1 Basic Concepts and Technologies 2

1.1 New Flow Regimes in MEMS 2

1.2 The Continuum Hypothesis 8

1.2.1 Molecular Magnitudes 12

1.2.2 Mixed Flow Regimes 17

1.2.3 Experimental Evidence 18

1.3 The Pioneers 22

1.4 Full-System Simulation of MEMS 25

1.5 Modeling of Micro Flows 32

2 Governing Equations and Slip Models 39

2.1 The Basic Equations of Fluid Dynamics 39

2.1.1 Incompressible Flow 42

2.1.2 Reduced Models 44

2.2 Compressible Flow 45

2.2.1 First-Order Models 47

2.2.2 The Role of the Accommodation CoeÆcients 49

2.3 High-Order Models 53

2.3.1 Derivation of High-Order Slip Models 54

2.3.2 General Slip Condition 57

2.3.3 Comparison of Slip Models 60

3 Shear-Driven and Separated Micro Flows 63

3.1 Couette Flow 63

3.2 Cavity Flow 67

3.3 Grooved Channel Flow 69

3.4 Separated Internal Flows 71

3.4.1 Validation of Slip Models with DSMC 77

3.5 Separated External Flows 83

4 Pressure-Driven Micro Flows: Slip Flow Regime 87

4.1 Isothermal Compressible Flows 87

4.2 Adiabatic Compressible Flows - Fanno Theory 95

4.3 Inlet Flows 101

4.4 Validation of Slip Models with DSMC 102

4.5 Effects of Roughness 109

5 Pressure-Driven Micro Flows: Transition and Free-Molecular Regimes 112

5.1 Transition and Free-Molecular Flow Regimes 112

5.2 Burnett Equations in Micro Channels 116

5.3 A Unified Flow Model 118

5.3.1 Velocity Scaling 118

5.3.2 Flowrate Scaling 121

5.3.3 Model for Pipe and Duct Flows 126

6 Thermal Effects in Micro Scales 138

6.1 Thermal Creep (Transpiration) 138

6.1.1 Simulation Results 140

6.1.2 A Thermal Creep Experiment 144

6.1.3 Knudsen Compressors 145

6.1.4 Other Temperature-Induced Flows 146

6.1.5 Heat Conduction and the Ghost Effect 148

6.2 Heat Transfer in Micro Poiseuille Flows 150

6.3 Heat Transfer in Micro Couette Flows 157

7 Prototype Applications of Gas Micro Flows 162

7.1 Gas Damping and Dynamic Response of MEMS 162

7.1.1 Reynolds Equation 165

7.1.2 Squeezed Film Effects in Accelerometers 172

7.2 Micro Propulsion and Micro Nozzle Flows 177

7.2.1 Micro Propulsion Analysis 179

7.2.2 Rarefaction and Other Effects 184

8 Electrokinetically-Driven Liquid Micro Flows 191

8.1 Electrokinetic Effects - Review 192

8.2 The Electric Double Layer 193

8.3 Near-Wall Potential Distribution 195

8.4 Governing Equations for Electro-osmotic Flows 197

8.4.1 Numerical Formulation and Validation 198

8.5 Electrokinetic Micro Channel Flows 200

8.6 Electro-osmotic Slip Velocity 205

8.7 Complex Geometry Flows 207

8.7.1 Cross-Flow Junctions 208

8.7.2 Array of Circular and Square Posts 210

8.8 Dielectrophoresis 213

9 Numerical Methods for Continuum Simulation 219

9.1 A High-Order Numerical Method: The mu-Flow Code 220

9.1.1 Formulation for Incompressible Micro Flows 224

9.1.2 Formulation for Compressible Micro Flows 227

9.1.3 Implementation of Slip Boundary Conditions 232

9.1.4 Validation Problems 233

9.2 A Meshless Numerical Method 235

9.3 The Force Coupling Method for Particulate Micro Flows 242

10 Numerical Methods for Atomistic Simulation 252

10.1 Molecular Dynamics (MD) Method 252

10.1.1 MD-Continuum Coupling 258

10.2 Direct Simulation Monte Carlo (DSMC) Method 261

10.2.1 Limitations and Errors in DSMC 264

10.2.2 DSMC-Information Preservation Method 269

10.2.3 DSMC-Continuum Coupling 270

10.3 The Boltzmann Equation 274

10.3.1 General Theory 274

10.3.2 Classical Solutions of Boltzmann Equation 279

10.3.3 Sone's Asymptotic Theory of Boltzmann Equation 283

10.3.4 Numerical Solutions of Boltzmann Equation 292

10.3.5 Non-Isothermal Flows 296

10.4 Lattice-Boltzmann Method (LBM) 298

10.4.1 Comparison with Navier-Stokes Solutions 301

10.4.2 LBM Simulation of Micro Flows 303

Bibliography 305

Index 329