Application of Navier-Stokes equations to high Knudsen number flow in a fine capillary

Abstract

Several analytical and numerical techniques to solve the Navier-Stokes equations are known making its application convenient to fluid flows. However, it is perceived that these equations cannot describe gas flow in capillaries and microchannels, due to the failure of continuum assumption at high Knudsen numbers encountered in these cases. The possibility of using the Navier-Stokes equations is explored in this paper. It is found that a slight modification to the slip coefficients to C 1= 1.3466, C 2= 0.06 can describe the flow up to a Knudsen number of four, which is well beyond the breakdown limit of the continuum hypothesis. The study opens the exciting possibility of employing the Navier-Stokes equations for a large range of Knudsen number.