Knudsen number

The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named after Danish physicist Martin Knudsen (1871–1949).

Definition

The Knudsen number is defined as:

$\mathit{Kn} = \frac {\lambda}{L} = \frac {k_B T}{\sqrt{2}\pi\sigma^2 P L}$

where

$λ$ = m)^*
L = representative physical length scale (m)
k_B = K)
T = temperature (K)
$σ$ = particle diameter (m)
P = total pressure (Pa)

(* For particle dynamics in the atmosphere, and assuming standard temperature and pressure, i.e. 25°C, 1 atm, we have $λ$ = 8×10^-8 m. )

Application

The Knudsen number is useful for determining whether fluid mechanics is no longer a good approximation. In this case statistical methods must be used.

Problems with high Knudsen numbers include the calculation of the motion of a dust particle through the lower Stokes' Law can be used in the Cunningham correction factor, this is a drag force correction due to slip in small particles (i.e. d_p <5 µm).

Knudsen number

Definition

Application

See also