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The Physics of Microdroplets

By Jean Berthier and Kenneth A. Brakke
Copyright: 2012   |   Status: Published
ISBN: 9780470938805  |  Hardcover  |  
390 pages | 471 color illustrations
Price: $154 USD
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One Line Description
This book brings a unique approach to understand, calculate and predict the behaviour of droplets and interfaces in modern microsystems.

The core market for this book is scientists and researchers in biotechnology, biology, bioengineering, and materials science.
In addiiton, engineers and scientists involved in 3D microelectronics, optofluidics, and mechatronics, will find much value in the book.

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 nonintuitive, 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,
*presents the theory and application of electrowetting.

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Author / Editor Details
Jean Berthier is a scientist at the CEA/LETI and teaches at the University of Grenoble. He received an engineering diploma from the Institut National Polytechnique, and an MS in mathematics from 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 first published by 2005 with a second edition in 2010. He is also the author of the book Microdrops and Digital Microfluidics published in 2008.

Kenneth 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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Table of Contents
Preface. Introduction
1 Fundamentals of Capillarity
1.1 Abstract
1.2 Interfaces and Surface Tension
1.2.1 The Notion of Interface
1.2.2 The Effect of Temperature on Surface Tension
1.2.3 The Effect of Surfactants
1.2.4 Surface Tension of a Fluid Containing Particles
1.3 Laplace�s Law and Applications
1.3.1 Curvature and Radius of Curvature
1.3.2 Derivation of Laplace�s Law
1.3.3 Examples of Application of Laplace�s Law
1.3.4 Wetting - Partial or Total Wetting
1.3.5 Contact Angle - Young�s Law
1.3.6 Work of Adhesion, Work of Cohesion and the Young-Dupr� Equation
1.3.7 Capillary Force, Force on a Triple Line
1.4 Measuring the Surface Tension of Liquids
1.4.1 Using Pressure (Bubble Pressure Method)
1.4.2 Using Gravity: the Pendant Drop Method
1.4.3 Surface Free Energy
1.5 Minimization of the Surface Energy and Minimal Surfaces
1.5.1 Minimization of the Surface Energy
1.5.2 Conclusion
1.6 References
2 Minimal Energy and Stability Rubrics
2.1 Abstract
2.2 Spherical Shapes as Energy Minimizers
2.3 Symmetrization and the Rouloids
2.3.1 Steiner Symmetrization
2.3.2 Rouloids
2.3.3 Rouloid Summary
2.4 Increasing Pressure and Stability
2.4.1 Wedge
2.4.2 In a Square
2.4.3 Round Well
2.4.4 Square Well
2.5 The Double-Bubble Instability
2.5.1 Conditions for the Double-bubble Instability
2.5.2 Plateau-Rayleigh Instability
2.5.3 Plateau-Rayleigh Instability in Corners and Grooves
2.5.4 Instability of a Cylinder on a Hydrophilic Strip
2.5.5 Double-bubble Instability in Bulging Liquid Bridge
2.5.6 Lower-pressure Comparison Theorem
2.6 Conclusion
2.7 References
3 Droplets: Shape, Surface and Volume
3.1 Abstract
3.2 The Shape of Micro-drops
3.2.1 Sessile Droplets � the Bond Number
3.3 Electric Bond Number
3.4 Shape, Surface Area and Volume of Sessile Droplets
3.4.1 Height of a �Large� Droplet
3.4.2 Microscopic Drops
3.4.3 Droplets Between Two Parallel Plates
3.4.4 Shape of a Droplet Flattened Between Two Horizontal Planes
3.4.5 Curvature Radius of the Free Interface
3.4.6 Convex Droplet Shape
3.4.7 Volume of a Droplet Flattened by Two Horizontal Planes with Different Contact Angles with the Two Planes (Convex Case)
3.4.8 Surface Area (Convex Case)
