Gas Flow Through Trapezoidal Microgaps

Abstract

A generalized approach based on a model of the Boltzmann equation is suggested for predicting velocity profiles and gas flow rates through trapezoidal microgaps. Sample results are given for selected trapezoidal, rectangular, square, and circular cross section passages for Knudsen numbers ranging from 0.1 to about 10. Comparison of predicted flow rates for rectangular passages with available empirical data seems to indicate that where passage size is characterized by a single dimension, a simple across-channel measurement is inappropriate. While relative velocity profiles are independent of this value, flow rates are not. Accuracy of predictions may be enhanced by matching with analytical or empirical results for similar geometries of larger size. A flow rate from the low Knudsen number end of the transition regime is matched with one from the overlapping region of the slip-flow regime and an arbitrary adjustment is made in the characterization of passage size. This adjustment can then be incorporated into the results throughout the transition regime.