shape, Surface Area and Volume of Sessile Droplets
    5. 3.5 Conclusion
    6. 3.6 References
  11. Chapter 4: Sessile Droplets
    1. 4.1 Abstract
    2. 4.2 Droplet Self-motion Under the Effect of a Contrast or Gradient of Wettability
    3. 4.3 Contact Angle Hysteresis
    4. 4.4 Pinning and Canthotaxis
    5. 4.5 Sessile Droplet on a Non-ideally Planar Surface
    6. 4.6 Droplet on Textured or Patterned Substrates
    7. 4.7 References
  12. Chapter 5: Droplets Between Two Non-parallel Planes: From Tapered Planes to Wedges
    1. 5.1 Abstract
    2. 5.2 Droplet Self-motion Between Two Non-parallel Planes
    3. 5.3 Droplet in a Corner
    4. 5.4 Conclusion
    5. 5.5 References
  13. Chapter 6: Microdrops in Microchannels and Microchambers
    1. 6.1 Abstract
    2. 6.2 Droplets in Micro-wells
    3. 6.3 Droplets in Microchannels
    4. 6.4 Conclusion
    5. 6.5 References
  14. Chapter 7: Capillary Effects: Capillary Rise, Capillary Pumping, and Capillary Valve
    1. 7.1 Abstract
    2. 7.2 Capillary Rise
    3. 7.3 Capillary Pumping
    4. 7.4 Capillary Valves
    5. 7.5 Conclusions
    6. 7.6 References
  15. Chapter 8: Open Microfluidics
    1. 8.1 Abstract
    2. 8.2 Droplet Pierced by a Wire
    3. 8.3 Liquid Spreading Between Solid Structures – Spontaneous Capillary Flow
    4. 8.4 Liquid Wetting Fibers
    5. 8.5 Conclusions
    6. 8.6 References
    7. 8.7 Appendix: Calculation of the Laplace Pressure for a Droplet on a Horizontal Cylindrical Wire
  16. Chapter 9: Droplets, Particles and Interfaces
    1. 9.1 Abstract
    2. 9.2 Neumann’s Construction for Liquid Droplets
    3. 9.3 The Difference Between Liquid Droplets and Rigid Spheres at an Interface
    4. 9.4 Liquid Droplet Deposited at a Liquid Surface
    5. 9.5 Immiscible Droplets in Contact and Engulfment
    6. 9.6 Non-deformable (Rigid) Sphere at an Interface
    7. 9.7 Droplet Evaporation and Capillary Assembly
    8. 9.8 Conclusion
    9. 9.9 References
  17. Chapter 10: Digital Microfluidics
    1. 10.1 Abstract
    2. 10.2 Electrowetting and EWOD
    3. 10.3 Droplet Manipulation with EWOD
    4. 10.4 Examples of EWOD in Biotechnology – Cell Manipulation
    5. 10.5 Examples of Electrowetting for Optics – Tunable Lenses and Electrofluidic Display
    6. 10.6 Conclusion
    7. 10.7 References
  18. Chapter 11: Capillary Self-assembly for 3D Microelectronics
    1. 11.1 Abstract
    2. 11.2 Ideal Case: Total Pinning on the Chip and Pad Edges
    3. 11.3 Real Case: Spreading and Wetting
    4. 11.4 The Importance of Pinning and Confinement
    5. 11.5 Conclusion
    6. 11.6 Appendix A: Shift Energy and Restoring Force
    7. 11.7 Appendix B: Twist Energy and Restoring Torque
    8. 11.8 Appendix C: Lift Energy and Restoring Force
    9. 11.9 References
  19. Chapter 12: Epilogue
  20. Index