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

#include <Tortuosity.h>

Inheritance diagram for Tortuosity:

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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.

Attention: This class currently does not have any test cases or examples. Its implementation may be incomplete, and future changes to Cantera may unexpectedly cause this class to stop working. If you use this class, please consider contributing examples or test cases. In the absence of new tests or examples, this class may be deprecated and removed in a future version of Cantera. See https://github.com/Cantera/cantera/issues/267 for additional information.

Deprecated:: To be removed after Cantera 2.4

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.)

Definition at line 46 of file Tortuosity.h.

Constructor & Destructor Documentation

◆ Tortuosity()

Tortuosity ( double setPower = 1.5 )

inline

Default constructor uses Bruggeman exponent of 1.5.

Definition at line 50 of file Tortuosity.h.

Member Function Documentation

◆ tortuosityFactor()

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 59 of file Tortuosity.h.

References Tortuosity::expBrug_.

◆ McMillan()

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 72 of file Tortuosity.h.

References Tortuosity::expBrug_.