DebyeHuckel Class Reference

Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality. More...

#include <DebyeHuckel.h>

Inheritance diagram for DebyeHuckel:

Collaboration diagram for DebyeHuckel:

Public Member Functions
	DebyeHuckel ()
	Default Constructor. More...
	DebyeHuckel (const DebyeHuckel &)
	Copy constructor. More...
DebyeHuckel &	operator= (const DebyeHuckel &)
	Assignment operator. More...
	DebyeHuckel (const std::string &inputFile, const std::string &id="")
	Full constructor for creating the phase. More...
	DebyeHuckel (XML_Node &phaseRef, const std::string &id="")
	Full constructor for creating the phase. More...
virtual	~DebyeHuckel ()
	Destructor. More...
ThermoPhase *	duplMyselfAsThermoPhase () const
	Duplicator from the ThermoPhase parent class. More...
virtual void	setParameters (int n, doublereal *const c)
	Set the equation of state parameters. More...
virtual void	getParameters (int &n, doublereal *const c) const
	Get the equation of state parameters in a vector. More...
virtual void	setParametersFromXML (const XML_Node &eosdata)
	Set equation of state parameter values from XML entries. More...
virtual void	initThermo ()
	Initialize the object's internal lengths after species are set. More...
virtual void	initThermoXML (XML_Node &phaseNode, const std::string &id)
	Process the XML file after species are set up. More...
virtual double	A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const
	Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol)) More...
virtual double	dA_DebyedT_TP (double temperature=-1.0, double pressure=-1.0) const
	Value of the derivative of the Debye Huckel constant with respect to temperature. More...
virtual double	d2A_DebyedT2_TP (double temperature=-1.0, double pressure=-1.0) const
	Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More...
virtual double	dA_DebyedP_TP (double temperature=-1.0, double pressure=-1.0) const
	Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure. More...
double	AionicRadius (int k=0) const
	Reports the ionic radius of the kth species. More...
int	formDH () const
	Returns the form of the Debye-Huckel parameterization used. More...
Array2D &	get_Beta_ij ()
	Returns a reference to M_Beta_ij. More...
Utilities
virtual int	eosType () const
	Equation of state type flag. More...
Molar Thermodynamic Properties of the Solution
virtual doublereal	enthalpy_mole () const
	Molar enthalpy of the solution. Units: J/kmol. More...
virtual doublereal	intEnergy_mole () const
	Molar internal energy of the solution. Units: J/kmol. More...
virtual doublereal	entropy_mole () const
	Molar entropy. Units: J/kmol/K. More...
virtual doublereal	gibbs_mole () const
	Molar Gibbs function. Units: J/kmol. More...
virtual doublereal	cp_mole () const
	Molar heat capacity at constant pressure. Units: J/kmol/K. More...
virtual doublereal	cv_mole () const
	Molar heat capacity at constant volume. Units: J/kmol/K. More...
Activities, Standard States, and Activity Concentrations
The activity \(a_k\) of a species in solution is related to the chemical potential by \[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \] The quantity \(\mu_k^0(T,P)\) is the chemical potential at unit activity, which depends only on temperature and the pressure. Activity is assumed to be molality-based here.
virtual void	getActivityConcentrations (doublereal *c) const
	This method returns an array of generalized concentrations. More...
virtual doublereal	standardConcentration (size_t k=0) const
	Return the standard concentration for the kth species. More...
virtual doublereal	logStandardConc (size_t k=0) const
	Natural logarithm of the standard concentration of the kth species. More...
virtual void	getUnitsStandardConc (double *uA, int k=0, int sizeUA=6) const
	Returns the units of the standard and generalized concentrations. More...
virtual void	getActivities (doublereal *ac) const
	Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration. More...
virtual void	getMolalityActivityCoefficients (doublereal *acMolality) const
	Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration. More...
Partial Molar Properties of the Solution
virtual void	getChemPotentials (doublereal *mu) const
	Get the species chemical potentials. Units: J/kmol. More...
virtual void	getPartialMolarEnthalpies (doublereal *hbar) const
	Returns an array of partial molar enthalpies for the species in the mixture. More...
virtual void	getPartialMolarEntropies (doublereal *sbar) const
	Returns an array of partial molar entropies of the species in the solution. More...
virtual void	getPartialMolarCp (doublereal *cpbar) const
	Return an array of partial molar heat capacities for the species in the mixture. More...
virtual void	getPartialMolarVolumes (doublereal *vbar) const
	Return an array of partial molar volumes for the species in the mixture. More...
Chemical Equilibrium
virtual void	setToEquilState (const doublereal *lambda_RT)
	This method is used by the ChemEquil equilibrium solver. More...
Saturation properties.
These methods are only implemented by subclasses that implement full liquid-vapor equations of state.
virtual doublereal	satTemperature (doublereal p) const
	Return the saturation temperature given the pressure. More...
virtual doublereal	satPressure (doublereal T)
	Get the saturation pressure for a given temperature. More...
virtual doublereal	vaporFraction () const
	Return the fraction of vapor at the current conditions. More...
virtual void	setState_Tsat (doublereal t, doublereal x)
	Set the state to a saturated system at a particular temperature. More...
virtual void	setState_Psat (doublereal p, doublereal x)
	Set the state to a saturated system at a particular pressure. More...
Public Member Functions inherited from MolalityVPSSTP
	MolalityVPSSTP ()
	Default Constructor. More...
	MolalityVPSSTP (const MolalityVPSSTP &b)
	Copy constructor. More...
MolalityVPSSTP &	operator= (const MolalityVPSSTP &b)
	Assignment operator. More...
virtual void	setStateFromXML (const XML_Node &state)
	Set equation of state parameter values from XML entries. More...
void	setState_TPM (doublereal t, doublereal p, const doublereal *const molalities)
	Set the temperature (K), pressure (Pa), and molalities (gmol kg-1) of the solutes. More...
void	setState_TPM (doublereal t, doublereal p, compositionMap &m)
	Set the temperature (K), pressure (Pa), and molalities. More...
void	setState_TPM (doublereal t, doublereal p, const std::string &m)
	Set the temperature (K), pressure (Pa), and molalities. More...
virtual void	getdlnActCoeffdlnN (const size_t ld, doublereal *const dlnActCoeffdlnN)
	Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers. More...
virtual std::string	report (bool show_thermo=true) const
	returns a summary of the state of the phase as a string More...
void	setpHScale (const int pHscaleType)
	Set the pH scale, which determines the scale for single-ion activity coefficients. More...
int	pHScale () const
	Reports the pH scale, which determines the scale for single-ion activity coefficients. More...
void	setSolvent (size_t k)
	This routine sets the index number of the solvent for the phase. More...
size_t	solventIndex () const
	Returns the solvent index. More...
void	setMoleFSolventMin (doublereal xmolSolventMIN)
	Sets the minimum mole fraction in the molality formulation. More...
doublereal	moleFSolventMin () const
	Returns the minimum mole fraction in the molality formulation. More...
void	calcMolalities () const
	Calculates the molality of all species and stores the result internally. More...
void	getMolalities (doublereal *const molal) const
	This function will return the molalities of the species. More...
void	setMolalities (const doublereal *const molal)
	Set the molalities of the solutes in a phase. More...
void	setMolalitiesByName (compositionMap &xMap)
	Set the molalities of a phase. More...
void	setMolalitiesByName (const std::string &name)
	Set the molalities of a phase. More...
int	activityConvention () const
	This method returns the activity convention. More...
void	getActivityCoefficients (doublereal *ac) const
	Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration. More...
virtual double	osmoticCoefficient () const
	Calculate the osmotic coefficient. More...
void	getElectrochemPotentials (doublereal *mu) const
	Get the species electrochemical potentials. More...
void	initThermoXML (XML_Node &phaseNode, const std::string &id)
	Import and initialize a ThermoPhase object. More...
Public Member Functions inherited from VPStandardStateTP
	VPStandardStateTP ()
	Constructor. More...
	VPStandardStateTP (const VPStandardStateTP &b)
	Copy Constructor. More...
VPStandardStateTP &	operator= (const VPStandardStateTP &b)
	Assignment operator. More...
virtual	~VPStandardStateTP ()
	Destructor. More...
virtual int	standardStateConvention () const
	This method returns the convention used in specification of the standard state, of which there are currently two, temperature based, and variable pressure based. More...
virtual void	getdlnActCoeffdlnN_diag (doublereal *dlnActCoeffdlnN_diag) const
	Get the array of log concentration-like derivatives of the log activity coefficients. More...
void	getChemPotentials_RT (doublereal *mu) const
	Get the array of non-dimensional species chemical potentials. More...
virtual void	getStandardChemPotentials (doublereal *mu) const
	Get the array of chemical potentials at unit activity. More...
virtual void	getEnthalpy_RT (doublereal *hrt) const
	Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More...
virtual void	getEntropy_R (doublereal *sr) const
	Get the array of nondimensional Enthalpy functions for the standard state species at the current T and P of the solution. More...
