Documentation of Maxwell-Stefan fluxes

doc/handbook/dumux-handbook.bib

@@ -444,6 +444,7 @@
   journal = {Journal of Contaminant Hydrology},
   year = {2005}
 }
+
 @MastersThesis{nuske2009,
   title={{Determination of interfacial area-capillary pressure-saturation relationships for a single fracture}},
   author={Nuske, K. P.},
@@ -1078,6 +1079,7 @@ url = {http://www.sciencedirect.com/science/article/pii/S0169772204001160}
   year = {1979},
   author = {Aziz, K. and Settari, A.}
 }
+
 @book{daubert1989,
   title={{Physical and Thermodynamic Properties of Pure Chemicals: Design institute for physical property data, American institute of chemical engineers. vp}},
   author={Daubert, T. E. and Danner, R. P.},
@@ -1102,6 +1104,7 @@ url = {http://www.sciencedirect.com/science/article/pii/S0169772204001160}
   volume = {198},
   pages = {71--78}
 }
+
 @misc{cooper2008,
   title={{Release of the IAPWS formulation 2008 for the viscosity of ordinary water substance}},
   author={Cooper, J. R. and Dooley, R. B.},
@@ -1997,6 +2000,7 @@ url={https://doi.org/10.1007/s10765-012-1254-5}
     url = {https://link.springer.com/content/pdf/10.1007/BF00867119.pdf}
 }
 
+
 @article{Fichot2006,
 title = {The impact of thermal non-equilibrium and large-scale 2D/3D effects on debris bed reflooding and coolability},
 journal = {Nuclear Engineering and Design},
@@ -2008,3 +2012,19 @@ issn = {0029-5493},
 doi = {10.1016/j.nucengdes.2006.03.059},
 author = {F. Fichot and F. Duval and N. Trégourès and C. Béchaud and M. Quintard},
 }
+
+@Article{Krishna1997,
+  author      = {Krishna, R. and Wesselingh, J. A.},
+  journal     = {Chemical Engineering Science},
+  title       = {The Maxwell-Stefan approach to mass transfer},
+  year        = {1997},
+  number      = {6},
+  pages       = {861-911},
+  volume      = {52},
+  abstract    = {The limitations of the Fick's law for describing diffusion are discussed. It is argued that the Maxwell-Stefan formulation provides the most general, and convenient, approach for describing mass transport which takes proper account of thermodynamic non-idealities and influence of external force fields.  Furthermore, the Maxwell-Stefan approach can be extended to handle diffusion in macro- and microporous catalysts, adsorbents and membranes.},
+  affiliation = {Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 1661018 WV AmsterdamThe Netherlands; Department of Chemical Engineering, University of Groningen, Nijenborgh 49747 AG GroningenThe Netherlands},
+  keywords    = {Multicomponent diffusion; porous media; membrane separations; Fick's law; ionic diffusion; zeolities},
+  language    = {English},
+}
+
+

dumux/flux/maxwellstefanslaw.hh

@@ -19,8 +19,23 @@
 /*!
  * \file
  * \ingroup Flux
- * \brief This file contains the data which is required to calculate
- *        diffusive mass fluxes due to molecular diffusion with Maxwell-Stefan's law.
+ * \brief Diffusive mass fluxes according to Maxwell-Stefan's law
+ *
+ * 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 \cite Krishna1997. \n
+ * 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 \f$\textbf{j}_{diff}^i\f$ the Maxwell-Stefan formulation can be defined as:
+ *
+ * \f[
+ * \frac{x^i \textbf{grad}_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)
+ * \f]
+ *
+ * With \f$\eta^i\f$ 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
+ * \f$D^{ij}=D^{ji}\f$.
+ *
  */
 #ifndef DUMUX_FLUX_MAXWELL_STEFAN_LAW_HH
 #define DUMUX_FLUX_MAXWELL_STEFAN_LAW_HH