# Interdisciplinary Applied Mathematics

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The geometric complexity of microfilters is very important. In the simplest form, the microfilters are very short channels or sudden constrictions in the    flow    field.    Therefore, simple    analysis    based    on    the    fully    developed

flow assumption    cannot    be    used.    Furthermore,    the    filter    holes    have    com

plicated shapes, such as rectangular, hexagonal, circular, elliptic, or square cross-sections. The filters may also have geometric variations along the filter thickness, sharp or smooth inlets and exits. For example, the side-wall geometry is shown to affect the overall pressure drop across the microfilter devices (Yang et al., 2001).

Empirical formulas for pressure drop in conventional filters were obtained in earlier studies (Weighardt, 1953; Derbunovich et al., 1998). However, these scaling laws were valid for high Reynolds number flows (Re ^ 100), and they cannot be applied to microfilters (Yang et al., 2001). The initial work on microfilters was done by (Kittilsland et al., 1990), who fabricated a filter that consisted of two silicon membranes with holes. By changing the membrane separation distance, they were able to build filters for separation of particles as small as 50 nm. Later, (Yang et al., 1999b) developed a MEMS-based microfilter using a micron-thick silicon-nitride membrane coated with    Parylene,    which    was    used    both    to    control    the    opening area

of the filter and to provide strength. Experimental and numerical studies have shown that the flow in the microfilters depends strongly on the opening factor в (the ratio of the hole area to the total filter area). The power requirements and the pressure drop through the microfilters have also been studied in (Yang et al., 1999b). It has been shown that

• the power dissipation is a function of the opening factor, the ratio of the filter thickness to hole diameter, and the Reynolds number.

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