virtual void	getGibbs_RT (doublereal *grt) const
	Get the nondimensional Gibbs functions for the species at their standard states of solution at the current T and P of the solution. More...
void	getPureGibbs (doublereal *gpure) const
	Get the standard state Gibbs functions for each species at the current T and P. More...
virtual void	getIntEnergy_RT (doublereal *urt) const
	Returns the vector of nondimensional internal Energies of the standard state at the current temperature and pressure of the solution for each species. More...
virtual void	getCp_R (doublereal *cpr) const
	Get the nondimensional Heat Capacities at constant pressure for the standard state of the species at the current T and P. More...
virtual void	getStandardVolumes (doublereal *vol) const
	Get the molar volumes of each species in their standard states at the current T and P of the solution. More...
virtual const vector_fp &	getStandardVolumes () const
doublereal	pressure () const
	Returns the current pressure of the phase. More...
virtual void	updateStandardStateThermo () const
	Updates the standard state thermodynamic functions at the current T and P of the solution. More...
virtual void	getEnthalpy_RT_ref (doublereal *hrt) const
	Returns the vector of nondimensional enthalpies of the reference state at the current temperature of the solution and the reference pressure for the species. More...
virtual void	getGibbs_RT_ref (doublereal *grt) const
	Returns the vector of nondimensional Gibbs free energies of the reference state at the current temperature of the solution and the reference pressure for the species. More...
virtual void	getGibbs_ref (doublereal *g) const
virtual void	getEntropy_R_ref (doublereal *er) const
virtual void	getCp_R_ref (doublereal *cprt) const
virtual void	getStandardVolumes_ref (doublereal *vol) const
	Get the molar volumes of the species reference states at the current T and P_ref of the solution. More...
void	setVPSSMgr (VPSSMgr *vp_ptr)
	set the VPSS Mgr More...
VPSSMgr *	provideVPSSMgr ()
	Return a pointer to the VPSSMgr for this phase. More...
void	createInstallPDSS (size_t k, const XML_Node &s, const XML_Node *phaseNode_ptr)
PDSS *	providePDSS (size_t k)
const PDSS *	providePDSS (size_t k) const
Public Member Functions inherited from ThermoPhase
	ThermoPhase ()
	Constructor. More...
virtual	~ThermoPhase ()
	Destructor. Deletes the species thermo manager. More...
	ThermoPhase (const ThermoPhase &right)
	Copy Constructor for the ThermoPhase object. More...
ThermoPhase &	operator= (const ThermoPhase &right)
	Assignment operator. More...
doublereal	_RT () const
	Return the Gas Constant multiplied by the current temperature. More...
virtual doublereal	refPressure () const
	Returns the reference pressure in Pa. More...
virtual doublereal	minTemp (size_t k=npos) const
	Minimum temperature for which the thermodynamic data for the species or phase are valid. More...
doublereal	Hf298SS (const int k) const
	Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...
virtual void	modifyOneHf298SS (const int k, const doublereal Hf298New)
	Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More...
virtual doublereal	maxTemp (size_t k=npos) const
	Maximum temperature for which the thermodynamic data for the species are valid. More...
bool	chargeNeutralityNecessary () const
	Returns the chargeNeutralityNecessity boolean. More...
virtual doublereal	cv_vib (int, double) const
void	setElectricPotential (doublereal v)
	Set the electric potential of this phase (V). More...
doublereal	electricPotential () const
	Returns the electric potential of this phase (V). More...
virtual void	getLnActivityCoefficients (doublereal *lnac) const
	Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration. More...
void	getElectrochemPotentials (doublereal *mu) const
	Get the species electrochemical potentials. More...
virtual void	getPartialMolarIntEnergies (doublereal *ubar) const
	Return an array of partial molar internal energies for the species in the mixture. More...
virtual void	getdPartialMolarVolumes_dT (doublereal *d_vbar_dT) const
	Return an array of derivatives of partial molar volumes wrt temperature for the species in the mixture. More...
virtual void	getdPartialMolarVolumes_dP (doublereal *d_vbar_dP) const
	Return an array of derivatives of partial molar volumes wrt pressure for the species in the mixture. More...
virtual void	getdStandardVolumes_dT (doublereal *d_vol_dT) const
	Get the derivative of the molar volumes of the species standard states wrt temperature at the current T and P of the solution. More...
virtual void	getdStandardVolumes_dP (doublereal *d_vol_dP) const
	Get the derivative molar volumes of the species standard states wrt pressure at the current T and P of the solution. More...
virtual void	getIntEnergy_RT_ref (doublereal *urt) const
	Returns the vector of nondimensional internal Energies of the reference state at the current temperature of the solution and the reference pressure for each species. More...
virtual void	setReferenceComposition (const doublereal *const x)
	Sets the reference composition. More...
virtual void	getReferenceComposition (doublereal *const x) const
	Gets the reference composition. More...
doublereal	enthalpy_mass () const
	Specific enthalpy. More...
doublereal	intEnergy_mass () const
	Specific internal energy. More...
doublereal	entropy_mass () const
	Specific entropy. More...
doublereal	gibbs_mass () const
	Specific Gibbs function. More...
doublereal	cp_mass () const
	Specific heat at constant pressure. More...
doublereal	cv_mass () const
	Specific heat at constant volume. More...
void	setElementPotentials (const vector_fp &lambda)
	Stores the element potentials in the ThermoPhase object. More...
bool	getElementPotentials (doublereal *lambda) const
	Returns the element potentials stored in the ThermoPhase object. More...
virtual doublereal	critTemperature () const
	Critical temperature (K). More...
virtual doublereal	critPressure () const
	Critical pressure (Pa). More...
virtual doublereal	critDensity () const
	Critical density (kg/m3). More...
void	saveSpeciesData (const size_t k, const XML_Node *const data)
	Store a reference pointer to the XML tree containing the species data for this phase. More...
const std::vector< const XML_Node * > &	speciesData () const
	Return a pointer to the vector of XML nodes containing the species data for this phase. More...
void	setSpeciesThermo (SpeciesThermo *spthermo)
	Install a species thermodynamic property manager. More...
virtual SpeciesThermo &	speciesThermo (int k=-1)
	Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More...
virtual void	initThermoFile (const std::string &inputFile, const std::string &id)
virtual void	installSlavePhases (Cantera::XML_Node *phaseNode)
	Add in species from Slave phases. More...
virtual void	getdlnActCoeffds (const doublereal dTds, const doublereal *const dXds, doublereal *dlnActCoeffds) const
	Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space. More...
virtual void	getdlnActCoeffdlnX_diag (doublereal *dlnActCoeffdlnX_diag) const
	Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only. More...
virtual void	getdlnActCoeffdlnN_numderiv (const size_t ld, doublereal *const dlnActCoeffdlnN)
virtual void	reportCSV (std::ofstream &csvFile) const
	returns a summary of the state of the phase to a comma separated file. More...
virtual void	setState_TPX (doublereal t, doublereal p, const doublereal *x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...
virtual void	setState_TPX (doublereal t, doublereal p, compositionMap &x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...
virtual void	setState_TPX (doublereal t, doublereal p, const std::string &x)
	Set the temperature (K), pressure (Pa), and mole fractions. More...
virtual void	setState_TPY (doublereal t, doublereal p, const doublereal *y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
virtual void	setState_TPY (doublereal t, doublereal p, compositionMap &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
virtual void	setState_TPY (doublereal t, doublereal p, const std::string &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...
virtual void	setState_PX (doublereal p, doublereal *x)
	Set the pressure (Pa) and mole fractions. More...
virtual void	setState_PY (doublereal p, doublereal *y)
	Set the internally stored pressure (Pa) and mass fractions. More...
virtual void	setState_HP (doublereal h, doublereal p, doublereal tol=1.e-4)
	Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More...
virtual void	setState_UV (doublereal u, doublereal v, doublereal tol=1.e-4)
	Set the specific internal energy (J/kg) and specific volume (m^3/kg). More...
virtual void	setState_SP (doublereal s, doublereal p, doublereal tol=1.e-4)
	Set the specific entropy (J/kg/K) and pressure (Pa). More...
virtual void	setState_SV (doublereal s, doublereal v, doublereal tol=1.e-4)
	Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More...
Public Member Functions inherited from Phase
	Phase ()
	Default constructor. More...
virtual	~Phase ()
	Destructor. More...
	Phase (const Phase &right)
	Copy Constructor. More...
Phase &	operator= (const Phase &right)
	Assignment operator. More...
XML_Node &	xml ()
	Returns a reference to the XML_Node stored for the phase. More...
void	saveState (vector_fp &state) const
	Save the current internal state of the phase Write to vector 'state' the current internal state. More...
void	saveState (size_t lenstate, doublereal *state) const
	Write to array 'state' the current internal state. More...
void	restoreState (const vector_fp &state)
	Restore a state saved on a previous call to saveState. More...
