= Rarefied gas flow approximations
For $\mathrm{Kn}\ll1$, frequent gas–gas <collisions> can establish a local <Maxwellian> before macroscopic conditions change appreciably. Under this additional near-equilibrium assumption, the <hydrodynamic limit of the Boltzmann equation> motivates a <continuum approximation> with <Navier-Stokes equations> and heat conduction. A <no-slip boundary condition> is a leading wall approximation, not a statement about individual molecular <velocities>.
With a small but finite <Knudsen number>, a useful slip approximation retains continuum bulk equations and corrects wall <velocity> and <temperature>. A <Navier slip boundary condition> can represent the leading tangential <velocity> correction, but its <slip length> must come from the relevant gas–wall interaction model. A nearby <Knudsen layer> still requires kinetic treatment if its detailed structure is wanted. Slip corrections are perturbations; extending them into order-one <Knudsen numbers> has no general accuracy guarantee. At order-one <Knudsen number>, wall and intermolecular <collisions> both matter; this transitional situation calls for a <kinetic theory> model. At $\mathrm{Kn}\gg1$, <free molecular flow> becomes a useful limiting approximation. These are scale comparisons, with accuracy depending on geometry, flow conditions and the observable, rather than universal sharp numerical boundaries. https://ntrs.nasa.gov/api/citations/19860015045/downloads/19860015045.pdf#page=3[Frank G. Collins (1985), Low Density Gas Dynamic Wall Boundary Conditions, introduction]{ref}
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