Extending the Navier–Stokes solutions to transition regime in two-dimensional micro- and nanochannel flows using information preservation scheme

Abstract

The kinetic-theory-based numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier–Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as Knudsen number approaches the upper bound. One remedy is to consider the rarefaction effects in calculating the NS viscosity coefficient. In this work, we use the shear stress distribution derived from our IP simulations, extend an analytical expression for the viscosity coefficient, impose it in the NS equations, and evaluate it via solving the transition regime. Using the new viscosity coefficient, we also derive an analytical expression for the mass flow rate, which provides accurate solutions for Kn<0.5 and even beyond in micro- and nanochannel flows. We also show that the obtained streamwise pressure distribution agrees well with that of the DSMC-IP in this range. The current study is concerned with low speed diatomic gas flow through two-dimensional micro- and nanochannels.