# Interdisciplinary Applied Mathematics

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A possible experimental procedure is as follows: First, both of the pressure release valves are open, and therefore, the system is in equilibrium with the ambient conditions. Then, the pressure release valves are closed. The temperature and the pressure of the system are recorded to ensure that the two reservoirs are at identical thermodynamic state. Second, the reservoirs are dipped into constant-temperature fluid baths at different temperatures T and T2. The pressure and the temperature in the reservoirs should be recorded in time. If the continuum hypothesis is valid, the pressure in the reservoirs should be unchanged. If thermal creep effects are present, the pressure in the cold reservoir should decrease, and the pressure in the hot reservoir should increase. The experiments should run until a stationary state is observed. The time scale of the experiment is directly related to the size of the reservoirs. Therefore, the reservoirs should be designed as small as possible. However, they should be large enough to maintain continuum description for the gas in them (i.e., Kn < 0.001). It is possible to increase the rarefaction effects in the experiments by performing the experiment at lower pressures than atmospheric conditions. Therefore, a systematic study of thermal creep as a function of Kn can be performed. Also, the temperature of the fluid baths can be changed from one experiment to another in order to verify the sensitivity of thermal creep to temperature gradients for a given Kn.

###### 5.1.3 Knudsen Compressors

Micromolecular compressors are useful for various microscale gas pumping applications. For example, compressors pumping gas samples through micromass spectrometers can be used to detect pollutants and various chemical or biological agents. MEMS-based thermal transpiration Knudsen compressors were proposed in (Pham-van-Diep et al., 1995), and in (Beskok et al., 1995). The idea in (Pham-van-Diep et al., 1995), is based on utilization of a cascade of multiple stages to obtain large pressure variations. Each stage consists of an array of capillaries and a connector section. The temperature increase imposed along the capillary pumps the gas from cold toward the hot direction, resulting in pressure increase in the capillary section. The gas is cooled in the connector section, and thus the temperature drops to the value corresponding to the inlet of the capillary section. This creates periodically repeatable temperature variations in each stage of the compressor. Since the pressure in the connector section drops only slightly, it is possible to have a net pressure built up with multistage units.

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