# Interdisciplinary Applied Mathematics

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law can be due to the extremely small opening factor = 0.25) and large (t/h) ratio used in Motts’s studies. The simulation parameters in (Ahmed and Beskok,    2002),    were    closer to    those    of    Yang’s    experiments    than    the

values used by Mott et al.

Using the    simulation    data,    a    modified    relation    for    the scaling    law    was

developed, as shown in Figure 6.24. Since the (t/h) ratio is fixed and a finite radius of curvature at the channel inlet and exit (r/h = 0.1) are

FIGURE 6.24. Modified scaling law that fits the data from numerical simulations in (Ahmed and Beskok, 2002).

utilized, the following scaling law was obtained:

к = 2.833/Г2 ( ^ + 0.22 J .    (6.27)

For a general filter geometry, the constant 2.833 should be a function of (t/h) and (r/h). One also expects an explicit Knudsen number dependence in the model, which requires further studies beyond the slip flow regime (Kn > 0.1). Filter performance in the transition flow regime can be investigated using the DSMC method (Mott et al., 2001; Aktas et al., 2001; Aktas and Aluru, 2002), as we discuss in Section 6.5.3.

###### 6.5.1 Drag Force Characteristics

The drag force has two components: viscous- and form-drag. The viscous-drag is    due    to skin friction    distribution    on    the    body    in    the    streamwise

direction. The form-drag is due to the differences between the fore and aft pressure distributions on the body, in the streamwise direction. Due to the symmetry of    the    filter    geometry    and    steady flow,    there are    no    lift    forces.

In the    top    and bottom    plots    of    Figure    6.25,    we    plot the    slip    and    no-slip

form-drag and viscous-drag data as a function of the Reynolds number.

FIGURE 6.25. Form-drag (upper) and viscous-drag (lower) variation in microfilters as a function of the Reynolds number.

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