Cunningham correction factor

In fluid dynamics, the Cunningham correction factor, or Cunningham slip correction factor (denoted $C$), 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, $C$, given below.

Ebenezer Cunningham derived the correction factor in 1910 and with Robert Andrews Millikan, verified the correction in the same year.


 * $$C = 1+ \frac{2\lambda}{d} \left(A_1+A_2 e^{\frac{-A_3 d}{\lambda}} \right)$$

where
 * $C$ is the correction factor
 * $λ$ is the mean free path
 * $d$ is the particle diameter
 * $A_{n}$ are experimentally determined coefficients.
 * For air (Davies, 1945):
 * A1 = 1.257
 * A2 = 0.400
 * A3 = 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.