Tortuosity Class Reference

Specific Class to handle tortuosity corrections for diffusive transport in porous media using the Bruggeman exponent. More...

#include <Tortuosity.h>

Inheritance diagram for Tortuosity:

Public Member Functions
	Tortuosity (double setPower=1.5)
	Default constructor uses Bruggeman exponent of 1.5. More...
virtual double	tortuosityFactor (double porosity)
	The tortuosity factor models the effective increase in the diffusive transport length. More...
virtual 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...

Protected Attributes
double	expBrug_
	Bruggeman exponent: power to which the tortuosity depends on the volume fraction. More...

Detailed Description

Specific Class to handle tortuosity corrections for diffusive transport in porous media using the Bruggeman exponent.

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 Bruggeman. The exponent is referred to as the Bruggeman exponent.

Note that the total diffusional flux is generally written as

\[ \frac{ \phi C_T D_i \nabla X_i }{ \tau^2 } \]

where \( \phi \) is the volume fraction of the transported phase, \( \tau \) is referred to as the tortuosity. (Other variables are \( C_T \), the total concentration, \( D_i \), the diffusion coefficient, and \( X_i \), the mole fraction with Fickian transport assumed.)

The tortuosity comes into play in conjunction the the

Definition at line 42 of file Tortuosity.h.

Constructor & Destructor Documentation

Tortuosity ( double  setPower = 1.5 )

inline

Default constructor uses Bruggeman exponent of 1.5.

Definition at line 47 of file Tortuosity.h.

Member Function Documentation

virtual 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 in TortuosityMaxwell, and TortuosityPercolation.

Definition at line 56 of file Tortuosity.h.

References Tortuosity::expBrug_.

virtual 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 in TortuosityMaxwell, and TortuosityPercolation.

Definition at line 70 of file Tortuosity.h.

References Tortuosity::expBrug_.

Member Data Documentation

double expBrug_

protected

Bruggeman exponent: power to which the tortuosity depends on the volume fraction.

Definition at line 76 of file Tortuosity.h.

Referenced by Tortuosity::McMillan(), and Tortuosity::tortuosityFactor().

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

• Tortuosity.h