void	restoreState (size_t lenstate, const doublereal *state)
	Restore the state of the phase from a previously saved state vector. More...
doublereal	molecularWeight (size_t k) const
	Molecular weight of species k. More...
void	getMolecularWeights (vector_fp &weights) const
	Copy the vector of molecular weights into vector weights. More...
void	getMolecularWeights (doublereal *weights) const
	Copy the vector of molecular weights into array weights. More...
const vector_fp &	molecularWeights () const
	Return a const reference to the internal vector of molecular weights. More...
doublereal	size (size_t k) const
	This routine returns the size of species k. More...
doublereal	charge (size_t k) const
	Dimensionless electrical charge of a single molecule of species k The charge is normalized by the the magnitude of the electron charge. More...
doublereal	chargeDensity () const
	Charge density [C/m^3]. More...
size_t	nDim () const
	Returns the number of spatial dimensions (1, 2, or 3) More...
void	setNDim (size_t ndim)
	Set the number of spatial dimensions (1, 2, or 3). More...
virtual void	freezeSpecies ()
	Call when finished adding species. More...
bool	speciesFrozen ()
	True if freezeSpecies has been called. More...
virtual bool	ready () const
int	stateMFNumber () const
	Return the State Mole Fraction Number. More...
std::string	id () const
	Return the string id for the phase. More...
void	setID (const std::string &id)
	Set the string id for the phase. More...
std::string	name () const
	Return the name of the phase. More...
void	setName (const std::string &nm)
	Sets the string name for the phase. More...
std::string	elementName (size_t m) const
	Name of the element with index m. More...
size_t	elementIndex (const std::string &name) const
	Return the index of element named 'name'. More...
const std::vector< std::string > &	elementNames () const
	Return a read-only reference to the vector of element names. More...
doublereal	atomicWeight (size_t m) const
	Atomic weight of element m. More...
doublereal	entropyElement298 (size_t m) const
	Entropy of the element in its standard state at 298 K and 1 bar. More...
int	atomicNumber (size_t m) const
	Atomic number of element m. More...
int	elementType (size_t m) const
	Return the element constraint type Possible types include: More...
int	changeElementType (int m, int elem_type)
	Change the element type of the mth constraint Reassigns an element type. More...
const vector_fp &	atomicWeights () const
	Return a read-only reference to the vector of atomic weights. More...
size_t	nElements () const
	Number of elements. More...
void	checkElementIndex (size_t m) const
	Check that the specified element index is in range Throws an exception if m is greater than nElements()-1. More...
void	checkElementArraySize (size_t mm) const
	Check that an array size is at least nElements() Throws an exception if mm is less than nElements(). More...
doublereal	nAtoms (size_t k, size_t m) const
	Number of atoms of element m in species k. More...
void	getAtoms (size_t k, double *atomArray) const
	Get a vector containing the atomic composition of species k. More...
size_t	speciesIndex (const std::string &name) const
	Returns the index of a species named 'name' within the Phase object. More...
std::string	speciesName (size_t k) const
	Name of the species with index k. More...
std::string	speciesSPName (int k) const
	Returns the expanded species name of a species, including the phase name This is guaranteed to be unique within a Cantera problem. More...
const std::vector< std::string > &	speciesNames () const
	Return a const reference to the vector of species names. More...
size_t	nSpecies () const
	Returns the number of species in the phase. More...
void	checkSpeciesIndex (size_t k) const
	Check that the specified species index is in range Throws an exception if k is greater than nSpecies()-1. More...
void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies(). More...
void	setMoleFractionsByName (compositionMap &xMap)
	Set the species mole fractions by name. More...
void	setMoleFractionsByName (const std::string &x)
	Set the mole fractions of a group of species by name. More...
void	setMassFractionsByName (compositionMap &yMap)
	Set the species mass fractions by name. More...
void	setMassFractionsByName (const std::string &x)
	Set the species mass fractions by name. More...
void	setState_TRX (doublereal t, doublereal dens, const doublereal *x)
	Set the internally stored temperature (K), density, and mole fractions. More...
void	setState_TRX (doublereal t, doublereal dens, compositionMap &x)
	Set the internally stored temperature (K), density, and mole fractions. More...
void	setState_TRY (doublereal t, doublereal dens, const doublereal *y)
	Set the internally stored temperature (K), density, and mass fractions. More...
void	setState_TRY (doublereal t, doublereal dens, compositionMap &y)
	Set the internally stored temperature (K), density, and mass fractions. More...
void	setState_TNX (doublereal t, doublereal n, const doublereal *x)
	Set the internally stored temperature (K), molar density (kmol/m^3), and mole fractions. More...
void	setState_TR (doublereal t, doublereal rho)
	Set the internally stored temperature (K) and density (kg/m^3) More...
void	setState_TX (doublereal t, doublereal *x)
	Set the internally stored temperature (K) and mole fractions. More...
void	setState_TY (doublereal t, doublereal *y)
	Set the internally stored temperature (K) and mass fractions. More...
void	setState_RX (doublereal rho, doublereal *x)
	Set the density (kg/m^3) and mole fractions. More...
void	setState_RY (doublereal rho, doublereal *y)
	Set the density (kg/m^3) and mass fractions. More...
void	getMoleFractionsByName (compositionMap &x) const
	Get the mole fractions by name. More...
doublereal	moleFraction (size_t k) const
	Return the mole fraction of a single species. More...
doublereal	moleFraction (const std::string &name) const
	Return the mole fraction of a single species. More...
doublereal	massFraction (size_t k) const
	Return the mass fraction of a single species. More...
doublereal	massFraction (const std::string &name) const
	Return the mass fraction of a single species. More...
void	getMoleFractions (doublereal *const x) const
	Get the species mole fraction vector. More...
virtual void	setMoleFractions (const doublereal *const x)
	Set the mole fractions to the specified values There is no restriction on the sum of the mole fraction vector. More...
virtual void	setMoleFractions_NoNorm (const doublereal *const x)
	Set the mole fractions to the specified values without normalizing. More...
void	getMassFractions (doublereal *const y) const
	Get the species mass fractions. More...
const doublereal *	massFractions () const
	Return a const pointer to the mass fraction array. More...
virtual void	setMassFractions (const doublereal *const y)
	Set the mass fractions to the specified values and normalize them. More...
virtual void	setMassFractions_NoNorm (const doublereal *const y)
	Set the mass fractions to the specified values without normalizing. More...
void	getConcentrations (doublereal *const c) const
	Get the species concentrations (kmol/m^3). More...
doublereal	concentration (const size_t k) const
	Concentration of species k. More...
virtual void	setConcentrations (const doublereal *const conc)
	Set the concentrations to the specified values within the phase. More...
const doublereal *	moleFractdivMMW () const
	Returns a const pointer to the start of the moleFraction/MW array. More...
doublereal	temperature () const
	Temperature (K). More...
virtual doublereal	density () const
	Density (kg/m^3). More...
doublereal	molarDensity () const
	Molar density (kmol/m^3). More...
doublereal	molarVolume () const
	Molar volume (m^3/kmol). More...
doublereal	mean_X (const doublereal *const Q) const
	Evaluate the mole-fraction-weighted mean of an array Q. More...
doublereal	mean_Y (const doublereal *const Q) const
	Evaluate the mass-fraction-weighted mean of an array Q. More...
doublereal	meanMolecularWeight () const
	The mean molecular weight. Units: (kg/kmol) More...
doublereal	sum_xlogx () const
	Evaluate \( \sum_k X_k \log X_k \). More...
doublereal	sum_xlogQ (doublereal *const Q) const
	Evaluate \( \sum_k X_k \log Q_k \). More...
void	addElement (const std::string &symbol, doublereal weight=-12345.0)
	Add an element. More...
void	addElement (const XML_Node &e)
	Add an element from an XML specification. More...
void	addUniqueElement (const std::string &symbol, doublereal weight=-12345.0, int atomicNumber=0, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
	Add an element, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...
void	addUniqueElement (const XML_Node &e)
	Add an element, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...
void	addElementsFromXML (const XML_Node &phase)
	Add all elements referenced in an XML_Node tree. More...
void	freezeElements ()
	Prohibit addition of more elements, and prepare to add species. More...
bool	elementsFrozen ()
	True if freezeElements has been called. More...
size_t	addUniqueElementAfterFreeze (const std::string &symbol, doublereal weight, int atomicNumber, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
	Add an element after elements have been frozen, checking for uniqueness The uniqueness is checked by comparing the string symbol. More...
void	addSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0)
void	addUniqueSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0)
	Add a species to the phase, checking for uniqueness of the name This routine checks for uniqueness of the string name. More...

