diff --git a/CHANGELOG.md b/CHANGELOG.md
index a6907a3b8b293089ac8d66184cd8ad7517b44a47..0bae5e80654a04e0f4eb06df0238b26d5b32c11f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,8 @@ Differences Between DuMuX 2.9 and DuMuX 2.10
 * IMPROVEMENTS and ENHANCEMENTS:
     - Integrated geostatistical tool gstat for generating random fields
     - multidomain should now work with all compilers (optimzed) without segfaults
+    - The computation of the tortuosity tau with the Millington Quirk model
+      was optimized. Tests show an speedup of up to 5% for a 2p2c simulation.
 
 * IMMEDIATE INTERFACE CHANGES not allowing/requiring a deprecation period:
     - The problem class interface needs to provide the method maxTimeStepSize().
@@ -23,8 +25,13 @@ Differences Between DuMuX 2.9 and DuMuX 2.10
   compiler will not print any warning if a deprecated property or parameter name
   is used. However, a run-time warning should appear in the summary lines after
   the corresponding run.
+    - The property tau was renamed to TauTortuosity to make the name more telling.
+      For the models 1p2c, 2p2c, 3p3c it got the default value 0.5.
 
 * Deprecated CLASSES/FILES, to be removed after 2.10:
+    - The class `DiffusivityConstantTau<TypeTag, Scalar>` was renamed to
+      `DiffusivityConstant<TypeTag>` and is located in a according new header. The
+      old class, its header and the property `tau` are deprecated.
 
 * Deprecated MEMBER FUNCTIONS, to be removed after 2.10:
 
diff --git a/doc/handbook/dumux-handbook.bib b/doc/handbook/dumux-handbook.bib
index 96c774ad67a619366d702408a34f3f11d73adec4..0f0cb3089a3923351d191ef686225e9c81b73895 100644
--- a/doc/handbook/dumux-handbook.bib
+++ b/doc/handbook/dumux-handbook.bib
@@ -193,6 +193,15 @@
   year = {2007}
 }
 
+@BOOK{BEAR1972,
+  title = {Dynamics of Fluids in Porous Media},
+  author = {Bear, Jacob},
+  isbn = {9780486656755},
+  series = {Dover Civil and Mechanical Engineering Series},
+  year = {1972},
+  publisher = {Dover}
+}
+
 @BOOK{BASTIAN1999,
   title = {{Numerical Computation of Multiphase Flows in Porous Media}},
   publisher = {Habilitationsschrift, University of Kiel},
@@ -339,6 +348,18 @@
   publisher = {Springer}
 }
 
+@ARTICLE{CARMAN1937,
+  author = {Carman, Philip C.},
+  title = {Fluid flow through granular beds},
+  journal = {Transactions, Institution of Chemical Engineers},
+  year = {1937},
+  volume = {15},
+  pages = {150--166},
+  number = {},
+  doi = {10.1016/S0263-8762(97)80003-2},
+  note = {reprinted in \emph{Chemical Engineering Research and Design}, 75:S32--S48, 1997}
+}
+
 @ARTICLE{Chen2000,
   author = {Z. Chen and Q. Guan and R. E. Ewing},
   title = {{Analysis of a compositional model for fluid flow in porous media},
@@ -347,20 +368,7 @@
   volume = {60},
   pages = {747-777},
   number = {3},
-  owner = {faigle},
-  review = {3phase model derivation finite element discretizattion Beschreibung
-	des sequenziellen numerischen L\"osungsschemas verwendete ELLAM methode
-
-
-	Trangenstein + pC
-
-
-	assumpt: no mass transfer between water and gas/oil (black oil)
-
-	rho_w = const
-
-	s(p, ...) und nicht s(p+pc, ...)},
-  timestamp = {2011.11.29}
+  owner = {faigle}
 }
 
 @BOOK{CLASS2007,
@@ -862,6 +870,18 @@
   url={https://www.osti.gov/scitech/biblio/6760030}
 }
 
