Interdisciplinary Applied Mathematics

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Providence, Rhode Island, USA    George Em Karniadakis


College Station, Texas, USA    Ali Beskok


Urbana, Illinois, USA    Narayan R. Aluru

Contents


Foreword by Chih-Ming Ho    v


Preface    vii


1    Basic Concepts and Technologies    1


1.1    New Flow Regimes in Microsystems …………. 1


1.2    The Continuum Hypothesis……………… 8


1.2.1    Molecular Magnitudes…………….. 13


1.2.2    Mixed Flow Regimes……………… 18


1.2.3    Experimental Evidence ……………. 19


1.3    The Pioneers…………………….. 24


1.4    Modeling of Microflows ……………….. 30


1.5    Modeling of Nanoflows………………… 34


1.6    Numerical Simulation at All Scales………….. 37


1.7    Full-System Simulation of Microsystems……….. 38


1.7.1    Reduced-Order Modeling …………… 40


1.7.2    Coupled Circuit/Device Modeling ………. 41


2    Governing    Equations and Slip Models    51


2.1    The Basic Equations of Fluid Dynamics……….. 51


2.1.1    Incompressible Flow……………… 54


2.1.2    Reduced Models……………….. 56


2.2    Compressible Flow………………….. 57


2.2.1    First-Order Models………………. 59


2.2.2    The Role of the Accommodation    Coefficients ….    61


2.3    High-Order Models………………….. 66


2.3.1    Derivation of High-Order Slip Models …….. 67


2.3.2    General Slip Condition…………….. 70


2.3.3    Comparison of Slip Models………….. 74


3    Shear-Driven Flows    79


3.1    Couette Flow: Slip Flow Regime …………… 79


3.2    Couette Flow: Transition and Free-Molecular


Flow Regimes…………………….. 83


3.2.1    Velocity Model………………… 83


3.2.2    Shear Stress Model………………. 86


3.3    Oscillatory Couette Flow ………………. 90


3.3.1    Quasi-Steady Flows ……………… 91


3.3.2    Unsteady Flows………………… 96


3.3.3    Summary…………………… 109


3.4    Cavity Flow……………………… 110


3.5    Grooved Channel Flow………………… 112

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