add equations and curve figures to fluidmatixinteractions

slides/materialsystem.md

@@ -19,13 +19,7 @@ title: Material system
 * Solid system
 * Binary coefficients
 * Fluid-matrix interactions
-
-## <ins> Chemical properties and equation of states: </ins>
-
 * Chemistry
-* Equation of state (Eos)
-
-**Note:** _These contains some specific example implementations. One can implement specific things according to their need here._
 
 ## <ins> Dumux-specific containers and solvers </ins>
 
@@ -114,8 +108,27 @@ _Specifying a solid system is only necessary if you work with a non-isothermal o
 
 ## <ins> Example implementations: </ins>
 
-* _VanGenuchten_ :
-* _BrooksCorey_ :
+* Available parametrizations for the capillary pressure-saturation relationship are:
+    * _Van Genuchten_
+    * _Brooks Corey_
+
+## Van-Genuchten
+$\begin{equation}
+p_c = \frac{1}{\alpha}\left(S_e^{-1/m} -1\right)^{1/n}
+\end{equation}$
+
+<img src="img/pcgw-sw_VanGenuchten.png" width="500"/>
+
+**--->** Necessary are here the empirical parameters $\alpha$ and $n$.
+
+## Brooks-Corey
+$\begin{equation}
+p_c = p_d S_e^{-1/\lambda}
+\end{equation}$
+
+<img src="img/pc-Sw_BrooksCorey.png" width="500"/>
+
+**--->** Necessary parameters are here the entry pressure $p_d$ and the shape factor $\lambda$.
 
 # Material system: Chemistry
 
@@ -125,10 +138,13 @@ _Specifying a solid system is only necessary if you work with a non-isothermal o
 
 ## <ins> What it does: </ins>
 
-Reactions between different components. There are extra models, usually they are realized with the introduction of a **source term**.
+Reactions between different components. There are extra models or they are realized with the introduction of a source term.
+
+**Note:** _This contains some specific example implementations. One can implement specific things according to their need._
 
 ## <ins> Example implementations: </ins>
-Expresses the **electrochemical models for a fuel cell application**
+Expresses the **electrochemical models for a fuel cell application**:
+
 * _Electrochemistry_ : for isothermal system
 * _Electrochemistryni_ : for non-isothermal system
 
@@ -145,8 +161,8 @@ Expresses the **electrochemical models for a fuel cell application**
 
 ## <ins> Example implementations: </ins>
 
- * _ImmiscibleFluidState_ : assumes immiscibility of the fluid phases. Phase compositions and fugacity coefficients do not need to be stored explicitly
- * _CompositionalFluidState_ : assumes thermodynamic equilibrium, only a single temperature needs to be stored
+ * _ImmiscibleFluidState_ : assumes immiscibility of the fluid phases. Phase compositions and fugacity coefficients do not need to be stored explicitly.
+ * _CompositionalFluidState_ : assumes thermodynamic equilibrium, only a single temperature needs to be stored.
 
 # Material system: Solid state
 
@@ -161,9 +177,9 @@ Expresses the **electrochemical models for a fuel cell application**
 
 ## <ins> Example implementations: </ins>
 
-* _InertSolidState_ : assumes an inert solid phase. Solid volume fractions do not change
+* _InertSolidState_ : assumes an inert solid phase. Solid volume fractions do not change. This is the **default**.
 
-* _CompositionalSolidState_ : assumes a solid matrix composed out of two components. The volume fractions can change and properties such as heat capacity are adapted
+* _CompositionalSolidState_ : assumes a solid matrix composed out of two components. The volume fractions can change and properties such as heat capacity are adapted.
 
 # Material system: Constraint Solver
 
@@ -193,7 +209,7 @@ _CompositionFromFugacities_ : takes all component fugacities, the temperature an
 ## Include headers in properties file: components
 
 ```cpp
-// The two-phase immiscible fluid system
+// The two-phase fluid system for compents water and air
 #include <dumux/material/fluidsystems/h2oair.hh>
 // The water component
 #include <dumux/material/components/h2o.hh>
@@ -204,7 +220,6 @@ _CompositionFromFugacities_ : takes all component fugacities, the temperature an
 ## Specify fluid system in properties file:
 
 ```cpp
-
 template<class TypeTag>
 struct FluidSystem<TypeTag, TTag::H2OAir>
 {
@@ -212,8 +227,10 @@ private:
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
 public:
     using type = FluidSystems::H2OAir<Scalar,
-                 Components::TabulatedComponent<Components::H2O<Scalar>>,
-                 FluidSystems::H2OAirDefaultPolicy</*fastButSimplifiedRelations=*/true>,
+                 Components::TabulatedComponent
+                 <Components::H2O<Scalar>>,
+                 FluidSystems::H2OAirDefaultPolicy
+                 </*fastButSimplifiedRelations=*/true>,
                  true /*useKelvinEquation*/>;
 };
 ```
@@ -236,7 +253,8 @@ struct SolidSystem<TypeTag, TTag::ThermoChem>
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
     using ComponentOne = Components::ModifiedCaO<Scalar>;
     using ComponentTwo = Components::CaO2H2<Scalar>;
-    using type = SolidSystems::CompositionalSolidPhase<Scalar, ComponentOne, ComponentTwo>;
+    using type = SolidSystems::CompositionalSolidPhase
+                 <Scalar, ComponentOne, ComponentTwo>;
 };
 ```