Difference between revisions of "Hauptseminar Porous Media SS 2021/Theory of diffusion"
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== Contents ==  == Contents ==  
−  In this talk an introduction to the description of diffusion and transport is given. For this a short introduction to [https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations hydrodynamics] is given with the focus on characterizing the flow with dimensionless numbers including the [https://en.wikipedia.org/wiki/Reynolds_number Reynods], [https://en.wikipedia.org/wiki/Mach_number]  +  In this talk an introduction to the description of diffusion and transport is given. For this a short introduction to [https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations hydrodynamics] is given with the focus on characterizing the flow with dimensionless numbers including the [https://en.wikipedia.org/wiki/Reynolds_number Reynods], [https://en.wikipedia.org/wiki/Mach_number Mach] ,[https://en.wikipedia.org/wiki/Capillary_number Capillary] and [https://en.wikipedia.org/wiki/Knudsen_number Knudsen] number. After that the contributions to the [https://en.wikipedia.org/wiki/Convection%E2%80%93diffusion_equation reactiondiffusion advection equation] are discussed and the [https://en.wikipedia.org/wiki/P%C3%A9clet_number Peclet] number is introduced. Finally the [https://en.wikipedia.org/wiki/Onsager_reciprocal_relations Onsager theory for transport coefficients] is presented and the differences between the self, collective and transport diffusion are highlighted. This should also include the connection to [https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion Fick’s law of diffusion], the [https://en.wikipedia.org/wiki/Mean_squared_displacement meansquared displacement] and the [https://en.wikipedia.org/wiki/Green%E2%80%93Kubo_relations GreenKubo relation] to determine the diffusion coefficients from particle trajectories. 
== Literature ==  == Literature == 
Revision as of 18:26, 9 February 2021
 Date
 TBA"TBA" contains an extrinsic dash or other characters that are invalid for a date interpretation.
 Time
 TBA
 Topic
 Theory of Diffusion
 Speaker
 TBD
 Tutor
 Alexander Reinauer
Contents
In this talk an introduction to the description of diffusion and transport is given. For this a short introduction to hydrodynamics is given with the focus on characterizing the flow with dimensionless numbers including the Reynods, Mach ,Capillary and Knudsen number. After that the contributions to the reactiondiffusion advection equation are discussed and the Peclet number is introduced. Finally the Onsager theory for transport coefficients is presented and the differences between the self, collective and transport diffusion are highlighted. This should also include the connection to Fick’s law of diffusion, the meansquared displacement and the GreenKubo relation to determine the diffusion coefficients from particle trajectories.
Literature

Hendrik Frentrup and Carlos Avenda\ no and Martin Horsch and Alaaeldin Salih and Erich A. Müller.
"Transport diffusivities of fluids in nanopores by nonequilibrium molecular dynamics simulation".
Molecular Simulation 38(7)(540553), 2012.
[DOI] 
Kärger, Jörg and Ruthven, Douglas M.
"Diffusion in nanoporous materials: fundamental principles, insights and challenges".
New Journal of Chemistry 40(5)(4027–4048), 2016.
[DOI] 
Kärger, Jörg and Ruthven, Douglas M and Theodorou, Doros N.
"Diffusion in Nanoporous Materials, 2 Volume Set".
John Wiley & Sons, 2012.

Hansen, JeanPierre and McDonald, Ian Ranald.
"Theory of simple liquids: with applications to soft matter".
Academic Press, 2013.