Micro flows : fundamentals and simulation Machine generated contents note: 1 Basic Concepts and Technologies 1 1.1 New Flow Regimes in MEMS1 1.2 The Continuum Hypothesis7 1.2.1 Molecular Magnitudes11 1.2.2 Mixed Flow Regimes16 1.2.3 Experimental Evidence17 1.3 The Pioneers21 1.4 Full System Simulation of MEMS24 1.5 Modeling of Micro Flows31 2 Governing Equations and Slip Models 39 2.1 The Basic Equations of Fluid Dynamics39 2.1.1 Incompressible Flow42 2.1.2 Reduced Models44 2.2 Compressible Flow45 2.2.1 First Order Models47 2.2.2 The Role of the Accommodation Coefficients49 2.3 High Order Models53 2.3.1 Derivation of High Order Slip Models54 2.3.2 General Slip Condition57 2.3.3 Comparison of Slip Models61 3 Shear Driven and Separated Micro Flows 63 3.1 Couette Flow63 3.2 Cavity Flow67 3.3 Grooved Channel Flow68 3.4 Separated Internal Flows71 3.4.1 Validation of Slip Models with DSMC77 3.5 Separated External Flows83 4 Pressure Driven Micro Flows: Slip Flow Regime 87 4.1 Isothermal Compressible Flows87 4.2 Adiabatic Compressible Flows Fanno Theory95 4.3 Inlet Flows101 4.4 Validation of Slip Models with DSMC102 4.5 Effects of Roughness108 5 Pressue Driven Micro Flows: Transition and Free Molecular Regimes 113 5.1 Transition and Free Molecular Flow Regimes113 5.2 Burnett Equations in Micro Channels117 5.3 A Unified Flow Model119 5.3.1 Velocity Scaling 119 5.3.2 Flowrate Scaling122 5.3.3 Model for Pipe and Duct Flows127 6 Thermal Effects in Micro Scales 139 6.1 Thermal Creep (Transpiration)139 6.1.1 Simulation Results141 6.1.2 A Thermal Creep Experiment145 6.1.3 Knudsen Compressors146 6.1.4 Other Temperature Induced Flows147 6.1.5 Heat Conduction and the Ghost Effect149 6.2 Heat Transfer in Micro Poiseuille Flows151 6.3 Heat Transfer in Micro Couette Flows158 7 Prototype Applications of Gas Micro Flows 163 7.1 Gas Damping and Dynamic Response of MEMS163 7.1.1 Reynolds Equation166 7.1.2 Squeezed Film Effects in Accelerometers173 7.2 Micro Propulsion and Micro Nozzle Flows178 7.2.1 Micro Propulsion Analysis180 7.2.2 Rarefaction and Other Effects184 8 Electrokinetically Driven Liquid Micro Flows 193 8.1 Electrokinetic Effects Review194 8.2 The Electric Double Layer195 8.3 Near Wall Potential Distribution197 8.4 Governing Equations for Electroosmotic Flows199 8.4.1 Numerical Formulation and Validation200 8.5 Electrokinetic Micro Channel Flows202 8.6 EDL Bulk Flow Interface Velocity Matching Condition207 8.7 Electroosmotic Slip Condition208 8.7.1 Approximate Evaluation of Drag Force due to Electroosmotic Effects209 8.8 Complex Geometry Flows210 8.8.1 Cross Flow Junctions211 8.8.2 Array of Circular and Square Posts213 8.9 Dielectrophoresis215 9 Numerical Methods for Continuum Simulation 223 9.1 A High Order Numerical Method: The Flow Code224 9.1.1 Formulation for Incompressible Micro Flows228 9.1.2 Formulation for Compressible Micro Flows231 9.1.3 Implementation of Slip Boundary Conditions236 9.1.4 Validation Problems237 9.2 A Meshless Numerical Method239 9.3 The Force Coupling Method for Particulate Micro Flows246 10 Numerical Methods for Atomistic Simulation 257 10.1 Molecular Dynamics (MD) Method257 10.1.1 MD Continumm Coupling263 10.2 Direct Simulation Monte Carlo (DSMC) Method266 10.2.1 Limitations and Errors in DSMC269 10.2.2 DSMC Information Preservation Method274 10.2.3 DSMC Continuum Coupling275 10.3 The Boltzmann Equation279 10.3.1 General Theory279 10.3.2 Classical Solutions of Boltzmann Equation284 10.3.3 Sones Asymptotic Theory of Boltzmann Equation288 10.3.4 Numerical Solutions of Boltzmann Equation297 10.3.5 Non Isothermal Flows301 10.4 Lattice Boltzmann Method (LBM)303 10.4.1 Comparison with Navier Stokes Solution306 10.4.2 LBM Simulation of Micro Flows308 Bibliography 311 Index 335