Stokes-Einstein relation: Difference between revisions
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{{ | The '''Stokes-Einstein relation''', originally derived by William Sutherland <ref>[http://dx.doi.org/10.1080/14786440509463331 William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine '''9''' pp. 781-785 (1905)]</ref> but almost simultaneously published by [[Albert Einstein |Einstein]] <ref>[http://dx.doi.org/10.1002/andp.19053220806 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)]</ref>, 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> | |||
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== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1063/1.449616 Robert Zwanzig and Alan K. Harrison "Modifications of the Stokes–Einstein formula", Journal of Chemical Physics '''83''' pp. 5861-5862 (1985)] | |||
*[http://dx.doi.org/10.1063/1.2738063 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)] | |||
*[http://dx.doi.org/10.1103/PhysRevLett.107.165902 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)] | |||
[[category: Non-equilibrium thermodynamics]] | [[category: Non-equilibrium thermodynamics]] | ||
Latest revision as of 13:28, 14 October 2011
The Stokes-Einstein relation, originally derived by William Sutherland [1] but almost simultaneously published by Einstein [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[edit]
- ↑ 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)
- 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)