Cantera  2.0
TortuosityMaxwell.h
1 /**
2  * @file TortuosityBase.h
3  * Virtual base class to compute the increase in diffusive path length associated with
4  * tortuous path diffusion through, for example, porous media.
5  */
6 
7 /*
8  * Copyright (2005) Sandia Corporation. Under the terms of
9  * Contract DE-AC04-94AL85000 with Sandia Corporation, the
10  * U.S. Government retains certain rights in this software.
11  */
12 
13 #ifndef CT_TORTUOSITYBRUGGEMAN_H
14 #define CT_TORTUOSITYBRUGGEMAN_H
15 
16 #include "TortuosityBase.h"
17 
18 namespace Cantera
19 {
20 
21 //! Maxwell model for tortuosity
22 /*!
23  *
24  * This class implements transport coefficient corrections
25  * appropriate for porous media with a dispersed phase.
26  * This model goes back to Maxwell. The formula for the
27  * conductivity is expressed in terms of the volume fraction
28  * of the continuous phase, \f$ \phi \f$, and the relative
29  * conductivities of the dispersed and continuous phases,
30  * \f$ r = \kappa_d / \kappa_0 \f$. For dilute particle
31  * suspensions the effective conductivity is
32  *
33  * \f[
34  * \kappa / \kappa_0 = 1 + 3 ( 1 - \phi ) ( r - 1 ) / ( r + 2 )
35  * + O(\phi^2)
36  * \f]
37  *
38  * The class is derived from the TortuosityBase class.
39  *
40  */
42 {
43 
44 public:
45  //! Default constructor uses Maxwelln exponent of 1.5
46  /*!
47  * @param setPower Exponent in the Maxwell factor. The default is 1.5
48  */
49  TortuosityMaxwell(double relativeConductivites = 0.0);
50 
51  //! Copy Constructor
52  /*!
53  * @param right Object to be copied
54  */
56 
57  //! Default destructor for TortuosityMaxwell
58  virtual ~TortuosityMaxwell();
59 
60  //! Assignment operator
61  /*!
62  * @param right Object to be copied
63  */
65 
66  //! Duplication operator
67  /*!
68  * @return Returns a pointer to a duplicate of the current object given a
69  * base class pointer
70  */
72 
73  //! The tortuosity factor models the effective increase in the
74  //! diffusive transport length.
75  /*!
76  * This method returns \f$ 1/\tau^2 \f$ in the description of the flux
77  *
78  * \f$ C_T D_i \nabla X_i / \tau^2 \f$.
79  *
80  *
81  */
82  virtual doublereal tortuosityFactor(doublereal porosity);
83 
84  //! The McMillan number is the ratio of the flux-like
85  //! variable to the value it would have without porous flow.
86  /**
87  * The McMillan number combines the effect of tortuosity
88  * and volume fraction of the transported phase. The net flux
89  * observed is then the product of the McMillan number and the
90  * non-porous transport rate. For a conductivity in a non-porous
91  * media, \f$ \kappa_0 \f$, the conductivity in the porous media
92  * would be \f$ \kappa = (\rm McMillan) \kappa_0 \f$.
93  */
94  virtual doublereal McMillanFactor(doublereal porosity);
95 
96 
97 protected:
98 
99  //! Relative conductivities of the dispersed and continuous phases,
100  /*!
101  *
102  * \f[
103  * \code{relativeConductivites_} = \kappa_d / \kappa_0
104  * \f]
105  */
107 
108 };
109 
110 
111 
112 }
113 
114 #endif
115