Mesoscopic Simulation of Rarefied Flow in Narrow Channels and Porous Media

Rarefied gas flow in channels and computer-aided reconstructions of porous media is simulated using the direct simulation Monte Carlo (DSMC) method and a modified lattice-Boltzmann (LB) method that can account for rarefaction effects. An increase of two orders of magnitude was noted for the gas permeability as the Knudsen number increased from 0.1 to 10. It was found that incorporation of a Bosanquet expression for the viscosity in the dusty gas flux equations leads to the recovery of the well known Klinkenberg expression for the gas permeability, revealing an explicit relation of the, thus far empirical, permeability correction factor to the fluid and structure properties. The expression for the effective gas viscosity in the transition flow regime is also incorporated in the LB method, which is then validated against the DSMC method by comparing predictions for the velocity profiles in straight channels over the entire transition flow regime. The new LB method offers the additional advantages of simplicity in the code implementation and great savings in computational time and memory compared to the DSMC method. It is shown that the rough adjustment of a single parameter suffices to make the LB method suitable for the reliable prediction of the gas permeability in porous media over the entire transition flow regime.