Cunningham correction factor

In fluid dynamics, the Cunningham correction factor, or Cunningham slip correction factor (denoted Template:Mvar), 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, Template:Mvar, given below.

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

$C=1+\frac{2\lambda }{d}(A_1+A_2{e}^{\frac{-A_{3}d}{\lambda }})$

where

• Template:Mvar is the correction factor
• Template:Math is the mean free path
• Template:Mvar is the particle diameter
• Template:Mvar 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.

References

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