In fluid dynamics, the Cunningham correction factor, or Cunningham slip correction factor (denoted ), is used to account for non-continuum 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 numbers. 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.
The drag coefficient calculated with standard correlations is divided by the Cunningham correction factor, , given below.
Ebenezer Cunningham derived the correction factor in 1910 and with Robert Andrews Millikan, verified the correction in the same year.
where
* is the correction factor
* is the mean free path
* is the particle diameter
* are experimentally determined coefficients.
:For air (Davies, 1945):
::A = 1.257
::A = 0.400
::A = 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.