# Interdisciplinary Applied Mathematics

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1994) are also included. We see that the pressure distribution agrees with the high-order curve. The discrepancies are due to the neglected inertial terms in equation (4.9). Also included in the plot are the experimental data for nitrogen    taken from    (Pong    et    al.,    1994).    We    see    that    the trends of ex

perimental data and the simulations are qualitatively the same. They both predict smaller deviations from linear pressure drop than the corresponding no-slip flow. There are quantitative differences such as the maximum deviation location from linear pressure drop, which is at X/L « 0.4 for the experiments, and X/L « 0.55 for the simulation.

Remark: Before we end this section, we comment on the limitations of the analytic formulas given in equations (4.6) and (4.7). First, the second-order corrections to the flowrate and pressure distribution are negligible in the slip flow regime, and equivalent first-order slip formulas can be obtained by simply neglecting the Kn2 terms in these formulas. Second, derivation of these formulas is based on the additional assumptions that density and pressure across the channel at any streamwise location are constant. Thermal effects are also completely neglected. Due to these limitations the analytic formulas can be applied to low Mach number flows (typically Mo < 0.10). In our simulations we have detected density variations across the channel, especially for large pressure drop cases of nitrogen and air flows. By evaluating the relative importance of inertial terms compared to the cross flow diffusion terms ( « Rey) using the aspect ratio L/h = 20, and for the Reynolds number range reported in Table 4.1, the difference between the analytic formula predictions and the solution of full Navier-Stokes equations is approximately 20%. Finally, we also note that entrance effects for pressure-driven flows, e.g., through microfilters and short channels, are addressed in Section 6.5.

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