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In [[fluid dynamics]], the '''Cunningham correction factor''' or '''Cunningham slip correction factor''' is used to account for noncontinuum effects when calculating the drag on small particles. The derivation of [[Stokes Law]], which is used to calculate the drag force on small particles, assumes a [[No-slip condition]] which is no longer correct at high [[Knudsen number]]. The Cunningham slip correction factor allows predicting the [[drag force]] on a particle moving a fluid with [[Knudsen number]] between the continuum regime and [[free molecular flow]].
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The [[drag coefficient]] calculated with standard correlations is divided by the Cunningham correction factor, C given below.
 
[[Ebenezer Cunningham]]<ref name="Cunningham">Cunningham, E., "On the velocity of steady fall of spherical particles through fluid medium," ''Proc. Roy. Soc. A'' 83(1910)357. {{doi|10.1098/rspa.1910.0024}}</ref> derived the correction factor in 1910 and verified with [[Robert Andrews Millikan]] the correction in the same year.
 
:<math>C = 1+ \frac{2\lambda}{d}\cdot (A_1+A_2\cdot e^{\frac{-A_3\cdot d}{\lambda}})</math>
 
where
:''C'' is the correction factor
:λ is the [[mean free path]]
:''d'' is the particle diameter
:''A<sub>n</sub>'' are experimentally determined coefficients.
:For air (Davies, 1945):
::''A''<sub>1</sub> = 1.257
::''A''<sub>2</sub> = 0.400
::''A''<sub>3</sub> = 0.55
 
The Cunningham correction factor becomes significant when particles become smaller than 15 micrometers, for air at ambient conditions.
 
For sub-micrometer particles, [[Brownian motion]] must be taken into account.
 
==References==
{{Reflist}}
 
[[Category:Fluid dynamics]]
[[Category:Dimensionless numbers]]
[[Category:Aerosols]]
 
{{fluiddynamics-stub}}

Latest revision as of 21:37, 29 July 2014

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