# Difference between revisions of "Stokes-Einstein relation"

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 $R$ immersed in a fluid,

$D=\frac{k_B T}{6\pi\eta R},$

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

$D=\mu k_B T,$

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

$\mu=\frac{1}{6\pi\eta R} ,$

produces the first equation.

## References

1. William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine 9 pp. 781-785 (1905)
2. 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)
3. Robert Zwanzig and Alan K. Harrison "Modifications of the Stokes–Einstein formula", Journal of Chemical Physics 83 pp. 5861-5862 (1985)
4. 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)