Interdisciplinary Applied Mathematics

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FIGURE 6.29. Slip velocity on channel walls normalized with the local mean velocity vo (line p7-p8 of Figure 6.27).

Effects of the Accommodation Coefficients

Incomplete accommodation is observed on very clean and smooth surfaces, or    for    cases in    which    the    surface    atoms are    much    heavier    than    the

gas molecules (see Section 2.2.2). Microfabrication techniques can provide methods to engineer the surface material for achieving lower accommodation coefficients. To predict the effects of incomplete accommodation, flow characteristics in microfilters are simulated using the Cercignani-Lampis model for surface scattering (see Section 15.4). For the simulations, tangential and normal energy accommodation coefficients are taken to be equal (at = an = a) and uniform on all physical surfaces (G and J in Figure 6.27). Simulations for filter 1 are performed using a = 0.75 and a = 0.5. The reduction in the accommodation coefficients results in various changes in the flow. We observe in Figure 6.29 that incomplete accommodation increases the slip velocities on channel surfaces; this is also the case on the filter membrane surface, i.e., lines p4-p9 and p5-p10 in Figure 6.27. The ratios of the slip velocity for a = 0.75 and a = 0.5 to the slip velocity for fully accommodating surfaces (a = 1) are 2.5 and 3.5, respectively.

The averge velocity obtained for filter 1 at a = 1.0, a = 0.75, and a = 0.5 are 16.2,18.0, and 19.5 m2/s), respectively. Therefore, the volumetric flowrates for a = 0.75 and a = 0.5 are 11% and 20% larger than that for the a = 1.0 case, while the average velocity obtained for filter 3 at a = 1.0, a = 0.75, and a = 0.5, are 2.59, 4.35, and 5.74 m2/s), respectively. Therefore, the volumetric flowrates for a = 0.75 and a = 0.5 are 65% and 120% larger than that for the a = 1.0 case. These results indicate that    for    a    given    value    of    a,    the    flowrate    of filter 3 increases by a    much

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