+@Article{MILLINGTON1961,
+author ={Millington, R. J. and Quirk, J. P.},
+title  ={Permeability of porous solids},
+journal  ={Trans. Faraday Soc.},
+year  ={1961},
+volume  ={57},
+issue  ={0},
+pages  ={1200--1207},
+doi  ={10.1039/TF9615701200}
+}
+
+
 @ARTICLE{MUALEM1976,
   author = {Y. Mualem},
   title = {{A new model for predicting the hydraulic conductivity of unsaturated
diff --git a/dumux/material/fluidmatrixinteractions/CMakeLists.txt b/dumux/material/fluidmatrixinteractions/CMakeLists.txt
index 2454da31dc0025c2780a24c2aa3dbd44a20ccb79..80442427bc50024fcdc3b3dfbdc1f2435edc9acc 100644
--- a/dumux/material/fluidmatrixinteractions/CMakeLists.txt
+++ b/dumux/material/fluidmatrixinteractions/CMakeLists.txt
@@ -6,6 +6,7 @@ add_subdirectory("mp")
 
 #install headers
 install(FILES
+diffusivityconstant.hh
 diffusivityconstanttau.hh
 diffusivitymillingtonquirk.hh
 DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/material/fluidmatrixinteractions)
diff --git a/dumux/material/fluidmatrixinteractions/diffusivityconstant.hh b/dumux/material/fluidmatrixinteractions/diffusivityconstant.hh
new file mode 100644
index 0000000000000000000000000000000000000000..c3f58a4d9f1249310d0749805ecd07e14ddf69e1
--- /dev/null
+++ b/dumux/material/fluidmatrixinteractions/diffusivityconstant.hh
@@ -0,0 +1,73 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 2 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ *
+ * \brief   Relation for the saturation-dependent effective diffusion coefficient
+ */
+#ifndef DIFFUSIVITY_CONSTANT_HH
+#define DIFFUSIVITY_CONSTANT_HH
+
+#include <dumux/common/parameters.hh>
+#include <dumux/common/basicproperties.hh>
+
+namespace Dumux
+{
+/*!
+ * \ingroup fluidmatrixinteractionslaws
+ *
+ * \brief Relation for the saturation-dependent effective diffusion coefficient
+ *
+ * The material law is:
+ * \f[
+ *  D_\text{eff,pm} = \phi * S_w * \tau * D
+ * \f]
+ *
+ * with a constant tau.
+ *
+ * The default value is 0.5, empirically obtained in Carman 1937:
+ * <i>Fluid flow through granular beds</i> \cite carman1937
+ * Additionally, Bear 1972 \cite bear1972 mentions values 0.4 and in the
+ * range of 0.56 to 0.8.
+ */
+template<class TypeTag>
+class DiffusivityConstant
+{
+    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+public:
+    /*!
+     * \brief Returns the effective diffusion coefficient \f$\mathrm{[m^2/s]}\f$ based
+     *        on a constant tortuosity value
+     *
+     * \param porosity The porosity
+     * \param saturation The saturation of the wetting phase
+     * \param diffCoeff The diffusion coefficient of the phase in \f$\mathrm{[m^2/s]}\f$
+     */
+    static Scalar effectiveDiffusivity(const Scalar porosity,
+                                       const Scalar saturation,
+                                       const Scalar diffCoeff)
+
+    {
+        Scalar tau = GET_PARAM(TypeTag, Scalar, TauTortuosity);
+
+        return porosity * saturation * tau * diffCoeff;
+    }
+};
+}
+#endif // DIFFUSIVITY_CONSTANT_HH
diff --git a/dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh b/dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh
index 805a5a1662826ea1c26423a55c116f4e211b0d66..92204bbad0e0b48c27c111c1504cfb952901e928 100644
--- a/dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh
+++ b/dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh
@@ -44,6 +44,9 @@ namespace Dumux
  *  \tau = \frac{1}{\phi^2} * \left(\phi S_w\right)^{7/3}
  * \f]
  *
+ * after Millington and Quirk 1961: <i>Permeability of porous solids</i> \cite millington1961
+ * and Helmig 1997: <i>Multiphase Flow and Transport Processes in the Subsurface: A Contribution
+ * to the Modeling of Hydrosystems</i>, page 129 \cite helmig1997
  */
 template<class Scalar>
 class DiffusivityMillingtonQuirk
diff --git a/dumux/porousmediumflow/1p2c/implicit/properties.hh b/dumux/porousmediumflow/1p2c/implicit/properties.hh
index 7736c97a54fc17f4885b886193285e41ce30df05..84848a997d26c5f76f1b064593ae5b090eef3fe6 100644
--- a/dumux/porousmediumflow/1p2c/implicit/properties.hh
+++ b/dumux/porousmediumflow/1p2c/implicit/properties.hh
@@ -72,6 +72,7 @@ NEW_PROP_TAG(ProblemEnableGravity); //!< Returns whether gravity is considered i
 NEW_PROP_TAG(UseMoles); //!< Defines whether mole (true) or mass (false) fractions are used
 NEW_PROP_TAG(Scaling); //!< Defines Scaling of the model
 NEW_PROP_TAG(SpatialParamsForchCoeff); //!< Property for the forchheimer coefficient
+NEW_PROP_TAG(TauTortuosity); //!< Tortuosity value (tau) used in macroscopic diffusion
 NEW_PROP_TAG(VtkAddVelocity); //!< Returns whether velocity vectors are written into the vtk output
 