Public Attributes
bool	m_useHelgesonFixedForm
	If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation. More...
int	m_form_A_Debye
	Form of the constant outside the Debye-Huckel term called A. More...

Protected Attributes
int	m_formDH
	form of the Debye-Huckel parameterization used in the model. More...
int	m_formGC
	Format for the generalized concentration: More...
vector_int	m_electrolyteSpeciesType
	Vector containing the electrolyte species type. More...
vector_fp	m_Aionic
	a_k = Size of the ionic species in the DH formulation units = meters More...
double	m_IionicMolality
	Current value of the ionic strength on the molality scale. More...
double	m_maxIionicStrength
	Maximum value of the ionic strength allowed in the calculation of the activity coefficients. More...
double	m_IionicMolalityStoich
	Stoichiometric ionic strength on the molality scale. More...
double	m_A_Debye
	Current value of the Debye Constant, A_Debye. More...
double	m_B_Debye
	Current value of the constant that appears in the denominator. More...
vector_fp	m_B_Dot
	Array of B_Dot values. More...
vector_fp	m_npActCoeff
	These are coefficients to describe the increase in activity coeff for non-polar molecules due to the electrolyte becoming stronger (the so-called salt-out effect) More...
PDSS_Water *	m_waterSS
	Pointer to the Water standard state object. More...
double	m_densWaterSS
	Storage for the density of water's standard state. More...
WaterProps *	m_waterProps
	Pointer to the water property calculator. More...
vector_fp	m_pp
	Temporary array used in equilibrium calculations. More...
vector_fp	m_tmpV
	vector of size m_kk, used as a temporary holding area. More...
vector_fp	m_speciesCharge_Stoich
	Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules. More...
Array2D	m_Beta_ij
	Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species. More...
vector_fp	m_lnActCoeffMolal
	Logarithm of the activity coefficients on the molality scale. More...
vector_fp	m_dlnActCoeffMolaldT
	Derivative of log act coeff wrt T. More...
vector_fp	m_d2lnActCoeffMolaldT2
	2nd Derivative of log act coeff wrt T More...
vector_fp	m_dlnActCoeffMolaldP
	Derivative of log act coeff wrt P. More...
Protected Attributes inherited from MolalityVPSSTP
size_t	m_indexSolvent
	Index of the solvent. More...
int	m_pHScalingType
	Scaling to be used for output of single-ion species activity coefficients. More...
size_t	m_indexCLM
	Index of the phScale species. More...
doublereal	m_weightSolvent
	Molecular weight of the Solvent. More...
doublereal	m_xmolSolventMIN
doublereal	m_Mnaught
	This is the multiplication factor that goes inside log expressions involving the molalities of species. More...
vector_fp	m_molalities
	Current value of the molalities of the species in the phase. More...
Protected Attributes inherited from VPStandardStateTP
doublereal	m_Pcurrent
	Current value of the pressure - state variable. More...
doublereal	m_Tlast_ss
	The last temperature at which the standard statethermodynamic properties were calculated at. More...
doublereal	m_Plast_ss
	The last pressure at which the Standard State thermodynamic properties were calculated at. More...
doublereal	m_P0
VPSSMgr *	m_VPSS_ptr
	Pointer to the VPSS manager that calculates all of the standard state info efficiently. More...
std::vector< PDSS * >	m_PDSS_storage
	Storage for the PDSS objects for the species. More...
Protected Attributes inherited from ThermoPhase
SpeciesThermo *	m_spthermo
	Pointer to the calculation manager for species reference-state thermodynamic properties. More...
std::vector< const XML_Node * >	m_speciesData
	Vector of pointers to the species databases. More...
doublereal	m_phi
	Stored value of the electric potential for this phase. More...
vector_fp	m_lambdaRRT
	Vector of element potentials. More...
bool	m_hasElementPotentials
	Boolean indicating whether there is a valid set of saved element potentials for this phase. More...
bool	m_chargeNeutralityNecessary
	Boolean indicating whether a charge neutrality condition is a necessity. More...
int	m_ssConvention
	Contains the standard state convention. More...
std::vector< doublereal >	xMol_Ref
	Reference Mole Fraction Composition. More...
Protected Attributes inherited from Phase
size_t	m_kk
	Number of species in the phase. More...
size_t	m_ndim
	Dimensionality of the phase. More...
vector_fp	m_speciesComp
	Atomic composition of the species. More...
vector_fp	m_speciesSize
	Vector of species sizes. More...
vector_fp	m_speciesCharge
	Vector of species charges. length m_kk. More...

