Interdisciplinary Applied Mathematics

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In the following we present a brief overview of the material covered in each chapter.


In Chapter 1 we provide highlights of the many concepts and devices that we will discuss in detail in the subsequent chapters. For historic reasons, we start with some prototype Micro-Electro-Mechanical-Systems (MEMS) devices and discuss such fundamental concepts as breakdown of constitutive laws, new flow regimes, and modeling issues encountered in microfluidic and nanofluidic systems. We also address the question of full-system simulation of microsystems and introduce the concept of macromodeling.


In Chapter 2 we first present the basic equations of fluid dynamics for both incompressible and compressible flows, and discuss appropriate nondi-mensionalizations. Subsequently, we consider the compressible Navier-Stok-es equations and develop a general boundary condition for velocity slip. The validity of this model is assessed in subsequent chapters.


In Chapter 3 we consider shear-driven gas flows with the objective of modeling several microsystem components. In order to circumvent the difficulty of understanding the flow physics for complex engineering geometries, we concentrate on prototype flows such as the linear and oscillatory Couette flows in the slip, transition, and free-molecular flow regimes, and flow in shear-driven microcavities and microgrooves.


In Chapter 4 we present pressure-driven gas flows in the slip, transition and free molecular flow regimes. In the slip flow regime, we first validate simulation results based on compressible Navier-Stokes solutions employing various slip models introduced in Chapter 2. In addition, we examine the accuracy of the one-dimensional Fanno theory for microchannel flows, and we study inlet flows and effects of roughness. In the transition and free-molecular regime we develop a unified model for predicting the velocity

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