Interdisciplinary Applied Mathematics

larger percentage compared to the increase in flowrate of filter 1. The weak dependence of flowrate on accommodation coefficients for filter 1 can be explained by its small length-to-height ratio, which results in losses due to the flow entrance effects. However, for filter 3, with larger length-to-height ratio,    the    flowrate is    limited    by the    interaction of the    gas    with    the    walls,

and an increase in the slip velocity increases the flowrate. The large increase in the flowrate for low values of incomplete accommodation can be utilized to design more efficient filters.

6.5.4 Summary

Gas flows through microfilters and short channels show significant differences compared to the flows through long microchannels, (see Section 4.1.1). Microfilters often experience rarefaction, compressibility, and viscous heating effects simultaneously. Since typically Re < 100, the inertial and viscous forces are equally important. For example, simulations performed in the 1 < Re < 15 range have shown that the values of viscous-drag are about 50% of the form-drag. In addition, the filters have various thicknesses, cross-sectional areas, side-wall shapes, and surface roughnesses. DSMC simulations have shown strong dependence of the volumetric flowrate on the accommodation coefficients and the length-to-height ratio of the filters. Despite the diverse geometric characteristics and complicated physics of microfilter flows, the general form of the scaling laws presented in equations (6.24)-(6.26) is useful. Similar scaling models, with different coefficients determined by numerical simulations and validated by careful experiments, can be employed for further developments.

6.6 Micropropulsion and Micronozzle Flows

The development of microspacecraft by NASA was motivated by the desire to reduce launch masses, to increase launch rates, and reduce mission risk (Mueller, 1997). A microspacecraft may contain only a single instrument. If a fleet of several microspacecraft are launched instead of a single larger spacecraft, mission flexibility is greatly increased, and the loss of one or more microvehicles would not render the mission unsuccessful. The microspacecraft could also be very useful for the next generation of global positioning system and other low Earth orbit communicating systems.

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