Extended Navier-Stokes Equations and Treatments of Micro-Channel Gas Flows

Abstract

Gas flows in micro-channels are, in general, theoretically treated with the Maxwell slip velocity as a boundary condition for the convection velocity at the wall. It is pointed out that wall slip is conventionally introduced in theoretical/numerical treatments of gas flows through micro-channels to obtain agreement with experimental results. In the present paper, we provide an alternative by solving the extended Navier-Stokes equations for compressible gas flows in micro-channels using the conventional no-slip velocity boundary condition for the convection velocity. Results obtained with this approach are presented and compared with experiments. It is also shown that the theoretical treatment of micro-channel gas flows using the “extended Navier-Stokes equations” also permits the phenomena such as the Knudsen paradox, to be treated in an analytical manner. Comparison with experimental data suggests that the derived analytical solution has excellent agreement up to Knudsen number of approximately 1, which shows the validity of extended Navier-Stokes equations with the conventional no-slip velocity boundary condition up to the early transition regime of micro-channel gas flows.

Keywords

• micro-channel gas flow
• self-mass diffusion
• knudsen paradox
• slip boundary condition