Interdisciplinary Applied Mathematics

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FIGURE 5.3. Proposed experimental apparatus for studying thermal creep effects.

net mass flowrate across the channel becomes zero, and the steady solution is obtained; this is shown in Figure 5.2 (b). A single streamline passing through the    channel center    is    also    shown    in    the    plot. It is seen    that    the

fluid recirculates in the channel and there is no net flow to either tank.

This pumping effect of thermal creep has been exploited by (Sone et al., 1996b), who designed a channel with periodic ditches, similar to the grooved channel of    Figure    3.25    but    with    the    groove    present    on    both    walls.    They

imposed a periodic temperature variation, whereby the temperature decays linearly on the groove side, but it increases linearly on the channel wall. This device produces a unidirectional flow with maximum mass flowrate at Kn «    0.3,    and    it    works    both    for    channels    as    well    as pipes. While    the

original studies in (Sone et al., 1996b), were based on DSMC, subsequently an experiment    was    conducted    to    verify    the    pumping effect    (Sone    et    al.,

2001).

5.1.2 A Thermal Creep Experiment

The purpose of this experiment is to examine the importance of thermal creep effects in microchannel flows. It is based on the numerical example presented above, also in (Beskok et al., 1995), and ideas similar to Knud-sen’s experiments (Loeb, 1961), but it differs from the early experiment of (Vargo and Muntz, 1996), where porous diaphragms were used rather than microchannels.

The objective is to test the thermal creep effects in an apparatus presented schematically in Figure 5.3. It consists of two reservoirs connected through a series of microchannels made out of silicon. The typical dimensions of the microchannels should be 1 ym thick, 100 ym wide, and few millimeters long. Using a series of microchannels increases the net flow area without effectively increasing the channel area to perimeter ratio.

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