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 reaction-diffusion 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 mean-squared displacement] and the [https://en.wikipedia.org/wiki/Green%E2%80%93Kubo_relations Green-Kubo 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 reaction-diffusion 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 mean-squared displacement and the Green-Kubo relation to determine the diffusion coefficients from particle trajectories.
Literature
-
Hendrik Frentrup, Carlos Avendaño, Martin Horsch, Alaaeldin Salih, Erich A. Müller.
Transport diffusivities of fluids in nanopores by non-equilibrium molecular dynamics simulation.
Molecular Simulation 38(7):540-553, 2012.
[DOI] -
Jörg Kärger, Douglas M Ruthven.
Diffusion in nanoporous materials: fundamental principles, insights and challenges.
New Journal of Chemistry 40(5):4027–4048, 2016.
[DOI] -
Jörg Kärger, Douglas M Ruthven, Doros N Theodorou.
Diffusion in Nanoporous Materials, 2 Volume Set.
John Wiley & Sons, 2012.
-
Jean-Pierre Hansen, Ian Ranald McDonald.
Theory of simple liquids: with applications to soft matter.
Academic Press, 2013.