 }
diff --git a/dumux/porousmediumflow/1p2c/implicit/propertydefaults.hh b/dumux/porousmediumflow/1p2c/implicit/propertydefaults.hh
index 355dbc51ed7cf547c1c9cc862c63a14d578d22ce..3bfa3bc08cc321bd3f35c60f5e599845056b4b66 100644
--- a/dumux/porousmediumflow/1p2c/implicit/propertydefaults.hh
+++ b/dumux/porousmediumflow/1p2c/implicit/propertydefaults.hh
@@ -120,6 +120,14 @@ SET_BOOL_PROP(OnePTwoC, ProblemEnableGravity, true);
 //        (Nield, Bejan, Convection in porous media, 2006, p. 10)
 SET_SCALAR_PROP(OnePTwoC, SpatialParamsForchCoeff, 0.55);
 
+/*!
+ * \brief default value for tortuosity value (tau) used in macroscopic diffusion
+ *
+ * Value is 0.5 according to Carman 1937: <i>Fluid flow through granular beds</i>
+ * \cite carman1937
+ */
+SET_SCALAR_PROP(OnePTwoC, TauTortuosity, 0.5);
+
 //! average is used as default model to compute the effective thermal heat conductivity
 SET_PROP(OnePTwoCNI, ThermalConductivityModel)
 { private :
diff --git a/dumux/porousmediumflow/2p2c/implicit/properties.hh b/dumux/porousmediumflow/2p2c/implicit/properties.hh
index 3f8da55d769ff86a09c5e39c27bffaeb87eb5b2d..aa494f5df69d08fc616179888ae60665c5589f39 100644
--- a/dumux/porousmediumflow/2p2c/implicit/properties.hh
+++ b/dumux/porousmediumflow/2p2c/implicit/properties.hh
@@ -79,6 +79,7 @@ NEW_PROP_TAG(ReplaceCompEqIdx); //!< The index of the total mass balance equatio
 NEW_PROP_TAG(VtkAddVelocity); //!< Returns whether velocity vectors are written into the VTK output
 NEW_PROP_TAG(BaseFluxVariables); //!< The base flux variables
 NEW_PROP_TAG(SpatialParamsForchCoeff); //!< Property for the forchheimer coefficient
+NEW_PROP_TAG(TauTortuosity); //!< Tortuosity value (tau) used in macroscopic diffusion
 }
 }
 
diff --git a/dumux/porousmediumflow/2p2c/implicit/propertydefaults.hh b/dumux/porousmediumflow/2p2c/implicit/propertydefaults.hh
index 032145d8647f9b28492f8078ed6d7f6f04097a42..23653d9a0c0a6436dede94627edb1c2711250906 100644
--- a/dumux/porousmediumflow/2p2c/implicit/propertydefaults.hh
+++ b/dumux/porousmediumflow/2p2c/implicit/propertydefaults.hh
@@ -184,6 +184,14 @@ SET_BOOL_PROP(TwoPTwoC, UseConstraintSolver, true);
 //        (Nield, Bejan, Convection in porous media, 2006, p. 10)
 SET_SCALAR_PROP(TwoPTwoC, SpatialParamsForchCoeff, 0.55);
 
