Upper and Lower Bounds on Knudsen Flow Rates

Abstract

Reciprocal variational principles are used to formulate upper and lower bounds on the low-pressure (Knudsen) flow rate of a gas through a channel of arbitrary geometry. The upper bound is equivalent to one obtained earlier by DeMarcus, but we believe the lower bound to be new. Explicit calculations are given for a short parallel-plate channel. The variational principles discussed here may be applied to a wide range of problems involving linear inhomogeneous integral equations.