3.4.9 Concave Droplet Shape
3.5 Conclusion
3.6 References
4 Sessile Droplets
4.1 Abstract
4.2 Droplet Self-motion Under the Effect of a Contrast or Gradient of Wettability
4.2.1 Drop Moving Over a Sharp Transition of Wettability
4.2.2 Drop Moving Uphill
4.2.3 Dynamic and Quasi-static Approach
4.2.4 Drop Moving Up a Step
4.2.5 Drop Moving Over a Gradient of Surface Concentration of Surfactant
4.2.6 Conclusion
4.3 Contact Angle Hysteresis
4.4 Pinning and Canthotaxis
4.4.1 Droplet Pinning on a Surface Defect
4.4.2 Droplet Pinning on an Edge � Canthotaxis
4.4.3 Droplet Pinning at a Wettability Separation Line
4.4.4 Pinning of an Interface by Pillars
4.5 Sessile Droplet on a Non-ideally Planar Surface
4.6 Droplet on Textured or Patterned Substrates
4.6.1 Wenzel�s Law
4.6.2 Cassie-Baxter Law
4.6.3 Contact on Microfabricated Surfaces: the Transition Between the Wen-zel and Cassie Laws
4.7 References
5 Droplets Between Two Non-parallel Planes: From Tapered Planes to Wedges
5.1 Abstract
5.2 Droplet Self-motion Between Two Non-parallel Planes
5.2.1 Identical Young Contact Angle with Both Plates
5.2.2 Different Young Contact Angles
5.2.3 Numerical Simulation � 2D and 3D Cases
5.2.4 A Reciprocal to the Hauksbee Problem
5.2.5 Example of Tapered System for Passive Pumping in Fuel Cells
5.2.6 Discussion
5.3 Droplet in a Corner
5.3.1 Dimensions of the Droplet and Effect of Gravity
5.3.2 Concus-Finn Relations
5.3.3 Numerical Approach
5.3.4 Example of a Liquid in a Micro-beaker
5.3.5 Extended Concus-Finn Relation
5.3.6 Droplet in a Wetting/Non-wetting Corner
5.3.7 Discussion
5.4 Conclusion
5.5 References
6 Microdrops in Microchannels and Microchambers
6.1 Abstract
6.2 Droplets in Micro-wells
6.2.1 Shape of the Liquid Surface in a Micro-well
6.2.2 Evaporation of Liquid in a Micro-well
6.2.3 Filling a Micro-well
6.3 Droplets in Microchannels
6.3.1 Capillary, Weber and Bond Numbers
6.3.2 Non-wetting Droplets and Plugs
6.3.3 Wetting Droplets and Plugs
6.3.4 Trains of Droplets � Compound Droplets
6.4 Conclusion
6.5 References
7 Capillary Effects: Capillary Rise, Capillary Pumping, and Capillary Valve
7.1 Abstract
7.2 Capillary Rise
7.2.1 Cylindrical Tubes: Jurin�s Law
7.2.2 Capillary Rise in Square Tubes
7.2.3 Capillary Rise on a Vertical Plate � Surface Tension Measurement by the Wilhelmy Method
7.2.4 Capillary Rise Between Two Parallel Vertical Plates
7.2.5 Capillary Rise in a Dihedral
7.2.6 Capillary Rise in an Array of Four Vertical Square Pillars
7.2.7 Comparison of Capillary Rise Between Wilhelmy Plate and Pillars
7.2.8 Oblique Tubes � Capillary Rise in a Pipette
7.3 Capillary Pumping
7.3.1 Principles of Capillary Pumping
7.3.2 Capillary Pumping and Channel Dimensions
7.3.3 The Dynamics of capillary Pumping: Horizontal Microchannel
7.3.4 The Dynamics of Capillary Pumping: General
7.3.5 Examples of Capillary Pumping
7.4 Capillary Valves
7.4.1 Principles of Capillary Valves
7.4.2 Valving Efficiency and Shape of the Orifice
7.4.3 Examples of Capillary Valves in Microsystems Stop Valve
7.4.4 Delay Valves5
7.5 Conclusions
7.6 References
8 Open Microfluidics
8.1 Abstract
8.2 Droplet Pierced by a Wire
8.2.1 Suspended Droplet
8.2.2 Small Droplet
8.2.3 Effect of Gravity on Small Droplets
8.2.4 Large Droplet
8.2.5 Sessile Droplet Pierced by a Wire
8.3 Liquid Spreading Between Solid Structures � Spontaneous Capillary Flow
8.3.1 Parallel Rails
8.3.2 Spontaneous Capillary Flow Between Parallel Rails
8.3.3 Spontaneous Capillary Flow in U-grooves
8.3.4 Spontaneous Capillary Flow in Asymmetric U-grooves � Spreading of Liquid Glue During Microfabrication
8.3.5 Spontaneous Capillary Flow in a Trapezoidal Channel
8.3.6 Spontaneous Capillary Flow in a Half-pipe
