Stokes-Einstein relation

The Stokes-Einstein relation, originally derived by William Sutherland but almost simultaneously published by Einstein , 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

Related reading

• 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)
• J. Brillo, A. I. Pommrich, and A. Meyer "Relation between Self-Diffusion and Viscosity in Dense Liquids: New Experimental Results from Electrostatic Levitation", Physical Review Letters 107 165902 (2011)