Critical Review of Fluid Flow Physics at Micro- to Nano‐scale Porous Media Applications in the Energy Sector

Table 1

Different flow regimes as a function of Knudsen number.

Kn		Flow regime	Physics	Applicable models
Lower bound	Upper bound
0	10^–2	Continuum (no slip flow)	Thermodynamic equilibrium and no-slip at the boundary	(1) Navier–Stokes equations, (2) Euler equations, (3) LBM
10^–2	10^–1	Slip flow	Nonequilibrium effects dominate near the walls. Assumptions of no-slip boundary condition, thermodynamic equilibrium, and linear stress-strain relationship fail	(1) Navier–Stokes equations with slip velocity and temperature jump boundary conditions, (2) Boltzmann gas-kinetic equation, (3) DSMC, (4) Burnett equations, (5) LBM, (6) gas-kinetic scheme, (7) method of moments
10^–1	10	Transition flow	Rarefaction effects dominate and slip models become more complex. Assumptions of no-slip boundary condition, thermodynamic equilibrium, and linear stress-strain relationship fail	(1) Navier–Stokes equations with slip velocity and temperature jump boundary conditions, (2) Boltzmann gas-kinetic equation, (3) DSMC, (4) Burnett equations, (5) LBM, (6) gas-kinetic scheme, (7) method of moments
10	∞	Free-molecule flow	Collisions between gas molecules and boundary surface become dominant compared to intermolecular collisions. Assumptions of no-slip boundary condition, thermodynamic equilibrium, and linear stress-strain relationship fail	(1) Boltzmann gas-kinetic equation, (2) DSMC method

Flow regimes as a function of medium and flow parameters.