Transport Phenomena in Microfluidic Systems

Fully comprehensive introduction to the rapidly emerging area of micro systems technology

Transport Phenomena in Micro Systems explores the fundamentals of the new technologies related to Micro-Electro-Mechanical Systems (MEMS). It deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale, such as nl, pl, fl, small size, low energy consumption, effects of the micro domain and heat transfer in the related devices. The author describes in detail and with extensive illustration micro fabrication, channel flow, transport laws, magnetophoresis, micro scale convection and micro sensors and activators, among others. This book spans multidisciplinary fields such as material science and mechanical engineering, engineering, physics, chemistry, microtechnology and biotechnology.

• Brings together in one collection recent and emerging developments in this fast-growing area of micro systems

• Covers multidisciplinary fields such as materials science, mechanical engineering, microtechnology and biotechnology, et al

• Comprehensive coverage of analytical models in microfluidics and MEMS technology

• Introduces micro fluidics applications include the development of inkjet printheads, micro-propulsion, and micro thermal technologies

• Presented in a very logical format

• Supplies readers with problems and solutions

Autorentext

Pradipta Panigrahi is a professor and head of the Centre for Laser Technology, IIT Kanpur. He obtained his PhD in Mechanical Engineering from Louisiana State University, USA, in 1997. He was awarded a master degree at Louisiana State University in mechanical engineering in 1993 and another master in system science in the same institution in 1997. He obtained his B.Sc degree in echanical engineering at UCE Burla, Sambalpur University, India. His areas of interest include optical techniques, turbulence, hot wire anemometry, Color Schlieren and design of thermal systems. He has published over 100 international journals, books and conference proceedings on a range of subjects including digital holography, particle image velocimetry, laser interferometry, liquid crystal thermography and soft computing based flow control. He was awarded the Swarnajayanti Fellowship by the Department of Science and Technology (India) in 2006. In 1981, Dr. Panigrahi was awarded the National Scholarship.

Inhalt

About the Author xv

Preface xvii

Acknowledgement xix

List of Figures xxi

List of Tables xxxvii

1 Introduction 1

1.1 History 1

1.2 Definition 2

1.3 Analogy of Microfluidics with Computing Technology 2

1.4 Interdisciplinary Aspects of Microfluidics 3

1.5 Overall Benefits of Microdevices 6

1.6 Microscopic Scales for Liquids and Gases 10

1.7 Physics at Micrometric Scale 11

1.8 Scaling Laws 13

1.9 Shrinking of Human Beings 19

2 Channel Flow 23

2.1 Introduction 23

2.2 Hydraulic Resistance 23

2.3 Two Connected Straight Channels 24

2.4 Equivalent Circuit Theory 26

2.5 Reynolds Number 27

2.6 Governing Equation for Arbitrary-Shaped Channel 30

2.7 Summary of Hydraulic Resistance in Straight Channels 40

2.8 Viscous Dissipation of Energy 41

2.9 Compliance 45

3 Transport Laws 51

3.1 Introduction 51

3.2 Boundary Slip 51

3.3 Slip Flow Boundary Condition in Gases 52

3.4 Slip Flow Boundary Condition in Liquids 57

3.5 Physical Parameters Affecting Slip 66

3.6 Possible Liquid Slip Mechanism 67

3.7 Thermal Creep Phenomena 68

3.8 Couette Flow with Slip Flow Boundary Condition 70

3.9 Compressibility Effect in Microscale Flows 74

3.10 Slip Flow between Two Parallel Plates 78

3.11 Fluid Flow Modeling 81

4 Diffusion, Dispersion, and Mixing 101

4.1 Introduction 101

4.2 RandomWalk Model of Diffusion 101

4.3 StokesEinstein Law 103

4.4 Fick's Law of Diffusion 103

4.5 Diffusivity and Mass Transport Nomenclature 104

4.6 Governing Equation for Multicomponent System 105

4.7 Characteristic Parameters 107

4.8 Diffusion Equation 109

4.9 Taylor Dispersion 113

4.10 Micromixer 117

4.11 Convective Diffusion 123

4.12 Detailed Analysis 127

4.13 Reverse Osmosis 135

5 Surface Tension-Dominated Flows 149

5.1 Surface Tension 149

5.2 Gibbs Free Energy and Surface Tension 151

5.3 Microscopic Model of Surface Tension 151

5.4 YoungLaplace Equation 152

5.5 Contact Angle 154

5.6 Dynamic Contact Angle 156

5.7 Superhydrophobicity and Superhydrophilicity 158

5.8 Microdrops 163

5.9 Capillary Rise and Dimensionless Numbers 166

5.10 Coating Flows 169

5.11 Enhanced Oil Recovery 171

5.12 Classification of Surface Tension Gradient-Driven Flow 172

5.13 Boundary Conditions 173

5.14 Thermocapillary Motion 174

5.15 Diffusocapillary Flow 177

5.16 Electrowetting 178

5.17 Marangoni Convection in Drops 181

5.18 Marangoni Instability 182

5.19 Micropropulsion System 184

5.20 Capillary Pump 186

5.21 Thermocapillary Motion of Droplets 188

5.22 Thermocapillary Pump 189

5.23 Taylor Flows 192

5.24 Two-Phase LiquidLiquid Poiseuille Flow 197

5.25 Hydrodynamics of Taylor Flow 199

5.26 Plug Motion in Capillary 201

5.27 Clogging Pressure 203

5.28 Digital Microfluidics 206

6 Charged Species Flow 213

6.1 Introduction 213

6.2 Electrical Conductivity and Charge Transport 214

6.3 Electrohydrodynamic Transport Theory 217

6.4 Electrolytic Cell Example 220

6.5 The Electric Double Layer and Electrokinetic Phenomena 226

6.6 Debye Layer Potential Distribution 228

6.7 Electrokinetic Phenomena Classification 232

6.8 Electroosmosis 233

6.9 Exact Expression for Cylindrical Channel EO Flow 237

6.10 EO Pump 242

6.11 EO Flow in Parallel Plate Channel 249 6.12 Elect...