Private Member Functions
double	_nonpolarActCoeff (double IionicMolality) const
	Static function that implements the non-polar species salt-out modifications. More...
double	_osmoticCoeffHelgesonFixedForm () const
	Formula for the osmotic coefficient that occurs in the GWB. More...
double	_lnactivityWaterHelgesonFixedForm () const
	Formula for the log of the water activity that occurs in the GWB. More...
doublereal	err (const std::string &msg) const
	Bail out of functions with an error exit if they are not implemented. More...
void	initLengths ()
	Initialize the internal lengths. More...
void	s_update_lnMolalityActCoeff () const
	Calculate the log activity coefficients. More...
void	s_update_dlnMolalityActCoeff_dT () const
	Calculation of temperature derivative of activity coefficient. More...
void	s_update_d2lnMolalityActCoeff_dT2 () const
	Calculate the temperature 2nd derivative of the activity coefficient. More...
void	s_update_dlnMolalityActCoeff_dP () const
	Calculate the pressure derivative of the activity coefficient. More...

Mechanical Equation of State Properties
In this equation of state implementation, the density is a function only of the mole fractions. Therefore, it can't be an independent variable. Instead, the pressure is used as the independent variable. Functions which try to set the thermodynamic state by calling setDensity() may cause an exception to be thrown.
virtual doublereal	pressure () const
	Return the thermodynamic pressure (Pa). More...
virtual void	setPressure (doublereal p)
	Set the internally stored pressure (Pa) at constant temperature and composition. More...
void	setDensity (const doublereal rho)
	Set the internally stored density (gm/m^3) of the phase. More...
virtual void	setMolarDensity (const doublereal conc)
	Set the internally stored molar density (kmol/m^3) of the phase. More...
virtual void	setTemperature (const doublereal temp)
	Set the temperature (K) More...
virtual void	setState_TP (doublereal t, doublereal p)
	Set the temperature (K) and pressure (Pa) More...
virtual doublereal	isothermalCompressibility () const
	The isothermal compressibility. More...
virtual doublereal	thermalExpansionCoeff () const
	The thermal expansion coefficient. More...
virtual void	calcDensity ()
	Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...

