Stokes-Einstein relation - Revision history

Carl McBride: Added a DOI

2011-10-14T11:28:50Z

Added a DOI

← Older revision		Revision as of 13:28, 14 October 2011
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	The '''Stokes-Einstein relation''', originally derived by William Sutherland <ref>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,		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>		:<math> D=\frac{k_B T}{6\pi\eta R}, </math>

Carl McBride: Added a recent publication

2011-10-14T11:21:49Z

Added a recent publication

← Older revision		Revision as of 13:21, 14 October 2011
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	~~{{Stub-general}}~~		The '''Stokes-Einstein relation''', originally derived by William Sutherland <ref>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,
	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>
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	produces the first equation.		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)~~		<references/>
	#[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)]		;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/10.1063/1.449616 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/10.1063/1.2738063 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]]

Dduque at 13:05, 18 December 2007

2007-12-18T13:05:08Z

← Older revision		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 [[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.


	~~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]].~~
	==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)

77.99.43.51: Changed r in equation to R

2007-12-17T12:27:47Z

Changed r in equation to R

← Older revision		Revision as of 14:27, 17 December 2007
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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]].		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]].

Dduque: $R$ defined

2007-12-16T14:50:28Z

<math>R</math> defined

← Older revision		Revision as of 16:50, 16 December 2007
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	{{Stub-general}}		{{Stub-general}}
	The '''Stokes-Einstein relation''', originally derived by William Sutherland (Ref. 1) but almost simultaneously published by [[Albert Einstein \|Einstein]] (Ref. 2), states		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>

Carl McBride at 12:26, 16 November 2007

2007-11-16T12:26:44Z

← Older revision		Revision as of 14:26, 16 November 2007
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	{{Stub-general}}		{{Stub-general}}
	The '''Stokes-Einstein relation''', originally derived by William Sutherland, states		The '''Stokes-Einstein relation''', originally derived by William Sutherland (Ref. 1) but almost simultaneously published by [[Albert Einstein \|Einstein]] (Ref. 2), states

	:<math> D=\frac{k_B T}{6\pi\eta r} </math>		:<math> D=\frac{k_B T}{6\pi\eta r} </math>
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	==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)
			#[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)]
	#[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/10.1063/1.449616 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/10.1063/1.2738063 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)]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride at 16:02, 8 November 2007

2007-11-08T16:02:09Z

← Older revision		Revision as of 18:02, 8 November 2007
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	:<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]].
	==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)

Carl McBride at 15:57, 8 November 2007

2007-11-08T15:57:41Z

← Older revision		Revision as of 17:57, 8 November 2007
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	{{Stub-general}}		{{Stub-general}}
			The '''Stokes-Einstein relation''', originally derived by William Sutherland, states

			:<math> D=\frac{k_B T}{6\pi\eta r} </math>
	==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)
	#[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/10.1063/1.449616 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/10.1063/1.2738063 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)]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: /* References */

2007-11-08T15:42:20Z

References

← Older revision		Revision as of 17:42, 8 November 2007
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	{{Stub-general}}		{{Stub-general}}
	==References==		==References==
			#[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/10.1063/1.2738063 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)]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Nice and Tidy at 11:34, 26 September 2007

2007-09-26T11:34:11Z

← Older revision		Revision as of 13:34, 26 September 2007
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			{{Stub-general}}
	==References==		==References==
	#[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/10.1063/1.2738063 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)]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]