Microchannels and Nanochannels Gas Flow for the Entire Knudsen Number Domain

Abstract

This paper presents an analytical solution for steady rarefied compressible viscous gas flow in the microchannels and nanochannels with constant or slowly varying cross section. It covers both all gas rarefaction regimes (from continuum to free molecular gas flow) and all Mach number regimes (from subsonic to supersonic). The solutions for the velocity and pressure distribution in the channels is obtained by the macroscopic approach, using the one-dimensional model of continuum equations. A specially modeled friction factor is attained by an approach that includes both the general velocity slip boundary condition, and the dynamic viscosity generalized by the rarefaction correction parameter. This method spreads the application of the solution to the entire range of Knudsen numbers. Moreover, inclusion of the inertia effect into the governing equations allows the application of the solution to both subsonic and supersonic gas flows. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging and microchannels and nanochannels with constant cross section.