Stokes-Einstein relation: Difference between revisions
Jump to navigation
Jump to search
(Changed r in equation to R) |
No edit summary |
||
| Line 2: | Line 2: | ||
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 14:05, 18 December 2007
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
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)