Added classes to compute effects of porous flow on species transport.

There are two primary methods in these classes: 

McMillan() that computes the ratio of the porous transport rate 
to the non-porous transport rate.

toruosityFactor() that computes the "tortuosity" component of this 
ratio (the increase in the diffusion length scale).

The base class implements a general Bruggemann formulation and subclasses
implement a percolation theory models and Maxwell's model.  

I did not put in copy constructors, etc., for these calsses yet.

Cantera/src/transport/Makefile.in

@@ -41,7 +41,7 @@ TRAN_OBJ    = TransportFactory.o MultiTransport.o MixTransport.o MMCollisionInt.
 TRAN_H  =  TransportFactory.h MultiTransport.h MixTransport.h \
            MMCollisionInt.h  SolidTransport.h DustyGasTransport.h \
            TransportBase.h L_matrix.h TransportParams.h WaterTransport.h \
-           SimpleTransport.h LiquidTranInteraction.h
+           SimpleTransport.h LiquidTranInteraction.h Tortuosity.h
 
 ifeq ($(do_electro),1)
 do_issp = 1

Cantera/src/transport/Tortuosity.h

@@ -0,0 +1,176 @@
+/** 
+ * @file Tortuosity.h
+ * Class to compute the increase in diffusive path length associated with 
+ * tortuous path diffusion through, for example, porous media.
+ */
+
+namespace Cantera {
+
+/**
+ * Class to compute the increase in diffusive path length associated with 
+ * tortuous path diffusion through, for example, porous media.
+ * This base class implementation relates tortuosity to volume fraction
+ * through a power-law relationship that goes back to Bruggemann.  The 
+ * exponent is referred to as the Bruggemann exponent.
+ * 
+ * Note that the total diffusional flux is generally written as 
+ * 
+ * \f[ 
+ *   \frac{ \phi C_T D_i \nabla X_i }{ \tau^2 } 
+ * \f]
+ * 
+ * where \f$ \phi \f$ is the volume fraction of the transported phase,
+ * \f$ \tau \f$ is referred to as the tortuosity.  (Other variables are 
+ * \f$ C_T \f$, the total concentration, \f$ D_i \f$, the diffusion 
+ * coefficient, and \f$ X_i \f$, the mole fraction with Fickian 
+ * transport assumed.)
+ *
+ * The tortuosity comes into play in conjunction the the 
+
+ */
+  class Tortuosity {
+    
+  public: 
+    //! Default constructor uses Bruggemann exponent of 1.5 
+    Tortuosity( double setPower = 1.5 ) : expBrug_(setPower) {
+    }
+    
+    //! The tortuosity factor models the effective increase in the
+    //! diffusive transport length.
+    /** 
+     * This method returns \f$ 1/\tau^2 \f$ in the description of the 
+     * flux \f$ \phi C_T D_i \nabla X_i / \tau^2 \f$.  
+     */ 
+    virtual double toruosityFactor( double porosity ) { 
+      return pow( porosity, expBrug_ - 1.0 );
+    }
+
+    //! The McMillan number is the ratio of the flux-like 
+    //! variable to the value it would have without porous flow.
+    /** 
+     * The McMillan number combines the effect of toruosity 
+     * and volume fraction of the transported phase.  The net flux
+     * observed is then the product of the McMillan number and the 
+     * non-porous transport rate.  For a conductivity in a non-porous 
+     * media, \f$ \kappa_0 \f$, the conductivity in the porous media
+     * would be \f$ \kappa = (\rm McMillan) \kappa_0 \f$.
+     */
+    virtual double McMillan( double porosity ) { 
+      return pow( porosity, expBrug_  );
+    }
+    
+  protected:
+    //! Bruggemann exponent: power to which the tortuosity depends on the volume fraction 
+    double expBrug_ ;
+    
+  };
+    
+
+
+  /** This class implements transport coefficient corrections 
+   * appropriate for porous media where percollation theory applies.
+   * It is derived from the Tortuosity class.
+   */
+    class TortuosityPercolation : public  Tortuosity  {
+      
+    public: 
+      //! Default constructor uses Bruggemann exponent of 1.5 
+      TortuosityPercolation( double percolationThreshold = 0.4, double conductivityExponent = 2.0 ) : percolationThreshold_(percolationThreshold), conductivityExponent_(conductivityExponent)  {
