Cunningham correction factor

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The Cunningham Slip Correction is a correction to the drag coefficient that is used to predict the drag force between a fluid and a particle moving through this fluid.

Cunningham derived the correction factor in 1910 and verified with Millikan the correction in the same year.

$C = 1+ \frac{2l}{d}\cdot (A_1+A_2\cdot e^{\frac{-A_3\cdot d}{l}})$

where

C is the correction factor

l 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 drag coefficient calculated with standard correlations is multiplied by the Cunningham correction factor, C, to account for the fact that when particles become small, the fluid may no longer be considered continuous.

The Cunningham correction factor becomes significant when particles become smaller than 15 micrometres, for air at ambient conditions.

For sub-micrometre particles, Brownian diffusion must be taken into account.