Stokes-Einstein relation: Difference between revisions
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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
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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)