A comment on `An improved macroscale model for gas slip flow in porous media'

TL;DR

This paper critiques a recent model for gas slip flow in porous media, demonstrating through kinetic simulations that the Navier-Stokes approach with first-order slip boundary conditions is only valid at very small Knudsen numbers, challenging previous nonlinear permeability claims.

Contribution

It provides numerical evidence that the Navier-Stokes equations with first-order slip boundary conditions are only accurate at very small Knudsen numbers, questioning prior nonlinear permeability results.

Findings

Navier-Stokes equations are accurate only at very small Knudsen numbers.

First-order velocity-slip boundary condition is insufficient for higher Knudsen numbers.

Previous nonlinear permeability results are questionable based on kinetic simulations.

Abstract

In a recent paper by Lasseux, Vald\'{e}s-Parada and Porter (J.~Fluid~Mech. \textbf{805} (2016) 118-146), it is found that the apparent gas permeability of the porous media is a nonlinear function of the Knudsen number. However, this result is highly questionable, because the adopted Navier-Stokes equations and the first-order velocity-slip boundary condition are first-order (in terms of the Knudsen number) approximations of the Boltzmann equation and the kinetic boundary condition for rarefied gas flows. Our numerical simulations based on the Bhatnagar-Gross-Krook kinetic equation and regularized 20-moment equations prove that the Navier-Stokes equations with the first-order velocity-slip boundary condition are only accurate at a very small Knudsen number limit, where the apparent gas permeability is a linear function of the Knudsen number.