Stokes law

This article refers to Stokes' law. For further regularities, rules and theorems established by the physicist and mathematician Sir George Gabriel Stokes, see Stokes' laws .

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 )

Web links

• Physics and chemistry of atmospheric aerosol , including Stokes' law and Cunningham's correction.

Individual evidence

1. ↑ ^{a b} E. Cunningham: On the velocity of steady fall of spherical particles through fluid medium . In: Proc. Roy. Soc. A. Band 83 , 1910, pp. 357-365 .
2. ^ CN Davies: Definitive equations for the fluid resistance of spheres . In: Proc. Phys. Soc. tape 57 , 1945, p. 259-270 .