# Difference between revisions of "Stokes-Einstein relation"

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The '''Stokes-Einstein relation''', originally derived by William Sutherland (Ref. 1) but almost simultaneously published by [[Albert Einstein |Einstein]] (Ref. 2), states that, for a sphere of radius <math>R</math> immersed in a fluid, | The '''Stokes-Einstein relation''', originally derived by William Sutherland (Ref. 1) but almost simultaneously published by [[Albert Einstein |Einstein]] (Ref. 2), states that, for a sphere of radius <math>R</math> immersed in a fluid, | ||

− | :<math> D=\frac{k_B T}{6\pi\eta R} </math> | + | :<math> D=\frac{k_B T}{6\pi\eta R}, </math> |

+ | |||

+ | where ''D'' is the diffusion constant, <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]] and <math>\eta</math> is the [[viscosity]]. Sometimes, | ||

+ | the name is given to the general relation: | ||

+ | |||

+ | :<math> D=\mu k_B T, </math> | ||

+ | |||

+ | where <math>\mu</math> is the [[mobility]]. This, coupled with Stokes' law for the drag upon a sphere moving though a fluid: | ||

+ | |||

+ | :<math> \mu=\frac{1}{6\pi\eta R} , </math> | ||

+ | |||

+ | produces the first equation. | ||

+ | |||

− | |||

==References== | ==References== | ||

#William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine '''9''' pp. 781-785 (1905) | #William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine '''9''' pp. 781-785 (1905) |

## Revision as of 15:05, 18 December 2007

The **Stokes-Einstein relation**, originally derived by William Sutherland (Ref. 1) but almost simultaneously published by Einstein (Ref. 2), states that, for a sphere of radius immersed in a fluid,

where *D* is the diffusion constant, is the Boltzmann constant, *T* is the temperature and is the viscosity. Sometimes,
the name is given to the general relation:

where is the mobility. This, coupled with Stokes' law for the drag upon a sphere moving though a fluid:

produces the first equation.

## References

- William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine
**9**pp. 781-785 (1905) - A. Einstein "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen", Annalen der Physik
**17**pp. 549-560 (1905) - Robert Zwanzig and Alan K. Harrison "Modifications of the Stokes–Einstein formula", Journal of Chemical Physics
**83**pp. 5861-5862 (1985) - M. Cappelezzo, C. A. Capellari, S. H. Pezzin, and L. A. F. Coelho "Stokes-Einstein relation for pure simple fluids", Journal of Chemical Physics
**126**224516 (2007)