TortuosityMaxwell Class Reference

This class implements transport coefficient corrections appropriate for porous media with a dispersed phase. More...

#include <Tortuosity.h>

Inheritance diagram for TortuosityMaxwell:

Collaboration diagram for TortuosityMaxwell:

Public Member Functions
	TortuosityMaxwell (double relativeConductivites=0.0)
	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	relativeConductivites_
	Relative conductivities of the dispersed and continuous phases, relativeConductivites_ \( = \kappa_d / \kappa_0 \). 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 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, \( \phi \), and the relative conductivities of the dispersed and continuous phases, \( r = \kappa_d / \kappa_0 \). For dilute particle suspensions the effective conductivity is

\[ \kappa / \kappa_0 = 1 + 3 ( 1 - \phi ) ( r - 1 ) / ( r + 2 ) + O(\phi^2) \]

The class is derived from the Tortuosity class.

Definition at line 151 of file Tortuosity.h.

Constructor & Destructor Documentation

TortuosityMaxwell ( double  relativeConductivites = 0.0 )

inline

Default constructor uses Bruggeman exponent of 1.5.

Definition at line 156 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 165 of file Tortuosity.h.

References TortuosityMaxwell::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 179 of file Tortuosity.h.

References TortuosityMaxwell::relativeConductivites_.

Referenced by TortuosityMaxwell::tortuosityFactor().

Member Data Documentation

double relativeConductivites_

protected

Relative conductivities of the dispersed and continuous phases, relativeConductivites_ \( = \kappa_d / \kappa_0 \).

Definition at line 186 of file Tortuosity.h.

Referenced by TortuosityMaxwell::McMillan().

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

• Tortuosity.h