# Stokes law

The Stokes' law , by George Gabriel Stokes , describes the dependence of friction force spherical bodies of various sizes :

${\ displaystyle F _ {\ mathrm {R}} = 6 \ pi \ cdot r \ cdot \ eta \ cdot v}$

With

• ${\ displaystyle r}$: Particle radius (in the case of non-spherical bodies, half of a suitable equivalent diameter is used as an approximation instead of the particle radius .)
• ${\ displaystyle \ eta}$: dynamic viscosity of the fluid in which the particle is located
• ${\ displaystyle v}$: Particle speed (the frictional force acts opposite to the speed).

Stokes' law is needed for the Millikan experiment .

With the Stokes equation based on this , one can calculate the sedimentation speed of such a particle.

## Cunningham correction

If the spheres sinking in a gas are so small that they are in the same order of magnitude as the mean free path of the gas molecules, the normal formula becomes imprecise. This can be remedied by the Cunningham correction derived by the British mathematician Ebenezer Cunningham in 1910 : ${\ displaystyle \ lambda}$

${\ displaystyle F _ {\ mathrm {R}} = {\ frac {6 \ pi \ cdot r \ cdot \ eta \ cdot v} {1 + {\ frac {\ lambda} {r}} \ left (A_ {1 } + A_ {2} \ cdot e ^ {- A_ {3} {\ frac {r} {\ lambda}}} \ right)}}}$

With:

• ${\ displaystyle A_ {n}}$ : experimentally determined constants, where for air ( = 68 nm under standard conditions ) applies: ${\ displaystyle \ lambda}$
• ${\ displaystyle A_ {1} = 1 {,} 257}$
• ${\ displaystyle A_ {2} = 0 {,} 400}$
• ${\ displaystyle A_ {3} = 1 {,} 10}$

The following relationship can also be used as an approximation for air:

${\ displaystyle F _ {\ mathrm {R}} \ approx {\ frac {6 \ pi \ cdot r \ cdot \ eta \ cdot v} {1 + 1 {,} 63 {\ frac {\ lambda} {r}} }}}$

## literature

• G. G. Stokes: On the effect of the internal friction of fluids on the motion of pendulums. In: Transactions of the Cambridge Philosophical Society , Volume 9, 1851, pp. 8-106. ( Online )