Mixing rule using logarithms of the mole fractions. More...

#include <LiquidTranInteraction.h>

Inheritance diagram for LTI_Log_MoleFracs:

Collaboration diagram for LTI_Log_MoleFracs:

Public Member Functions
	LTI_Log_MoleFracs (TransportPropertyType tp_ind=TP_UNKNOWN)

virtual	~LTI_Log_MoleFracs ()
	Copy constructor.

doublereal	getMixTransProp (doublereal valueSpecies, doublereal weightSpecies=0)
	Return the mixture transport property value.

doublereal	getMixTransProp (std::vector< LTPspecies * > LTPptrs)

void	getMatrixTransProp (DenseMatrix &mat, doublereal *speciesValues=0)
	Return the matrix of binary interaction parameters.

virtual void	init (const XML_Node &compModelNode=0, thermo_t *thermo=0)
	initialize LiquidTranInteraction objects with thermo and XML node

virtual void	setParameters (LiquidTransportParams &trParam)

Protected Attributes
LiquidTranMixingModel	m_model
	Model for species interaction effects Takes enum LiquidTranMixingModel.

TransportPropertyType	m_property
	enum indicating what property this is (i.e viscosity)

thermo_t *	m_thermo
	pointer to thermo object to get current temperature

std::vector< DenseMatrix * >	m_Aij
	Matrix of interaction coefficients for polynomial in molefraction*weight of speciesA (no temperature dependence, dimensionless)

std::vector< DenseMatrix * >	m_Bij
	Matrix of interaction coefficients for polynomial in molefraction*weight of speciesA (linear temperature dependence, units 1/K)

DenseMatrix	m_Eij
	Matrix of interactions (in energy units, 1/RT temperature dependence)

std::vector< DenseMatrix * >	m_Hij
	Matrix of interaction coefficients for polynomial in molefraction*weight of speciesA (in energy units, 1/RT temperature dependence)

std::vector< DenseMatrix * >	m_Sij
	Matrix of interaction coefficients for polynomial in molefraction*weight of speciesA (in entropy units, divided by R)

DenseMatrix	m_Dij
	Matrix of interactions.

Detailed Description

Mixing rule using logarithms of the mole fractions.

This model is based on the idea that liquid molecules are generally interacting with some energy and entropy of interaction. For transport properties that depend on these energies of interaction, the mixture transport property can be written in terms of its logarithm

\[ \ln \eta_{mix} = \sum_i X_i \ln \eta_i + \sum_i \sum_j X_i X_j ( S_{i,j} + E_{i,j} / T ) \]

.

These additional interaction terms multiply the mixture property by

\[ \exp( \sum_{i} \sum_{j} X_i X_j ( S_{i,j} + E_{i,j} / T ) ) \]

so that the self-interaction terms \( S_{i,j} \) and \( E_{i,j} \) should be zero.

Note that the energies and entropies of interaction should be a function of the composition themselves, but this is not yet implemented. (We might follow the input of Margules model thermodynamic data for the purpose of implementing this.)

Sample input for this method is

*    <transport model="Liquid">
*       <viscosity>
*          <compositionDependence model="logMoleFractions">
*             <interaction speciesA="Li+" speciesB="K+">
*               <!--
*                 interactions are from speciesA = LiCl(L)
*                 and speciesB = KCl(L).
*                   -->
*                <Eij units="J/kmol"> -1.0e3 </Eij>
*                <Sij units="J/kmol/K"> 80.0e-5 </Sij>
*             </interaction>
*          </compositionDependence>
*       </viscosity>
*    </transport>
*

Definition at line 370 of file LiquidTranInteraction.h.