+      }
+
+      //! The tortuosity factor models the effective increase in the
+      //! diffusive transport length.
+      /** 
+       * This method returns \f$ 1/\tau^2 \f$ in the description of the 
+       * flux \f$ \phi C_T D_i \nabla X_i / \tau^2 \f$.  
+       */ 
+      double toruosityFactor( double porosity ) { 
+	return McMillan( porosity ) / porosity;
+      }
+      
+      //! The McMillan number is the ratio of the flux-like 
+      //! variable to the value it would have without porous flow.
+      /** 
+       * The McMillan number combines the effect of toruosity 
+       * and volume fraction of the transported phase.  The net flux
+       * observed is then the product of the McMillan number and the 
+       * non-porous transport rate.  For a conductivity in a non-porous 
+       * media, \f$ \kappa_0 \f$, the conductivity in the porous media
+       * would be \f$ \kappa = (\rm McMillan) \kappa_0 \f$.
+       */
+      double McMillan( double porosity ) { 
+	return pow( ( porosity - percolationThreshold_ )
+		    / ( 1.0 - percolationThreshold_ ), 
+		    conductivityExponent_  );
+      }
+      
+    protected:
+      //! Critical volume fraction / site density for percolation
+      double percolationThreshold_;
+      //! Conductivity exponent
+      /**
+       * The McMillan number (ratio of effective conductivity 
+       * to non-porous conductivity) is 
+       * \f[ \kappa/\kappa_0 = ( \phi - \phi_c )^\mu \f]
+       * where \f$ \mu \f$ is the conductivity exponent (typical
+       * values range from 1.6 to 2.0) and \f$ \phi_c \f$
+       * is the percolation threshold.
+       */
+      double conductivityExponent_;
+    };
+
+
+
+  /** This class implements transport coefficient corrections 
+   * appropriate for porous media with a dispersed phase.
+   * This model goes back to Maxwell.  The formula for the 
+   * conductivity is expressed in terms of the volume fraction
+   * of the continuous phase, \f$ \phi \f$, and the relative 
+   * conductivities of the dispersed and continuous phases, 
+   * \f$ r = \kappa_d / \kappa_0 \f$.  For dilute particle
+   * suspensions the effective conductivity is 
+   * \f[ 
+   *    \kappa / \kappa_0 = 1 + 3 ( 1 - \phi ) ( r - 1 ) / ( r + 2 ) 
+   *                        + O(\phi^2)
+   * \f]  
+   * The class is derived from the Tortuosity class.
+   */
+    class TortuosityMaxwell : public Tortuosity {
+      
+    public: 
+      //! Default constructor uses Bruggemann exponent of 1.5 
+      TortuosityMaxwell( double relativeConductivites = 0.0 ) : relativeConductivites_(relativeConductivites)  {
+      }
+
+      //! The tortuosity factor models the effective increase in the
+      //! diffusive transport length.
+      /** 
+       * This method returns \f$ 1/\tau^2 \f$ in the description of the 
+       * flux \f$ \phi C_T D_i \nabla X_i / \tau^2 \f$.  
+       */ 
+      double toruosityFactor( double porosity ) { 
+	return McMillan( porosity ) / porosity;
+      }
+      
+      //! The McMillan number is the ratio of the flux-like 
+      //! variable to the value it would have without porous flow.
+      /** 
+       * The McMillan number combines the effect of toruosity 
+       * and volume fraction of the transported phase.  The net flux
+       * observed is then the product of the McMillan number and the 
+       * non-porous transport rate.  For a conductivity in a non-porous 
+       * media, \f$ \kappa_0 \f$, the conductivity in the porous media
+       * would be \f$ \kappa = (\rm McMillan) \kappa_0 \f$.
+       */
+      double McMillan( double porosity ) { 
+	return 1 + 3 * ( 1.0 - porosity ) * ( relativeConductivites_ - 1.0 ) / ( relativeConductivites_ + 2 );
+      }
+      
+    protected:
+      //! Relative  conductivities of the dispersed and continuous phases, 
+      //! \code{relativeConductivites_}\f$  = \kappa_d / \kappa_0 \f$.
+      double relativeConductivites_;
+
+    };
+
+}