Additional Inherited Members
Protected Member Functions inherited from MolalityVPSSTP
virtual void	getCsvReportData (std::vector< std::string > &names, std::vector< vector_fp > &data) const
	Fills names and data with the column names and species thermo properties to be included in the output of the reportCSV method. More...
virtual void	getUnscaledMolalityActivityCoefficients (doublereal *acMolality) const
	Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration. More...
virtual void	applyphScale (doublereal *acMolality) const
	Apply the current phScale to a set of activity Coefficients or activities. More...
Protected Member Functions inherited from VPStandardStateTP
virtual void	_updateStandardStateThermo () const
	Updates the standard state thermodynamic functions at the current T and P of the solution. More...
const vector_fp &	Gibbs_RT_ref () const
Protected Member Functions inherited from Phase
void	init (const vector_fp &mw)
void	setMolecularWeight (const int k, const double mw)
	Set the molecular weight of a single species to a given value. More...

Detailed Description

Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality.

The concentrations of the ionic species are assumed to obey the electroneutrality condition.

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Specification of Species Standard State Properties

---

The standard states are on the unit molality basis. Therefore, in the documentation below, the normal \( o \) superscript is replaced with the \( \triangle \) symbol. The reference state symbol is now \( \triangle, ref \).

It is assumed that the reference state thermodynamics may be
obtained by a pointer to a populated species thermodynamic property
manager class (see ThermoPhase::m_spthermo). How to relate pressure
changes to the reference state thermodynamics is resolved at this level.

For an incompressible,

stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_0 \hat v\) is subtracted from the specified molar enthalpy to compute the molar internal energy. The entropy is assumed to be independent of the pressure.

The enthalpy function is given by the following relation.

\[ h^\triangle_k(T,P) = h^{\triangle,ref}_k(T) + \tilde v \left( P - P_{ref} \right) \]

For an incompressible, stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_{ref} \tilde v\) is subtracted from the specified reference molar enthalpy to compute the molar internal energy.

\[ u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde v \]

The standard state heat capacity and entropy are independent of pressure. The standard state gibbs free energy is obtained from the enthalpy and entropy functions.

The vector Phase::m_speciesSize[] is used to hold the base values of species sizes. These are defined as the molar volumes of species at infinite dilution at 300 K and 1 atm of water. m_speciesSize are calculated during the initialization of the DebyeHuckel object and are then not touched.

The current model assumes that an incompressible molar volume for all solutes. The molar volume for the water solvent, however, is obtained from a pure water equation of state, waterSS. Therefore, the water standard state varies with both T and P. It is an error to request standard state water properties at a T and P where the water phase is not a stable phase, i.e., beyond its spinodal curve.

---

Specification of Solution Thermodynamic Properties

---

Chemical potentials of the solutes, \( \mu_k \), and the solvent, \( \mu_o \), which are based on the molality form, have the following general format:

\[ \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle}) \]

\[ \mu_o = \mu^o_o(T,P) + RT ln(a_o) \]

where \( \gamma_k^{\triangle} \) is the molality based activity coefficient for species \(k\).

Individual activity coefficients of ions can not be independently measured. Instead, only binary pairs forming electroneutral solutions can be measured.

<H3> Ionic Strength </H3>

Most of the parameterizations within the model use the ionic strength
as a key variable. The ionic strength, \form#185 is defined as follows

\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]

\( m_k \) is the molality of the kth species. \( z_k \) is the charge of the kth species. Note, the ionic strength is a defined units quantity. The molality has defined units of gmol kg-1, and therefore the ionic strength has units of sqrt( gmol kg-1).

In some instances, from some authors, a different formulation is used for the ionic strength in the equations below. The different formulation is due to the possibility of the existence of weak acids and how association wrt to the weak acid equilibrium relation affects the calculation of the activity coefficients via the assumed value of the ionic strength.

If we are to assume that the association reaction doesn't have an effect on the ionic strength, then we will want to consider the associated weak acid as in effect being fully dissociated, when we calculate an effective value for the ionic strength. We will call this calculated value, the stoichiometric ionic strength, \( I_s \), putting a subscript s to denote it from the more straightforward calculation of \( I \).

\[ I_s = \frac{1}{2} \sum_k{m_k^s z_k^2} \]

Here, \( m_k^s \) is the value of the molalities calculated assuming that all weak acid-base pairs are in their fully dissociated states. This calculation may be simplified by considering that the weakly associated acid may be made up of two charged species, k1 and k2, each with their own charges, obeying the following relationship:

\[ z_k = z_{k1} + z_{k2} \]

Then, we may only need to specify one charge value, say, \( z_{k1}\), the cation charge number, in order to get both numbers, since we have already specified \( z_k \) in the definition of original species. Then, the stoichiometric ionic strength may be calculated via the following formula.

\[ I_s = \frac{1}{2} \left(\sum_{k,ions}{m_k z_k^2}+ \sum_{k,weak_assoc}(m_k z_{k1}^2 + m_k z_{k2}^2) \right) \]

The specification of which species are weakly associated acids is made in the input file via the stoichIsMods XML block, where the charge for k1 is also specified. An example is given below:

<stoichIsMods>
      NaCl(aq):-1.0
</stoichIsMods>

Because we need the concept of a weakly associated acid in order to calculated \( I_s \) we need to catalog all species in the phase. This is done using the following categories:

• cEST_solvent Solvent species (neutral)
• cEST_chargedSpecies Charged species (charged)
• cEST_weakAcidAssociated Species which can break apart into charged species. It may or may not be charged. These may or may not be be included in the species solution vector.
• cEST_strongAcidAssociated Species which always breaks apart into charged species. It may or may not be charged. Normally, these aren't included in the speciation vector.
• cEST_polarNeutral Polar neutral species
• cEST_nonpolarNeutral Non polar neutral species

Polar and non-polar neutral species are differentiated, because some additions to the activity coefficient expressions distinguish between these two types of solutes. This is the so-called salt-out effect.