+/*!
+ * \brief default value for tortuosity value (tau) used in macroscopic diffusion
+ *
+ * Value is 0.5 according to Carman 1937: <i>Fluid flow through granular beds</i>
+ * \cite carman1937
+ */
+SET_SCALAR_PROP(TwoPTwoC, TauTortuosity, 0.5);
+
 //! Somerton is used as default model to compute the effective thermal heat conductivity
 SET_PROP(TwoPTwoCNI, ThermalConductivityModel)
 {
diff --git a/dumux/porousmediumflow/3p3c/implicit/properties.hh b/dumux/porousmediumflow/3p3c/implicit/properties.hh
index 52a2762e8cc94ecfa98f31174dd919fe722abd56..f4760715f8e0825b0e73a901030aebce57f2fae2 100644
--- a/dumux/porousmediumflow/3p3c/implicit/properties.hh
+++ b/dumux/porousmediumflow/3p3c/implicit/properties.hh
@@ -75,6 +75,7 @@ NEW_PROP_TAG(ImplicitMobilityUpwindWeight); //!< Weight for the upwind mobility
 NEW_PROP_TAG(UseConstraintSolver); //!< Determines whether a constraint solver should be used explicitly
 NEW_PROP_TAG(BaseFluxVariables); //! The base flux variables
 NEW_PROP_TAG(SpatialParamsForchCoeff); //!< Property for the forchheimer coefficient
+NEW_PROP_TAG(TauTortuosity); //!< Tortuosity value (tau) used in macroscopic diffusion
 NEW_PROP_TAG(VtkAddVelocity); //!< Returns whether velocity vectors are written into the vtk output
 }
 }
diff --git a/dumux/porousmediumflow/3p3c/implicit/propertydefaults.hh b/dumux/porousmediumflow/3p3c/implicit/propertydefaults.hh
index 020072e7800e0c94a057511536a5711536af1597..43b4f098aa1e0ffdb69cca8561d8f8982dbef751 100644
--- a/dumux/porousmediumflow/3p3c/implicit/propertydefaults.hh
+++ b/dumux/porousmediumflow/3p3c/implicit/propertydefaults.hh
@@ -163,6 +163,14 @@ SET_BOOL_PROP(ThreePThreeC, ProblemEnableGravity, true);
 //        (Nield, Bejan, Convection in porous media, 2006, p. 10)
 SET_SCALAR_PROP(BoxModel, SpatialParamsForchCoeff, 0.55);
 
+/*!
+ * \brief default value for tortuosity value (tau) used in macroscopic diffusion
+ *
+ * Value is 0.5 according to Carman 1937: <i>Fluid flow through granular beds</i>
+ * \cite carman1937
+ */
+SET_SCALAR_PROP(ThreePThreeC, TauTortuosity, 0.5);
+
 //! Somerton is used as default model to compute the effective thermal heat conductivity
 SET_PROP(ThreePThreeCNI, ThermalConductivityModel)
 {
diff --git a/test/material/fluidmatrixinteractions/CMakeLists.txt b/test/material/fluidmatrixinteractions/CMakeLists.txt
index b8d2e9804ab554c3016c23e2afd84a4d9d6e126f..59815434cd1311c0c63618b7bed02ee2f0bffe36 100644
--- a/test/material/fluidmatrixinteractions/CMakeLists.txt
+++ b/test/material/fluidmatrixinteractions/CMakeLists.txt
@@ -9,6 +9,13 @@ add_dumux_test(test_effectivediffusivitymillingtonquirk test_effectivediffusivit
                          ${CMAKE_CURRENT_BINARY_DIR}/millingtonquirk_d_eff.dat
                  --command "${CMAKE_CURRENT_BINARY_DIR}/test_effectivediffusivitymillingtonquirk")
 
+add_dumux_test(test_effectivediffusivityconstant test_effectivediffusivityconstant test_effectivediffusivityconstant.cc
+              python ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+                 --script exact
+                 --files ${CMAKE_SOURCE_DIR}/test/references/effectivediffusivityconstanttau-reference.dat
+                         ${CMAKE_CURRENT_BINARY_DIR}/constant_d_eff.dat
+                 --command "${CMAKE_CURRENT_BINARY_DIR}/test_effectivediffusivityconstant")
+
 add_dumux_test(test_effectivediffusivityconstanttau test_effectivediffusivityconstanttau test_effectivediffusivityconstanttau.cc
               python ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
                  --script exact
diff --git a/test/material/fluidmatrixinteractions/effectivediffusivityconstantproblem.hh b/test/material/fluidmatrixinteractions/effectivediffusivityconstantproblem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..d08b43e34a6814400637383bf961b8a9d1813def
--- /dev/null
+++ b/test/material/fluidmatrixinteractions/effectivediffusivityconstantproblem.hh
@@ -0,0 +1,216 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 2 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ *
+ * \brief Test for the constant tau effective diffusivity model
+ */
+#ifndef DUMUX_EFFECTIVE_DIFFUSIVITY_CONSTANT_PROBLEM_HH
+#define DUMUX_EFFECTIVE_DIFFUSIVITY_CONSTANT_PROBLEM_HH
+
+#include <dumux/material/fluidsystems/h2on2.hh>
+
+#include <dumux/porousmediumflow/2p2c/implicit/model.hh>
+#include <dumux/porousmediumflow/implicit/problem.hh>
+#include <dumux/material/fluidmatrixinteractions/diffusivityconstant.hh>
+
+#include "effectivediffusivityspatialparams.hh"
+
+#define ISOTHERMAL 0
+
+namespace Dumux
+{
+template <class TypeTag>
+class EffectiveDiffusivityConstantProblem;
+
+namespace Properties
+{
+NEW_TYPE_TAG(EffectiveDiffusivityConstantProblem, INHERITS_FROM(BoxModel, TwoPTwoCNI, EffectiveDiffusivitySpatialParams));
+
+// Set the grid type
+SET_TYPE_PROP(EffectiveDiffusivityConstantProblem, Grid, Dune::YaspGrid<2>);
+
+// Set the problem property
+SET_TYPE_PROP(EffectiveDiffusivityConstantProblem, Problem, EffectiveDiffusivityConstantProblem<TypeTag>);
+
+// Set the wetting phase
+SET_TYPE_PROP(EffectiveDiffusivityConstantProblem, FluidSystem, FluidSystems::H2ON2<typename GET_PROP_TYPE(TypeTag, Scalar), false>);
+
+// Set thermal conductivity law
+SET_TYPE_PROP(EffectiveDiffusivityConstantProblem, EffectiveDiffusivityModel,
+              DiffusivityConstant<TypeTag>);
+}
+
+
+/*!
+ * \ingroup MaterialTestProblems
+ *
+ * \brief Test for the constant tau effective diffusivity model
+ *
+ * To run the test execute the following line in shell:
+ * <tt>./test_effectivediffusivityconstant</tt>
+ *
+ */
+template <class TypeTag >
+class EffectiveDiffusivityConstantProblem : public ImplicitPorousMediaProblem<TypeTag>
+{
+    typedef typename GET_PROP_TYPE(TypeTag, Scalar) Scalar;
+    typedef typename GET_PROP_TYPE(TypeTag, GridView) GridView;
+    typedef typename GridView::Grid Grid;
+
+    typedef ImplicitPorousMediaProblem<TypeTag> ParentType;
+    typedef typename GET_PROP_TYPE(TypeTag, FluidSystem) FluidSystem;
+
+    // copy some indices for convenience
+    typedef typename GET_PROP_TYPE(TypeTag, Indices) Indices;
+    enum {
+        pressureIdx = Indices::pressureIdx,
+        switchIdx = Indices::switchIdx,
+        temperatureIdx = Indices::temperatureIdx,
+
+        // Phase State
+        wPhaseOnly = Indices::wPhaseOnly,
+
+        // Grid and world dimension
+        dim = GridView::dimension,
+        dimWorld = GridView::dimensionworld
+    };
+
+    typedef typename GET_PROP_TYPE(TypeTag, PrimaryVariables) PrimaryVariables;
+    typedef typename GET_PROP_TYPE(TypeTag, BoundaryTypes) BoundaryTypes;
+    typedef typename GET_PROP_TYPE(TypeTag, TimeManager) TimeManager;
+
+    typedef typename GridView::template Codim<0>::Entity Element;
+    typedef typename GridView::template Codim<dim>::Entity Vertex;
+    typedef typename GridView::Intersection Intersection;
+
+    typedef typename GET_PROP_TYPE(TypeTag, FVElementGeometry) FVElementGeometry;
+
+    typedef Dune::FieldVector<Scalar, dimWorld> GlobalPosition;
+
+    //! property that defines whether mole or mass fractions are used
+    static const bool useMoles = GET_PROP_VALUE(TypeTag, UseMoles);
+
+public:
+    /*!
+     * \brief The constructor.
+     *
+     * \param timeManager The time manager
+     * \param gridView The grid view
+     */
+    EffectiveDiffusivityConstantProblem(TimeManager &timeManager, const GridView &gridView)
+        : ParentType(timeManager, gridView)
+    {
+        FluidSystem::init();
+        this->spatialParams().plotMaterialLaw();
+    }
