Interdisciplinary Applied Mathematics

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Driven by the growing number of microsystem applications, a number of experimental studies with microchannels were conducted in the late 1980s both for gases and liquids. The first recent experimental study of microflows using micromachined channels was reported in (Pfahler et al., 1991; Harley et al., 1995), in the Reynolds number range 0.50 < Re < 20. For gases, the Knudsen number was 0.001 < Kn < 0.363 for hydraulic channel diameter DH = 8 pm and channel length 11 mm. The corresponding Mach number at the inlet was    very    small,    but at the    exit    it    reached in    some cases    the    value

M = 0.7, corresponding to substantial pressure drop. The reported skin friction reduction due to apparent slip of the flow was confirmed in other

FIGURE 1.17. Mass flowrate normalized with its free-molecular value versus Knudsen number. Gas flow in smooth capillary tubes exhibits Knudsen’s minimum around    Kn    = 1, but    crimped    tubes    do    not    exhibit    a minimum    (Tison,


similar experimental    studies    with gases    (Liu    et    al.,    1993;    Pong et    al.,    1994;

Arkilic et al., 1994) using different microfabrication techniques to make the microchannels. In particular, the paper in (Liu et al., 1993), describes the first-ever fabricated microchannel with several in situ pressure sensors as an integral part of the microchannel.

One particular set of highly accurate data, which can be used for validation of theory and simulations in microflows, was obtained by Breuer and collaborators    (Arkilic    and    Breuer,    1993;    Arkilic    et    al.,    1994;    Arkilic,

1997). A schematic of the microchannel used in the measurements is shown in Figure 1.18. It has length L = 7.5 mm, width W = 52.25 p,m, and height H = 1.33 p,m. Examination of scanning electron microscope (SEM) images showed that the height was uniform and that the roughness was below 65 nm. The    pressures    at    the    inlet    and outlet    are measured, as    well    as    the

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