The type of species is specified in the electrolyteSpeciesType XML block. Note, this is not considered a part of the specification of the standard state for the species, at this time. Therefore, this information is put under the activityCoefficient XML block. An example is given below

<electrolyteSpeciesType>
       H2L(L):solvent
       H+:chargedSpecies
       NaOH(aq):weakAcidAssociated
       NaCl(aq):strongAcidAssociated
       NH3(aq):polarNeutral
       O2(aq):nonpolarNeutral
</electrolyteSpeciesType>

Much of the species electrolyte type information is inferred from other information in the input file. For example, as species which is charged is given the "chargedSpecies" default category. A neutral solute species is put into the "nonpolarNeutral" category by default.

The specification of solute activity coefficients depends on the model assumed for the Debye-Huckel term. The model is set by the internal parameter m_formDH. We will now describe each category in its own section.

<H3> Debye-Huckel Dilute Limit </H3>

DHFORM_DILUTE_LIMIT = 0

This form assumes a dilute limit to DH, and is mainly for informational purposes:

\[ \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I} \]

where \( I\) is the ionic strength

\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]

The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation.

\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \]

<H3> Bdot Formulation </H3>

  DHFORM_BDOT_AK       = 1

    This form assumes Bethke's format for the Debye Huckel activity coefficient:

\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}} + \log(10) B^{dot}_k I \]

Note, this particular form where \( a_k \) can differ in multielectrolyte solutions has problems with respect to a Gibbs-Duhem analysis. However, we include it here because there is a lot of data fit to it.

The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation. Here, we use:

\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{1/2} \left[ \sum_k{\frac{1}{2} m_k z_k^2 \sigma( B_{Debye} a_k \sqrt{I} ) } \right] - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]

where

\[ \sigma (y) = \frac{3}{y^3} \left[ (1+y) - 2 \ln(1 + y) - \frac{1}{1+y} \right] \]

Additionally, Helgeson's formulation for the water activity is offered as an alternative.

<H3> Bdot Formulation with Uniform Size Parameter in the Denominator </H3>

DHFORM_BDOT_AUNIFORM = 2

This form assumes Bethke's format for the Debye-Huckel activity coefficient

\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + \log(10) B^{dot}_k I \]

The value of a is determined at the beginning of the calculation, and not changed.

\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]

<H3> Beta_IJ formulation </H3>

DHFORM_BETAIJ        = 3

This form assumes a linear expansion in a virial coefficient form.
It is used extensively in the book by Newmann, "Electrochemistry Systems",
and is the beginning of more complex treatments for stronger electrolytes,
fom Pitzer and from Harvey, Moller, and Weire.

\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + 2 \sum_j \beta_{j,k} m_j \]

In the current treatment the binary interaction coefficients, \( \beta_{j,k}\), are independent of temperature and pressure.

\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]

In this formulation the ionic radius, \( a \), is a constant. This must be supplied to the model, in an ionicRadius XML block.

The \( \beta_{j,k} \) parameters are binary interaction parameters. They are supplied to the object in an DHBetaMatrix XML block. There are in principle \( N (N-1) /2 \) different, symmetric interaction parameters, where \( N \) are the number of solute species in the mechanism. An example is given below.

An example activityCoefficients XML block for this formulation is supplied below

<activityCoefficients model="Beta_ij">
       <!-- A_Debye units = sqrt(kg/gmol) -->
       <A_Debye> 1.172576 </A_Debye>
       <!-- B_Debye units = sqrt(kg/gmol)/m   -->
       <B_Debye> 3.28640E9 </B_Debye>
       <ionicRadius default="3.042843"  units="Angstroms">
       </ionicRadius>
       <DHBetaMatrix>
             H+:Cl-:0.27
             Na+:Cl-:0.15
             Na+:OH-:0.06
       </DHBetaMatrix>
       <stoichIsMods>
              NaCl(aq):-1.0
       </stoichIsMods>
       <electrolyteSpeciesType>
              H+:chargedSpecies
              NaCl(aq):weakAcidAssociated
       </electrolyteSpeciesType>
</activityCoefficients>

Pitzer Beta_IJ formulation

DHFORM_PITZER_BETAIJ = 4

This form assumes an activity coefficient formulation consistent with a truncated form of Pitzer's formulation. Pitzer's formulation is equivalent to the formulations above in the dilute limit, where rigorous theory may be applied.

\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye}}{3} \frac{\sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} -2 z_k^2 \frac{A_{Debye}}{3} \frac{\ln(1 + B_{Debye} a \sqrt{I})}{ B_{Debye} a} + 2 \sum_j \beta_{j,k} m_j \]

\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} \frac{(I)^{3/2} }{1 + B_{Debye} a \sqrt{I} } - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]

Specification of the Debye Huckel Constants

In the equations above, the formulas for \( A_{Debye} \) and \( B_{Debye} \) are needed. The DebyeHuckel object uses two methods for specifying these quantities. The default method is to assume that \( A_{Debye} \) is a constant, given in the initialization process, and stored in the member double, m_A_Debye. Optionally, a full water treatment may be employed that makes \( A_{Debye} \) a full function of T and P.

\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]

where

\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]

Therefore:

\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]

where

• \( N_a \) is Avogadro's number
• \( \rho_w \) is the density of water
• \( e \) is the electronic charge
• \( \epsilon = K \epsilon_o \) is the permittivity of water
• \( K \) is the dielectric constant of water
• \( \epsilon_o \) is the permittivity of free space
• \( \rho_o \) is the density of the solvent in its standard state.

Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^1/2 based on:

• \( \epsilon / \epsilon_0 \) = 78.54 (water at 25C)
• T = 298.15 K
• B_Debye = 3.28640E9 (kg/gmol)^1/2 m^-1

An example of a fixed value implementation is given below.

<activityCoefficients model="Beta_ij">
      <!-- A_Debye units = sqrt(kg/gmol)  -->
      <A_Debye> 1.172576 </A_Debye>
      <!-- B_Debye units = sqrt(kg/gmol)/m  -->
      <B_Debye> 3.28640E9 </B_Debye>
</activityCoefficients>

An example of a variable value implementation is given below.

<activityCoefficients model="Beta_ij">
      <A_Debye model="water" />
      <!-- B_Debye units = sqrt(kg/gmol)/m  -->
      <B_Debye> 3.28640E9 </B_Debye>
</activityCoefficients>

Currently, \( B_{Debye} \) is a constant in the model, specified either by a default water value, or through the input file. This may have to be looked at, in the future.

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Application within Kinetics Managers

---

For the time being, we have set the standard concentration for all species in this phase equal to the default concentration of the solvent at 298 K and 1 atm. This means that the kinetics operator essentially works on an activities basis, with units specified as if it were on a concentration basis.

