Stokes-Einstein relation

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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 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.


  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)
  3. Robert Zwanzig and Alan K. Harrison "Modifications of the Stokes–Einstein formula", Journal of Chemical Physics 83 pp. 5861-5862 (1985)
  4. 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)