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In this log-log plot, we can easily identify three distinct flow regimes, although the corresponding values at the boundaries between the different flow regimes, are somewhat different from the aforementioned ones (Schaaf and Chambre, 1961). 6 and the transition regime up to Kn = 17. It is interesting to notice the very slow variation of mass flowrate in terms of the pressure difference in the transition regime. 13 also suggests that a nonlinear pressure drop exists in this rarefied pipe flow. This was also verified in the slip flow experiments of (Sreekanth, 1969) in pipes with a diameter of 2 inches at low pressures.

16 1. Basic Concepts and Technologies • At what scales will the statistical fluctuations be significant? It turns out that sampling a volume that contains 10,000 molecules results in 1% statistical fluctuations in the averaged quantities. 7 × 10−22 m3 . If we try to measure the macroscopic gradients (like velocity, density, and temperature) in threedimensional space, one side of our sampling volume will be about 65nm. A key nondimensional parameter for gas microflows is the Knudsen number, which is defined as the ratio of the mean free path over a characteristic geometric length or a length over which very large variations of a macroscopic quantity may take place.

We then discuss techniques of coupling DSMC with continuum descriptions, and we analyze microfilters as an example. We also include an overview of the Boltzmann equation as well as benchmark solutions in the slip flow and transitional regimes, that could be useful to the reader for validation of experimental and numerical results. Finally, we present the lattice Boltzmann method, which solves the Boltzmann equation fast but in a constrained subspace. This method too could be a very effective tool for simulating flows in complex microgeometries.

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