+
+    /*!
+     * \name Problem parameters
+     */
+    // \{
+
+    /*!
+     * \brief The problem name.
+     *
+     * This is used as a prefix for files generated by the simulation.
+     */
+    const std::string name() const
+    { return "test_effectivediffusivity_ct"; }
+
+
+    //! \copydoc ImplicitProblem::sourceAtPos()
+    void sourceAtPos(PrimaryVariables &values,
+                     const GlobalPosition &globalPos) const
+    {
+        values = 0;
+    }
+
+    // \}
+
+    /*!
+     * \name Boundary conditions
+     */
+    // \{
+
+
+    //! \copydoc ImplicitProblem::boundaryTypesAtPos()
+    void boundaryTypesAtPos(BoundaryTypes &values,
+                            const GlobalPosition &globalPos) const
+    {
+        values.setAllDirichlet();
+    }
+
+
+    //! \copydoc ImplicitProblem::dirichletAtPos()
+    void dirichletAtPos(PrimaryVariables &values, const GlobalPosition &globalPos) const
+    {
+        initial_(values, globalPos);
+    }
+
+
+    //! \copydoc ImplicitProblem::neumann()
+    void neumann(PrimaryVariables &values,
+                 const Element &element,
+                 const FVElementGeometry &fvGeometry,
+                 const Intersection &intersection,
+                 const int scvIdx,
+                 const int boundaryFaceIdx) const
+    {
+        values = 0;
+    }
+
+    // \}
+
+    /*!
+     * \name Volume terms
+     */
+    // \{
+
+
+    //! \copydoc ImplicitProblem::initialAtPos()
+    void initialAtPos(PrimaryVariables &values, const GlobalPosition &globalPos) const
+    {
+        initial_(values, globalPos);
+    }
+
+
+    //! \copydoc InjectionProblem::initialPhasePresence()
+    int initialPhasePresence(const Vertex &vertex,
+                             int &vIdxGlobal,
+                             const GlobalPosition &globalPos) const
+    {
+        return wPhaseOnly;
+    }
+
+private:
+    // internal method for the initial condition (reused for the
+    // dirichlet conditions!)
+    void initial_(PrimaryVariables &values,
+                  const GlobalPosition &globalPos) const
+    {
+        Scalar densityW = 1000.0;
+        values[pressureIdx] = 1e5 + globalPos[1]*densityW*9.81;
+        values[switchIdx] = 0.0;
+        values[temperatureIdx] = 283.0 + globalPos[1]*0.03;
+    }
+};
+} //end namespace
+
+#endif
diff --git a/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.cc b/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.cc
new file mode 100644
index 0000000000000000000000000000000000000000..c24548f156a5c66dc7951bb2512f2c84e57b1532
--- /dev/null
+++ b/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.cc
@@ -0,0 +1,56 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 2 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ *
+ * \brief Test for the constant tau effective diffusivity model
+ */
+#include <config.h>
+#include "effectivediffusivityconstantproblem.hh"
+#include <dumux/common/start.hh>
+
+/*!
+ * \brief Provides an interface for customizing error messages associated with
+ *        reading in parameters.
+ *
+ * \param progName  The name of the program, that was tried to be started.
+ * \param errorMsg  The error message that was issued by the start function.
+ *                  Comprises the thing that went wrong and a general help message.
+ */
+void usage(const char *progName, const std::string &errorMsg)
+{
+    if (errorMsg.size() > 0) {
+        std::string errorMessageOut = "\nUsage: ";
+                    errorMessageOut += progName;
+                    errorMessageOut += " [options]\n";
+                    errorMessageOut += errorMsg;
+                    errorMessageOut += "\n\nThe list of mandatory options for this program is:\n"
+                                        "\t-TimeManager.TEnd      End of the simulation [s] \n"
+                                        "\t-TimeManager.DtInitial Initial timestep size [s] \n"
+                                        "\t                       definition in DGF format\n";
+
+        std::cout << errorMessageOut
+                  << "\n";
+    }
+}
+
+int main(int argc, char** argv)
+{
+    return Dumux::start<TTAG(EffectiveDiffusivityConstantProblem)>(argc, argv, usage);
+}
diff --git a/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.input b/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.input
new file mode 100644
index 0000000000000000000000000000000000000000..92d3655a0496e544dac90d8a1ed1d04476d49eef
--- /dev/null
+++ b/test/material/fluidmatrixinteractions/test_effectivediffusivityconstant.input
@@ -0,0 +1,13 @@
+[TimeManager]
+DtInitial = 1 # [s]
+TEnd = 2 # [s]
+
+[Grid]
+UpperRight = 6 4
+Cells = 48 32
+
+[Diffusivity]
+File = constant
+
+[]
+TauTortuosity = 0.3