Interdisciplinary Applied Mathematics

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In order to compensate for compressibility effects, we predicted the average Knudsen number in the channel by numerically integrating the density ratio variation, assuming constant temperature throughout the channel. The average Kn values and the predicted Fanning friction coefficient (fslip) are also given in Table 4.2. It is seen that the predictions overestimate the friction factor compared to the experimental values for case 1 and case 3. However, the predictions for case 2 are quite close to the experimental values. The reason for the discrepancies in the results is due to the use of theoretical (incompressible) Poiseuille number Po for calculating fslip.

The values of parameter Цу and the corresponding values for the choking length (Tchoke) are also given in Table 4.2. It is seen that slightly longer channels with the same inlet conditions would have choked the flow. Choking of the microchannels can be a significant disadvantage for applications, limiting the flowrate.

Finally, the one-dimensional theory used in this section predicts only the cross-section averaged quantities. Since the velocity, density, and pressure variations in the cross-flow direction are neglected, the current approach should be used only as a first approximation.

4.1.3 Validation of Slip Models with DSMC

In Section 4.1.1 we compared the continuum-based numerical models with existing experimental data in microflows. Although the experimental data show trends consistent with the slip flow theory, the uncertainties in the experimental measurements are relatively large, and pointwise measurements are not available with the exception of results reported in (Liu et al., 1993; Pong et    al.,    1994).    Therefore,    we    will    use    the DSMC method    (see    Section

15.1) to examine the validity of the slip models proposed in Section 2.3.

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