Knudsen Number

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DEFINITION

The Knudsen number is defined as:
:

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

where

$\lambda$ = mean free path ( M )^---

L = representative physical length scale (m)

k_B = Boltzmann's Constant (1.38×10^-23 J / K )

T = temperature (K)

$\sigma$ = 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 $\lambda$ = 8×10^-8 m. )

APPLICATION

The Knudsen number is useful for determining whether 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 Atmosphere , or the motion of a Satellite through the Exosphere . The solution of the flow around an Aircraft has a low Knudsen number. Using the Knudsen number an adjustment for 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).

SEE ALSO

Cunningham Correction Factor

Fluid Dynamics

Mach Number

Reynolds Number

EXTERNAL LINKS

Gas Dynamics Toolbox – Using the VHS model for calculating Knudsen numbers of gas mixtures

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	CATEGORIES ABOUT KNUDSEN NUMBER

	dimensionless numbers

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Information About

Knudsen Number