maxwellstefanslaw.hh File Reference

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.

Description

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 [50].
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 ${\mathbf{\text{j}}}_{diff}^i$ the Maxwell-Stefan formulation can be defined as:

$$\frac{x^i{\mathrm{\nabla }}_T{\eta }^i}{RT}=-\sum _{j=1,j\ne i}^N\frac{x^i{x}^j}{D^{ij}}(\frac{{\mathbf{\text{j}}}_{diff}^i}{{\varrho }^i}-\frac{{\mathbf{\text{j}}}_{diff}^j}{{\varrho }^j})=-\sum _{j=1,j\ne i}^N\frac{x^i{x}^j}{D^{ij}\varrho }(\frac{{\mathbf{\text{j}}}_{diff}^i}{X^i}-\frac{{\mathbf{\text{j}}}_{diff}^j}{X^j})$$

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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