Lattice Boltzmann Flow Simulation in Micro-Nano Transitional Porous Media

Abstract

In order to simulate heat and mass transfer in porous media whose scales range micron to nanometers, this work intends to provide a scheme for flow field simulation for such porous media. Since Navier-Stokes equations are no longer applicable to high Knudsen number (Kn) flow regimes, the conventional lattice Boltzmann method (LBM) cannot be applicable to flows in nanoscale porous media. Hence, a modified lattice Boltzmann method is applied for computing flows in micro-nano porous media in the transitional flow regimes at moderately high Knudsen numbers. The lattice Boltzmann equation applied is an extended version using an effective relaxation time associated with Kn and a regularization procedure coupled with Maxwell’s diffuse-scattering boundary condition for walls. For the flow field where the representative molecular mean free path varies (effectively the Kn varies locally), the locally defined Kn is introduced. In order to verify the LBM scheme, the results are compared with those of the molecular dynamics (MD) simulations by the Leonard-Jones potential. The flow fields considered are in modeled nano-porous media whose porosity is around 0.9. The results of micro-nanoscale porous media flows at Knudsen numbers: Kn = 0.04–0.24 show reasonable agreement in both the simulation methods and confirm the reliability of the presently applied LBM. Interestingly, in complex flow geometry, the advantage of higher order discrete velocity models of the LBM is not notable. Therefore, it is concluded that conventional discrete velocity models, say the D2Q9 and D3Q19 models are reasonably enough for flows in micro-nanoscale porous media.