Editing Knudsen number (section)

==Application==

The Knudsen number can be used to determine the rarefaction of a flow:<ref name="karniadakis-00">{{cite book|title=Microflows and nanoflows: fundamentals and simulation|year=2000|publisher=Springer|author=Karniadakis, G. and Beskok, A. and Aluru, N.}}</ref>
<ref name="Ziarani-00">{{cite conference|last=Ziarani A. S.|first=Aguilera R., Cui X. C.|title= Permeability of Tight Sand and Shale Formations: A Dual Mechanism Approach for Micro and Nanodarcy Reservoirs|publisher=SPE |year=2020|isbn=978-1-61399-685-0|conference=SPE Canada Unconventional Resources Conference. SPE-200010-MS}}</ref>
* <math>\mathrm{Kn} < 0.01 </math>: [[Continuum mechanics|Continuum flow]]
* <math>0.01 < \mathrm{Kn} < 0.1 </math>:  Slip flow
* <math> 0.1 < \mathrm{Kn} < 10 </math>:  Transitional flow
* <math>\mathrm{Kn} > 10 </math>: [[Free molecular flow]]<ref name=Laurendeau>{{cite book
|title=Statistical thermodynamics: fundamentals and applications
|first1=Normand M.
|last1=Laurendeau
|publisher=Cambridge University Press
|year=2005
|isbn=0-521-84635-8
|page=306
|url=https://books.google.com/books?id=QF6iMewh4KMC}}, [https://books.google.com/books?id=QF6iMewh4KMC&pg=PA434 Appendix N, page 434]
</ref>
This regime classification is empirical and problem dependent but has proven useful to adequately model flows.<ref name="karniadakis-00" />
<ref name="Cussler-00">{{cite book|last=Cussler|first=E. L.|title=Diffusion: Mass Transfer in Fluid Systems|publisher=Cambridge University Press|year=1997|isbn=0-521-45078-0}}</ref>

Problems with high Knudsen numbers include the calculation of the motion of a [[dust]] particle through the lower [[Earth's atmosphere|atmosphere]] and the motion of a [[satellite]] through the [[exosphere]]. One of the most widely used applications for the Knudsen number is in [[microfluidics]] and [[MEMS]] device design where flows range from continuum to free-molecular.<ref name="karniadakis-00" /> In recent years, it has been applied in other disciplines such as transport in porous media, e.g., petroleum reservoirs.<ref name="Ziarani-00"/> Movements of fluids in situations with a high Knudsen number are said to exhibit [[Knudsen flow]], also called [[free molecular flow]].{{cn|date=August 2024}}<!--I found definition claiming Knudsen flow is transitional.-->

Airflow around an [[aircraft]] such as an [[airliner]] has a low Knudsen number, making it firmly in the realm of continuum mechanics. 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''<sub>''p''</sub>&nbsp;< 5&nbsp;μm). The flow of water through a nozzle will usually be a situation with a low Knudsen number.<ref name=Laurendeau/>

Mixtures of gases with different molecular masses can be partly separated by sending the mixture through small holes of a thin wall because the numbers of molecules that pass through a hole is proportional to the pressure of the gas and inversely proportional to its molecular mass. The technique has been used to separate [[isotope|isotopic]] mixtures, such as [[uranium]], using porous membranes,<ref>{{cite book | last = Villani | first = S. | title = Isotope Separation | publisher = American Nuclear Society | date = 1976 | location = Hinsdale, Ill.}}</ref> It has also been successfully demonstrated for use in [[hydrogen production]] from water.<ref>{{cite journal | doi = 10.1016/S0360-3199(97)00038-4 | last = Kogan | first = A. | title = Direct solar thermal splitting of water and on-site separation of the products - II. Experimental feasibility study | journal = International Journal of Hydrogen Energy | volume = 23 | issue = 2 | pages = 89–98 | publisher = Elsevier Science Ltd | location = Great Britain | date = 1998| bibcode = 1998IJHE...23...89K }}</ref>

The Knudsen number also plays an important role in thermal conduction in gases. For insulation materials, for example, where gases are contained under low pressure, the Knudsen number should be as high as possible to ensure low [[thermal conductivity]].<ref>{{Cite web|url=https://www.tec-science.com/thermodynamics/heat/thermal-conductivity-of-gases/|title=Thermal conductivity of gases|last=tec-science|date=2020-01-27|website=tec-science|language=en-US|access-date=2020-03-22}}</ref>