Couette flow in a rectangular channel in the whole range of the gas rarefaction

Abstract

The mass flow rate of a Couette flow in a long rectangular channel is calculated for constant or linear wall velocities in the whole range of the gas rarefaction and in a wide range of the width-to-height ratio. Analytical solutions for arbitrary width-to-height ratios are given for the hydrodynamic regime, the slip regime, and the free molecular regime. Therefore, both the velocity field and the mass flow rate can be calculated. In the transitional regime, simulations via direct simulation Monte Carlo method are performed. The results are provided as reduced flow rates in tabulated data, which can be used for any constant or linear increasing wall velocity (e.g., bounding walls of working chambers in positive displacement vacuum pumps).