Interdisciplinary Applied Mathematics

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In the fourth section, we present theoretical and numerical results for Stokes flow past a sphere. We review the classical Stokes drag for external flows, and include rarefaction effects in the slip flow regime. We present drag formulas for the pressure-driven flow past a stationary sphere confined in a pipe. We verify these with numerical simulations in the slip flow regime, which shows drastic variations in the drag coefficient as a function of the Knudsen number, and the cylinder/sphere blocking ratio. The continuum flow (Kn ^ 0) results of this section are equally applicable to liquid flow past solid, electrically neutral spheres.

In the fifth part we summarize recent findings on gas flows through microfilters. Such devices are utilized for capturing and detecting airborne biological and chemical particles as well as for environmental monitoring applications.

In the last section, we consider high-speed rarefied flows in micronozzles, which are used for controlling the motion of microsatellites and nanosatellites.    Nozzles    with    a    throat    as small    as 20    pm    have    been fabricated    with

outlet Mach number exceeding four!

6.1 Gas Damping and Dynamic Response of Microsystems

The design of some MEMS devices requires good understanding of dynamic response characteristics of the system under various actuation conditions. This response can be analyzed by different methods, ranging from the most simplistic mass-spring-damper lumped analysis to the coupled interaction models, which resolve both the geometric and physical complexity of the problem (see    Section    18.2).    Since    most    of    the    MEMS    devices work    under

ambient conditions, the gas behavior can have significant effects in the dynamic response of these systems. Modeling of gas damping effects is difficult for the following reasons:

   Geometric complexity of MEMS devices,

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