Interdisciplinary Applied Mathematics

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4    Pressure-Driven Flows    117


4.1    Slip Flow Regime…………………… 117


4.1.1    Isothermal Compressible Flows………… 118


4.1.2    Adiabatic Compressible Flows —    Fanno Theory … 126


4.1.3    Validation of Slip Models with DSMC…….. 131


4.1.4    Effects of Roughness……………… 136


4.1.5    Inlet Flows………………….. 137


4.2    Transition and Free-Molecular Regimes ……….. 140


4.2.1    Burnett Equations………………. 144


4.2.2    A Unified Flow Model…………….. 146


4.2.3    Summary…………………… 166


5    Thermal Effects in Microscales    167


5.1    Thermal Creep (Transpiration)……………. 167


5.1.1    Simulation Results………………. 169


5.1.2    A Thermal Creep Experiment…………. 173


5.1.3    Knudsen Compressors…………….. 174


5.2    Other Temperature-Induced Flows………….. 175


5.3    Heat Conduction and the Ghost Effect………… 177


5.4    Heat Transfer in Poiseuille Microflows………… 179


5.4.1    Pressure-Driven Flows…………….. 179


5.4.2    Force-Driven Flows………………. 186


5.5    Heat Transfer in Couette Microflows…………. 188


6    Prototype Applications of    Gas Flows    195


6.1 Gas Damping and Dynamic Response of Microsystems . . . 196


6.1.1    Reynolds Equation……………….199


6.1.2    Squeezed Film Effects in Accelerometers…….210


6.2    Separated Internal Flows………………..214


6.3    Separated External Flows……………….221


6.4    Flow Past a Sphere: Stokes Flow Regime………..224


6.4.1    External Flow …………………224


6.4.2    Sphere-in-a-Pipe………………..225


6.5    Microfilters………………………227


6.5.1    Drag Force Characteristics …………..232


6.5.2    Viscous Heating Characteristics…………234


6.5.3    Short Channels and Filters…………..234


6.5.4    Summary……………………239


6.6    Micropropulsion and Micronozzle Flows………..239


6.6.1    Micropropulsion Analysis……………240


6.6.2    Rarefaction and Other Effects………….245


7    Electrokinetic Flows    255


7.1    Electrokinetic Effects………………….256


7.2    The Electric Double Layer (EDL)……………258

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