added preamble text for the runProtonicCell example

Documentation/publishedExamples/runProtonicCell.rst

@@ -6,7 +6,7 @@ PEM electrolyser with Gas Supply
 ================================
 *Generated from runProtonicCell.m*
 
-
+.. include:: runProtonicCellPreamble.rst
 
 json input data
 ===============

Documentation/publishedExamples/runProtonicCellPreamble.rst

@@ -0,0 +1,35 @@
+Model coupling
+==============
+
+We couple the :ref:`gas supply layer <runGasSupply>` with the anode of the :ref:`protonic membrane
+<runProtonicMembrane>`. The coupling occurs at the interface of the two regions. Along the anode, we assume a constant
+voltage, that is, we neglect the potential loss in this part.
+
+The chemical reaction at the interface is 
+
+.. math::
+
+   \ce{1/2 H2O <-> H^+ + e^- + 1/4 O2}
+
+It relates the mass fluxes in the gas supply layer and inside the anode in the following way
+
+.. math::
+
+   \begin{array}{rcl}
+    j_\ce{H2O}\cdot n &=& 2j_{\ce{H^+}}\cdot n\\
+    j_{\ce{O2}}\cdot n &=& -4j_{\ce{H^+}}\cdot n
+   \end{array}
+
+Here, :math:`n` denotes the normal at the interface (same orientation in the whole expression), so that, for example,
+:math:`j_\ce{H2O}\cdot n` denotes the mass of :math:`\ce{H2O}` leaving the gas layer in :math:`kg/m^2/s` (for a 3D
+model). For the gas layer, the fluxes are given by the sum of the convection and diffusion fluxes, so that, for
+:math:`\ce{H2O}`, we have
+
+.. math::
+
+    j_\ce{H2O}\cdot n = -D \nabla(\rho x_{\ce{H2O}})\cdot n - \frac{K}{\mu}\rho x_i \nabla p\cdot n
+
+and a similar expression for the flux of :math:`\ce{O2}` at the interface.
+
+
+