Editing Knudsen number (section)

==Definition==
The Knudsen number is a dimensionless number defined as

:<math>\mathrm{Kn}\ = \frac {\lambda}{L},</math>

where
: <math>\lambda</math> = [[mean free path]] [L<sup>1</sup>],
: <math>L</math> = representative physical length scale [L<sup>1</sup>].

The representative length scale considered, <math>L</math>, may correspond to various physical traits of a system, but most commonly relates to a ''gap length'' over which thermal transport or mass transport occurs through a gas phase. This is the case in porous and granular materials, where the thermal transport through a gas phase depends highly on its pressure and the consequent mean free path of molecules in this phase.<ref>{{cite journal| last1=Dai  |display-authors=etal | title= Effective Thermal Conductivity of Submicron Powders: A Numerical Study| journal= Applied Mechanics and Materials| year=2016 | volume=846| pages=500–505| url=https://www.researchgate.net/publication/305644421 |doi=10.4028/www.scientific.net/AMM.846.500 |s2cid=114611104 }}</ref> For a [[Boltzmann gas]], the [[mean free path]] may be readily calculated, so that

:<math>\mathrm{Kn}\ = \frac {k_\text{B} T}{\sqrt{2}\pi d^2 p L}=\frac {k_\text{B}}{\sqrt{2}\pi d^2 \rho R_{s} L},</math>

where
: <math>k_\text{B}</math> is the [[Boltzmann constant]] (1.380649 × 10<sup>−23</sup> J/K in [[SI]] units) [M<sup>1</sup> L<sup>2</sup> T<sup>−2</sup> Θ<sup>−1</sup>],
: <math>T</math> is the [[thermodynamic temperature]] [θ<sup>1</sup>],
: <math>d</math> is the particle hard-shell diameter [L<sup>1</sup>],
: <math>p</math> is the static pressure [M<sup>1</sup> L<sup>−1</sup> T<sup>−2</sup>],
: <math>R_{s}</math> is the [[Gas constant#Specific gas constant|specific gas constant]] [L<sup>2</sup> T<sup>−2</sup> θ<sup>−1</sup>] (287.05 J/(kg K) for air),
: <math>\rho</math> is the density [M<sup>1</sup> L<sup>−3</sup>].

If the temperature is increased, but the ''volume'' kept constant, then the Knudsen number (and the mean free path) doesn't change (for an [[ideal gas]]). In this case, the density stays the same. If the temperature is increased, and the ''pressure'' kept constant, then the gas expands and therefore its density decreases. In this case, the mean free path increases and so does the Knudsen number. Hence, it may be helpful to keep in mind that the mean free path (and therefore the Knudsen number) is really dependent on the thermodynamic variable density (proportional to the reciprocal of density), and only indirectly on temperature and pressure.

For particle dynamics in the [[atmosphere]], and assuming [[standard temperature and pressure]], i.e. 0&nbsp;°C and 1 atm, we have <math>\lambda</math> ≈ {{val|8e-8|u=m}} (80&nbsp;nm).