Faxén's law

  1. Equations of fluid dynamics


In fluid dynamics, Faxén's law relates a sphere's velocity v to the forces and flow it experiences:

\[ v = u(r) + b_0 F + \frac{a^2}{6} \nabla^2 u(r), \]

where

  • \(b_0\) is the mobility,
  • \( F \) is a force acting on the sphere,
  • \( a\) the sphere's radius and
  • \( r \) the spatial coordinate.

In the case that the pressure gradient is small compared with the length scale of the sphere's diameter. and when there is no external force, the last two terms may be neglected. In this case the external fluid flow simply advects the sphere.

Faxén's law is a correction to Stokes' law for the friction on spherical objects in a viscous fluid, valid where the object moves close to a wall of the container.[1]

This theory was introduced in 1922 by Swedish physicist Hilding Faxén, who at the time was active at Uppsala University.

See also

Notes

  1. ↑ Single molecule measurements and biological motors - Glossary, accessed on May 12, 2009

References

  • Faxén, H. (1922), "Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist", Annalen der Physik 373 (10): 89–119, Bibcode 1922AnP...373...89F, doi:10.1002/andp.19223731003
  • Happel, J.; Brenner, H. (1991), Low Reynolds Number Hydrodynamics, Dordrecht: Kluwer


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