Stokes-Einstein relation

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The Stokes-Einstein relation, originally derived by William Sutherland ^[1] but almost simultaneously published by Einstein ^[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

Related reading

[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)

[1]

[2]

Stokes-Einstein relation

References

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