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version 3.10-dev
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version 3.10-dev
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Diffusive mass fluxes according to Maxwell-Stefan's law. More...
#include <dumux/flux/maxwellstefanslaw_fwd.hh>#include <dumux/flux/cctpfa/maxwellstefanslaw.hh>#include <dumux/flux/box/maxwellstefanslaw.hh>#include <dumux/flux/staggered/freeflow/maxwellstefanslaw.hh>Go to the source code of this file.
Maxwell-Stefan's law describes the diffusive mass fluxes due to molecular diffusion. The diffusion phenomena results from coupling effects between the different molecules in a gas-mixture [48].
The Maxwell-Stefan formulation can be used to describe systems where Fick's law does not hold (e.g. diffusion of diluted gases in multicomponent systems).
For diffusive mass fluxes \(\textbf{j}_{diff}^i\) the Maxwell-Stefan formulation can be defined as:
\[ \frac{x^i \nabla_T \eta^i}{RT} = - \sum\limits_{j=1,j\neq i}^{N} \frac{x^ix^j}{D^{ij}}\left(\frac{\textbf{j}_{diff}^i}{\varrho^i}-\frac{\textbf{j}_{diff}^j}{\varrho^j}\right) = - \sum\limits_{j=1,j\neq i}^{N} \frac{x^ix^j}{D^{ij}\varrho}\left(\frac{\textbf{j}_{diff}^i}{X^i}-\frac{\textbf{j}_{diff}^j}{X^j}\right) \]
With \(\eta^i\) as the chemical potential of the species i. Note, the diffusion coefficients are based on the Onsager symmetry, thus the diffusion coefficients can be expressed as \(D^{ij}=D^{ji}\).
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