8.3.7 A Universal Law for Capillary Pumping
8.3.8 Spontaneous Capillary Flows in Cracks
8.3.9 Spontaneous Capillary Flow Triggered by a V-groove
8.3.10 Anisotropic Superhydrophilicity
8.3.11 Spontaneous Capillary Flow in Diverging U-grooves
8.3.12 Spontaneous Capillary Flow in Diverging-converging U-grooves
8.3.13 Capillary Flow Over a Hole
8.3.14 Suspended Microfluidics
8.3.15 Application to Droplet Dispensing in EWOD/LDEP Systems
8.3.16 Restriction of the Theory in the Case of Rounded Corners
8.4 Liquid Wetting Fibers
8.4.1 Droplet Between Parallel Fibers 0
8.4.2 Intersecting Fibers
8.4.3 Wicking in a Bundle of Fibers
8.4.4 Total Impregnation � Imbibition
8.4.5 Washburn�s Law
8.4.6 Fully Wetted Flow � Darcy�s Law
8.4.7 Paper-based Microfluidics
8.4.8 Thread-based Microfluidics
8.5 Conclusions
8.6 References
8.7 Appendix: Calculation of the Laplace Pressure for a Droplet on a Horizontal Cylindrical Wire
9 Droplets, Particles and Interfaces
9.1 Abstract
9.2 Neumann�s Construction for Liquid Droplets
9.3 The Difference Between Liquid Droplets and Rigid Spheres at an Interface
9.4 Liquid Droplet Deposited at a Liquid Surface
9.4.1 Introduction
9.4.2 Liquid Droplet Crossing an Interface
9.5 Immiscible Droplets in Contact and Engulfment
9.5.1 Introduction
9.5.2 Physical Analysis
9.5.3 Numerical Approach
9.5.4 Total Engulfment
9.6 Non-deformable (Rigid) Sphere at an Interface
9.6.1 Introduction
9.6.2 Capillary Problem� No Body-force
9.6.3 Body-force: Gravity
9.6.4 The Cases of Nearly Rigid Spheres
9.6.5 Rigid Spheres Attached to a Meniscus
9.6.6 Droplet Attached to a Solid Sphere
9.6.7 Body Force: Magnetic Force
9.7 Droplet Evaporation and Capillary Assembly
9.7.1 Introduction
9.7.2 Evaporation Rings
9.7.3 Evaporation Stains
9.7.4 The Use of Evaporation and Capillary Assembly
9.8 Conclusion
9.9 References
10 Digital Microfluidics
10.1 Abstract
10.2 Electrowetting and EWOD
10.2.1 Berge-Lippmann-Young Equation (BLY)
10.2.2 Electrowetting Force
10.2.3 Limitations of EWOD � Saturation, Dielectric Breakdown and Hysteresis
10.3 Droplet Manipulation with EWOD
10.3.1 Open vs. Covered EWOD System
10.3.2 Droplet Motion
10.3.3 Moving Droplet Velocity
10.3.4 Droplet Merging and Division
10.3.5 Droplet Dispensing
10.3.6 Coupling Between Covered and Open EWOD Systems
10.3.7 Special Electrodes � Jagged Electrodes and Star-shaped Electrodes
10.3.8 General EWOD Architecture
10.4 Examples of EWOD in Biotechnology � Cell Manipulation
10.4.1 DEP and EWOD
10.4.2 EWOD and OET
10.4.3 EWOD and Magnetic Beads
10.5 Examples of Electrowetting for Optics � Tunable Lenses and Electrofluidic Display
10.5.1 Tunable Lens
10.5.2 Electrowetting Display
10.6 Conclusion
10.7 References
11 Capillary Self-assembly for 3D Microelectronics
11.1 Abstract
11.1.1 Introduction to Self-assembly
11.1.2 Three-dimensional Assembly of Silicon Chips on a Wafer
11.2 Ideal Case: Total Pinning on the Chip and Pad Edges
11.2.1 First Mode: Horizontal Displacement (Shift)
11.2.2 Second Mode: Rotation Around z-axis (Twist)
11.2.3 Third Mode: Vertical Displacement (Lift)
11.2.4 Fourth Mode: Tilt (or Roll)
11.2.5 Coupled Modes
11.3 Real Case: Spreading and Wetting
11.4 The Importance of Pinning and Confinement
11.5 Conclusion
11.6 Appendix A: Shift Energy and Restoring Force
11.7 Appendix B: Twist Energy and Restoring Torque
11.8 Appendix C: Lift Energy and Restoring Force
11.9 References
12 Epilogue

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TCB: Biotechnology
TGM: Materials Science
PSB: Biochemistry

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Author/Editor Details
Table of Contents
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