Interdisciplinary Applied Mathematics

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Large-scale Knudsen compressors have low volumetric flowrate and inefficient energy usage; however, their microscale counterparts eliminate these disadvantages and result in low-power gas-pumping systems with nonmov-

ing components. (Vargo et al., 1998) built a microvacuum pump delivering 5 x 1014 molecules per second with a pump volume of 0.16 mL at inlet pressure of 10 mTorr and power input of 28.5 mW. Another micro pump with the same flowrate was built to operate at 1 mTorr. It required a volume of 13.9 mL and power input of 2.4 W. A tenfold decrease in the inlet pressure resulted in almost a hundred times increase in the power input and the volume of the    system.    The    flow in    the    capillary    section    of    the    Knud-

sen compressor is in transition or free-molecular flow regime, and thus the capillary radius is small, and thermal transpiration effects are dominant in this section. However, the dimensions of the connector section are considerably larger than the local mean free path, so that slip or continuum flow is present in this section. In the compressor built by Vargo et al., the capillary and the connector radii were 0.225 p,m and 10.795 mm, respectively. The bottleneck in the design of a Knudsen compressor is usually in determining the dimensions of the connector section, which becomes a limitation for low-pressure applications where the mean free path is already quite large.

In the experiments of Vargo et al., the maximum temperature variation in one stage of the compressor was about 20 to 30 K, with average temperature of 282 K. The inlet pressure and the working gas were varied. Good device performance for pressures as low as 1 mTorr was reported. Finally, Vargo et al. have developed a numerical model for predicting flowrate and pressure buildup in Knudsen compressors operating in the transition flow regime. The numerical predictions were validated using the experimental data, and the new algorithm was employed to study compressor performance under various flow conditions.

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