Interdisciplinary Applied Mathematics

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The operation regimes of typical microsystems at standard temperature and pressure are shown in Figure 1.12. MEMS devices operate in a wide range of flow regimes covering the continuum, slip, and transition flow. Further miniaturization of MEMS device components and applications in the emerging field of nano-electro-mechanical systems (NEMS) (Craighead, 2000; Ho, 2001) would result in higher Knudsen numbers, making it necessary to study mass, momentum, and energy transport in the entire Knudsen regime.

1.2.3 Experimental Evidence

An experimental illustration of the taxonomy described in Figure 1.11 is provided in Figure    1.13,    where    we    plot    data    obtained    by    S.    Tison    at    the

National Institute of Standards (NIST) (Tison, 1995) at very low pressures in a pipe    of    diameter    2a = 2 mm    (a    is    the    radius) and    length    L =    200

mm. Both inlet and outlet pressures were varied in the experiment, with

FIGURE 1.13. Variation of mass flowrate as a function of (P2n — P0ut). The data are for rarefied gas flow experiments conducted by S. Tison at NIST (Kn is based on the exit pressure).

the corresponding Knudsen number varied from almost 0 to 200. 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). In particular, the slip flow regime extends up to Kn = 0.6 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. The form of the plot in Figure 1.13 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.

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