Knudsen number#

Named after: Martin Knudsen (1871-1949).

$$\text{Kn} \stackrel{\text{def}}{=} \frac{\lambda}{L} \sim \frac{\text{molecular length}}{\text{continuum length}}$$

Measures molecular mean free path relative to a macroscopic length. It indicates whether continuum fluid assumptions are valid.

Name	Symbol	SI units	Dimension
mean free path	$\lambda$	$\mathrm{m}$	$\text L$
characteristic length	$L$	$\mathrm{m}$	$\text L$

Rarefied gas flow

Range	Regime	Description
0 – 0.01	continuum	Molecular mean free path is much smaller than the geometry. Navier-Stokes continuum models are usually appropriate.
0.01 – 0.1	slip	Continuum behavior mostly holds, but velocity slip and temperature jump at boundaries can be important.
0.1 – 10	transition	Continuum assumptions break down and kinetic effects must be modeled explicitly.
10 – ∞	free molecular	Molecular collisions with boundaries dominate over intermolecular collisions. Free molecular or kinetic descriptions are required.

Name	Symbol	SI units	Dimension
mean free path	\(\lambda\)	\(\mathrm{m}\)	\(\text L\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)