# 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 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)