The accurate description of flow in nano-scale pores or channels is very
important for the reliable design of materials and processes in the areas of MEMS,
mesoporous media, and vacuum technologies. Use of classical flow equations fails in
this regime since the continuum assumption is not valid. This is due to the fact that the
mean free path is comparable to the characteristic dimensions of the system, and
rarefaction effects dominate the process. Such a difficulty arises notably in the
intermediate Knudsen number regime (Kn=0.1 to 10), commonly referred to as the
“transition” flow regime. To remedy this, slip flow conditions have been adopted in the
literature, following the simple first-order approach of the velocity near the walls given
by Maxwell, and extended to higher-order treatments. Alternatively, direct deterministic
or stochastic atomistic and mesoscopic techniques have been employed for the flow
description, which solve the Boltzmann or the Burnett equations and use kinetic theory
approaches pertinent to this flow regime. A description of recent advances in simulation
techniques, namely, the “continuum” slip approaches, and some direct mesoscopic
techniques are presented in this chapter. Illustrative simulation results of permeability
and viscosity coefficients in mesoporous media using the DSMC and LB methods are
also given, followed by comparisons with classical continuum formulations.
Keywords: Rarefied flow, porous media, transition regime, direct simulation
monte carlo, lattice-boltzmann, reconstruction, fractional brownian motion, slip
flow, nanoscale pores, knudsen number, mesoscopic methods.
