TortuosityMaxwell Class Reference

Maxwell model for tortuosity. More...

#include <TortuosityMaxwell.h>

Inheritance diagram for TortuosityMaxwell:

Collaboration diagram for TortuosityMaxwell:

Public Member Functions
	TortuosityMaxwell (double relativeConductivites=0.0)
	Default constructor uses Maxwelln exponent of 1.5.
	TortuosityMaxwell (const TortuosityMaxwell &right)
	Copy Constructor.
virtual	~TortuosityMaxwell ()
	Default destructor for TortuosityMaxwell.
TortuosityMaxwell &	operator= (const TortuosityMaxwell &right)
	Assignment operator.
virtual TortuosityBase *	duplMyselfAsTortuosityBase () const
	Duplication operator.
virtual doublereal	tortuosityFactor (doublereal porosity)
	The tortuosity factor models the effective increase in the diffusive transport length.
virtual doublereal	McMillanFactor (doublereal porosity)
	The McMillan number is the ratio of the flux-like variable to the value it would have without porous flow.

Protected Attributes
doublereal	relativeConductivities_
	Relative conductivities of the dispersed and continuous phases,.

Detailed Description

Maxwell model for tortuosity.

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 TortuosityBase class.

Definition at line 41 of file TortuosityMaxwell.h.

Constructor & Destructor Documentation

TortuosityMaxwell

(

double

relativeConductivites = 0.0

)

Default constructor uses Maxwelln exponent of 1.5.

Parameters

setPower

Exponent in the Maxwell factor. The default is 1.5

Definition at line 23 of file TortuosityMaxwell.cpp.

Referenced by TortuosityMaxwell::duplMyselfAsTortuosityBase().

TortuosityMaxwell

(

const TortuosityMaxwell &

right

)

Copy Constructor.

Parameters

right

Object to be copied

Definition at line 33 of file TortuosityMaxwell.cpp.

~TortuosityMaxwell ( )

virtual

Default destructor for TortuosityMaxwell.

Definition at line 41 of file TortuosityMaxwell.cpp.

Member Function Documentation

TortuosityMaxwell & operator=

(

const TortuosityMaxwell &

right

)

Assignment operator.

Parameters

right

Object to be copied

Definition at line 50 of file TortuosityMaxwell.cpp.

References TortuosityBase::operator=(), and TortuosityMaxwell::relativeConductivities_.

TortuosityBase * duplMyselfAsTortuosityBase ( ) const

virtual

Duplication operator.

Returns

Returns a pointer to a duplicate of the current object given a base class pointer

Reimplemented from TortuosityBase.

Definition at line 67 of file TortuosityMaxwell.cpp.

References TortuosityMaxwell::TortuosityMaxwell().

doublereal tortuosityFactor ( doublereal  porosity )

virtual

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

This method returns \( 1/\tau^2 \) in the description of the flux

\( C_T D_i \nabla X_i / \tau^2 \).

Reimplemented from TortuosityBase.

Definition at line 80 of file TortuosityMaxwell.cpp.

References TortuosityMaxwell::McMillanFactor().

doublereal McMillanFactor ( doublereal  porosity )

virtual

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 TortuosityBase.

Definition at line 94 of file TortuosityMaxwell.cpp.

References TortuosityMaxwell::relativeConductivities_.

Referenced by TortuosityMaxwell::tortuosityFactor().

Member Data Documentation

doublereal relativeConductivities_

protected

Relative conductivities of the dispersed and continuous phases,.

\[ \code{relativeConductivites_} = \kappa_d / \kappa_0 \]

Definition at line 106 of file TortuosityMaxwell.h.

Referenced by TortuosityMaxwell::McMillanFactor(), and TortuosityMaxwell::operator=().

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

• TortuosityMaxwell.h
• TortuosityMaxwell.cpp