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TortuosityPercolation Class Reference

This class implements transport coefficient corrections appropriate for porous media where percolation theory applies. More...

#include <Tortuosity.h>

Inheritance diagram for TortuosityPercolation:
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Collaboration diagram for TortuosityPercolation:
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Public Member Functions

 TortuosityPercolation (double percolationThreshold=0.4, double conductivityExponent=2.0)
 Default constructor uses Bruggeman exponent of 1.5. More...
 
double tortuosityFactor (double porosity)
 The tortuosity factor models the effective increase in the diffusive transport length. More...
 
double McMillan (double porosity)
 The McMillan number is the ratio of the flux-like variable to the value it would have without porous flow. More...
 
- Public Member Functions inherited from Tortuosity
 Tortuosity (double setPower=1.5)
 Default constructor uses Bruggeman exponent of 1.5. More...
 

Protected Attributes

double percolationThreshold_
 Critical volume fraction / site density for percolation. More...
 
double conductivityExponent_
 Conductivity exponent. More...
 
- Protected Attributes inherited from Tortuosity
double expBrug_
 Bruggeman exponent: power to which the tortuosity depends on the volume fraction. More...
 

Detailed Description

This class implements transport coefficient corrections appropriate for porous media where percolation theory applies.

It is derived from the Tortuosity class.

Definition at line 86 of file Tortuosity.h.

Constructor & Destructor Documentation

TortuosityPercolation ( double  percolationThreshold = 0.4,
double  conductivityExponent = 2.0 
)
inline

Default constructor uses Bruggeman exponent of 1.5.

Definition at line 91 of file Tortuosity.h.

Member Function Documentation

double tortuosityFactor ( double  porosity)
inlinevirtual

The tortuosity factor models the effective increase in the diffusive transport length.

This method returns \( 1/\tau^2 \) in the description of the flux \( \phi C_T D_i \nabla X_i / \tau^2 \).

Reimplemented from Tortuosity.

Definition at line 100 of file Tortuosity.h.

References TortuosityPercolation::McMillan().

double McMillan ( double  porosity)
inlinevirtual

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 tortuosity 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, \( \kappa_0 \), the conductivity in the porous media would be \( \kappa = (\rm McMillan) \kappa_0 \).

Reimplemented from Tortuosity.

Definition at line 114 of file Tortuosity.h.

References TortuosityPercolation::conductivityExponent_, and TortuosityPercolation::percolationThreshold_.

Referenced by TortuosityPercolation::tortuosityFactor().

Member Data Documentation

double percolationThreshold_
protected

Critical volume fraction / site density for percolation.

Definition at line 122 of file Tortuosity.h.

Referenced by TortuosityPercolation::McMillan().

double conductivityExponent_
protected

Conductivity exponent.

The McMillan number (ratio of effective conductivity to non-porous conductivity) is

\[ \kappa/\kappa_0 = ( \phi - \phi_c )^\mu \]

where \( \mu \) is the conductivity exponent (typical values range from 1.6 to 2.0) and \( \phi_c \) is the percolation threshold.

Definition at line 132 of file Tortuosity.h.

Referenced by TortuosityPercolation::McMillan().


The documentation for this class was generated from the following file: