Interdisciplinary Applied Mathematics

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The experimental data of Figure 1.13 are for a relatively large pipe, but at    reduced    variable    pressure,    so    that    a    wide range of    Knudsen    numbers


is covered. However, similar trends have been observed in microchannels. Specifically, the pressure distribution along the microchannel was measured by using a surface micromachined system with a number of sensors as part of the    surface    (Liu    et    al.,    1993;    Pong    et    al.,    1994).    A    nonlinear pressure


distribution was clearly demonstrated in these experiments. Scaling of the mass flowrate with the difference of pressure squares is characteristic of


(Pin-Pout) [Pa]


FIGURE 1.14.    Variation    of    mass    flowrate    as    a    function    of    (Pin —    Pout).    Linear


pressure drop is obtained in the high Knudsen number flow regime (i.e., Kn > 17).


compressible low Reynolds number flows in long channels. To demonstrate this more clearly we replot the same data as mass flowrate versus linear pressure drop, which would be more appropriate for an incompressible pipe flow.    This is    shown    in    Figure    1.14,    where    we    see    that    in this    form there


are no particular trends or correlations, except in the free-molecular flow regime, where the pressure drop is linear, in accordance with the free-molecular flow theory, see (Kennard, 1938), p. 304.


Systematic experiments that show significant deviations from continuum behavior in microchannel flows were performed (starting in 1988) at the University of Pennsylvania (Pfahler et al., 1991). Figure 1.15 shows results from these first experiments. In particular, the ratio of Poiseuille number obtained experimentally over the Poiseuille number obtained theoretically for two different theoretical approaches is plotted. The ratio is defined as


(1.8)



400



от 100



ад


24



a Tison (NIST)






200 > Kn >17 /•»

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