# Interdisciplinary Applied Mathematics

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(Mott et al., 2001) employed two-dimensional DSMC to study gas transport through microfilters in the slip and early transition flow regimes. They have shown that Yang’s model becomes inaccurate in the transition flow regime and also for high Reynolds number flows. Based on the experimental data of (Yang et al., 2001) and their DSMC results, (Mott et al., 2001) proposed the following modified scaling law, which includes the Knudsen number as an additional parameter:

K-r2 (3-4 + 3) (S+022

0.0577 0.0577+ Kn

(6.26)

The assumptions and parameters in their model were:

1.    2-D geometry,

2.    Opening factor; в = 0.25,

3.    t/h ratio: 3,

4. Reynolds number; 0. 2 < Re < 1 ,

5. Knudsen number; 0.0309 < Kn < 0.233.

It is noteworthy to mention that the t/h ratio used in Mott’s studies was substantially larger than the values presented in (Yang et al., 1999b; Yang et al., 2001).

The scaling laws presented in equations (6.24)-(6.25) are developed starting from the fully developed Poiseuille flow assumption with added pressure

FIGURE 6.22.    Left:    Schematic    view    of    the    microfilter    (filter    front    and

cross-sectional views). Right: Schematic view of a simplified two-dimensional filter model. Various length scales are identified in the figure.

drop corrections    due    to    the    inlet    and    exit    effects.    (Mott et    al.,    2001)    de

scribe the evolution of these scaling laws, including the slip flow corrections given as a function of the Knudsen number in equation (6.26). The coefficients used in equations (6.24)-(6.26) are modified from the predictions given by simplified analytical models in order to match the experimental and numerical    data    (Yang    et    al.,    1999b;    Yang et    al.,    2001; Mott et    al.,

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