# Interdisciplinary Applied Mathematics

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temperature of a small tank where the mass is accumulated. One set of measurements for argon flow is shown in Figure 1.19; plotted is the mass flowrate versus the inlet-to-outlet pressure ratio. The exhaust pressure was kept at 101 kPa. Theoretical predictions based on no-slip and slip theory are also included in the plot, and they reveal a clear rarefaction effect. These measurements have been used by Breuer and collaborators (Arkilic et al., 1994) to obtain values of tangential momentum accommodation coefficients

FIGURE 1.18. Schematic of the channel used in high resolution measurements of mass flowrate (Arkilic, 1997). The channel height is H and the channel length is L. This is a dual-tank accumulation technique, coupled to high precision control of temperature and pressure fluctuations in the system. (Courtesy of K. Breuer.)

in silicon    microchannels    (see    Section    2.2.2    for    the    details).    The    resolution

of this mass flow system is down to 10~12 kg/sec. The system has also good rejection of common-mode noise (usually due to microthermal fluctuations in the testing environment) and can be adapted to measure mass flows at any range with any working fluid, including liquids.

An important and exciting result on the experimental side has been the development of techniques that can measure velocity profiles accurately in microchannels, e.g., using micro-particle-image velocimetry (microPIV) (Meinhart et al., 1999; Santiago et al., 1998). In Figure 1.20 we plot such measurements in a 30 p,m x300 p,m channel for Stokes flow (Meinhart et al., 1999). The two-dimensional velocity field is measured using micron resolution PIV. The spatial resolution, defined by the size of the first interrogation window, is 13.8 p,m x0.9 p,m. A 50% overlap between the interrogation spots yields a velocity vector spacing of 450 nm in the wall-normal direction near the wall. This high spatial resolution is made possible by using relatively low particle concentrations in the flow, and by incorporating a specialized interrogation algorithm to increase the signal to noise ratio. This algorithm averages in time a series of particle image correlation functions, and searches the time-averaged correlation function to determine the location of the displacement signal peak (Meinhart et al., 2000).

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