Cunningham correction factor explained

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^[1] derived the correction factor in 1910 and with Robert Andrews Millikan, verified the correction in the same year.

C = 1+ (2λ)/(d) \left(A _{1+A} _{2} e ^{(- A _{3} d)/(λ)} \right)

where

• is the correction factor
• is the mean free path
• is the particle diameter
• are experimentally determined coefficients.

For air (Davies, 1945):^[2]

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.

Notes and References

1. Cunningham, E., "On the velocity of steady fall of spherical particles through fluid medium," Proc. Roy. Soc. A 83(1910)357.
2. Davies. C.. Definitive equations for the fluid resistance of spheres. Proceedings of the Physical Society. 1945. 57. 4 . 259. 10.1088/0959-5309/57/4/301. 1945PPS....57..259D.