A. Beskok, <STRONG>Simulations and Models for Gas Flows in
Microgeometries</STRONG>,
<CITE>Ph.D. Thesis, Princeton University</CITE>, June 1996 (2062-T).

Gas microflows are encountered in many applications of Micro-Electro-Mechanical Systems (MEMS).

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Computational modeling and simulation can provide an effective predictive capability for
energy and momentum transfer in microscales as well as means of evaluating
the performance of a new microdevice before hardware fabrication.
In the first part of the thesis, the governing equations and appropriate models for simulating gas microflows in the slip-flow
regime are presented.
The standard slip flow formulation is based on the first-order
Maxwell/Smoluchowski boundary conditions that allow partial velocity and temperature slip at the walls.
In the current work, the following tasks have been performed

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<LI> Second-order slip models with identical first-order terms to Maxwell/ Smoluchowski slip 
conditions are developed.

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<LI> Simulations of microflows in prototype geometries are performed.
Four important effects are identified: Rarefaction, compressibility, viscous heating and thermal creep.
Benchmark experiments are proposed to systematically study these effects.

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<LI> The first- and second-order slip boundary conditions are validated with comparisons against the direct
simulation Monte Carlo (DSMC) and linearized Boltzmann solutions.

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<LI> The robustness of slip models is investigated for separated flows using backwards-facing step
geometry.

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In the second  part of the thesis, rarefied
gas flows in channels and  pipes are studied over a wide range
of Knudsen number. Continuum-based simplified models for MEMS and low-pressure 
flows are developed. In particular:

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<LI> A universal scaling for the velocity distribution in channel and pipe flows for the entire Knudsen regime
is obtained.

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<LI> A single parameter unified model for the prediction of volumetric and mass flowrate in
channel and pipe flows for the entire Knudsen regime is developed. The model is validated with comparisons
against DSMC and linearized Boltzmann solutions as well as experimental results.

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