For example, a bulk-phase binary reaction between liquid species j and k, producing a new liquid species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.

\[ R^1 = k^1 C_j^a C_k^a = k^1 (C_o a_j) (C_o a_k) \]

where

\[ C_j^a = C_o a_j \quad and \quad C_k^a = C_o a_k \]

\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C_o \) is the concentration of water at 298 K and 1 atm. \( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase. \(k^1 \) has units of m3 kmol-1 s-1.

The reverse rate constant can then be obtained from the law of microscopic reversibility and the equilibrium expression for the system.

\[ \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} ) \]

\( K^{o,1} \) is the dimensionless form of the equilibrium constant.

\[ R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l) \]

where

\[ k^{-1} = k^1 K^{o,1} C_o \]

\(k^{-1} \) has units of s-1.

Note, this treatment may be modified in the future, as events dictate.

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Instantiation of the Class

---

The constructor for this phase is NOT located in the default ThermoFactory for Cantera. However, a new DebyeHuckel object may be created by the following code snippets:

DebyeHuckel *DH = new DebyeHuckel("DH_NaCl.xml", "NaCl_electrolyte");

or

XML_Node *xm = get_XML_NameID("phase", "DH_NaCl.xml#NaCl_electrolyte", 0);
DebyeHuckel *dh = new DebyeHuckel(*xm);

or by the following call to importPhase():

XML_Node *xm = get_XML_NameID("phase", "DH_NaCl.xml#NaCl_electrolyte", 0);
DebyeHuckel dhphase;
importPhase(*xm, &dhphase);

---

XML Example

---

The phase model name for this is called StoichSubstance. It must be supplied as the model attribute of the thermo XML element entry. Within the phase XML block, the density of the phase must be specified. An example of an XML file this phase is given below.

 <phase id="NaCl_electrolyte" dim="3">
  <speciesArray datasrc="#species_waterSolution">
             H2O(L) Na+ Cl- H+ OH- NaCl(aq) NaOH(aq)
  </speciesArray>
  <state>
    <temperature units="K"> 300  </temperature>
    <pressure units="Pa">101325.0</pressure>
    <soluteMolalities>
           Na+:3.0
           Cl-:3.0
           H+:1.0499E-8
           OH-:1.3765E-6
           NaCl(aq):0.98492
           NaOH(aq):3.8836E-6
    </soluteMolalities>
  </state>
  <!-- thermo model identifies the inherited class
       from ThermoPhase that will handle the thermodynamics.
    -->
  <thermo model="DebyeHuckel">
     <standardConc model="solvent_volume" />
     <activityCoefficients model="Beta_ij">
              <!-- A_Debye units = sqrt(kg/gmol)  -->
              <A_Debye> 1.172576 </A_Debye>
              <!-- B_Debye units = sqrt(kg/gmol)/m   -->
              <B_Debye> 3.28640E9 </B_Debye>
              <ionicRadius default="3.042843"  units="Angstroms">
              </ionicRadius>
              <DHBetaMatrix>
                H+:Cl-:0.27
                Na+:Cl-:0.15
                Na+:OH-:0.06
              </DHBetaMatrix>
              <stoichIsMods>
                 NaCl(aq):-1.0
              </stoichIsMods>
              <electrolyteSpeciesType>
                 H+:chargedSpecies
                 NaCl(aq):weakAcidAssociated
              </electrolyteSpeciesType>
     </activityCoefficients>
     <solvent> H2O(L) </solvent>
  </thermo>
  <elementArray datasrc="elements.xml"> O H Na Cl </elementArray>
</phase>

Definition at line 600 of file DebyeHuckel.h.

Constructor & Destructor Documentation

DebyeHuckel

(

)

Default Constructor.

Definition at line 31 of file DebyeHuckel.cpp.

References DebyeHuckel::m_npActCoeff.

Referenced by DebyeHuckel::duplMyselfAsThermoPhase().

DebyeHuckel

(

const DebyeHuckel &

b

)

Copy constructor.

Definition at line 98 of file DebyeHuckel.cpp.

DebyeHuckel	(	const std::string &	inputFile,
		const std::string &	id = ""
	)

Full constructor for creating the phase.

Parameters

inputFile	File name containing the XML description of the phase
id	id attribute containing the name of the phase.

Definition at line 53 of file DebyeHuckel.cpp.

References ThermoPhase::initThermoFile(), and DebyeHuckel::m_npActCoeff.

DebyeHuckel	(	XML_Node &	phaseRef,
		const std::string &	id = ""
	)

Full constructor for creating the phase.

Parameters

phaseRef	XML phase node containing the description of the phase
id	id attribute containing the name of the phase.

Definition at line 76 of file DebyeHuckel.cpp.

References Cantera::findXMLPhase(), Cantera::importPhase(), and DebyeHuckel::m_npActCoeff.

~DebyeHuckel ( )

virtual

Destructor.

Definition at line 165 of file DebyeHuckel.cpp.

References DebyeHuckel::m_waterProps.

Member Function Documentation

DebyeHuckel & operator=

(

const DebyeHuckel &

b

)

Assignment operator.

Definition at line 121 of file DebyeHuckel.cpp.

References DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_B_Dot, DebyeHuckel::m_Beta_ij, DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_densWaterSS, DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_formDH, DebyeHuckel::m_formGC, DebyeHuckel::m_IionicMolality, DebyeHuckel::m_IionicMolalityStoich, DebyeHuckel::m_lnActCoeffMolal, DebyeHuckel::m_maxIionicStrength, DebyeHuckel::m_npActCoeff, DebyeHuckel::m_pp, DebyeHuckel::m_speciesCharge_Stoich, DebyeHuckel::m_tmpV, DebyeHuckel::m_useHelgesonFixedForm, DebyeHuckel::m_waterProps, DebyeHuckel::m_waterSS, and MolalityVPSSTP::operator=().

ThermoPhase * duplMyselfAsThermoPhase ( ) const

virtual

Duplicator from the ThermoPhase parent class.

Given a pointer to a ThermoPhase object, this function will duplicate the ThermoPhase object and all underlying structures. This is basically a wrapper around the copy constructor.

Returns

returns a pointer to a ThermoPhase

Reimplemented from MolalityVPSSTP.

Definition at line 173 of file DebyeHuckel.cpp.

References DebyeHuckel::DebyeHuckel().

int eosType ( ) const

virtual

Equation of state type flag.

The base class returns zero. Subclasses should define this to return a unique non-zero value. Constants defined for this purpose are listed in mix_defs.h.

Reimplemented from MolalityVPSSTP.

Definition at line 178 of file DebyeHuckel.cpp.

References Cantera::cDebyeHuckel0, and DebyeHuckel::m_formGC.

doublereal enthalpy_mole ( ) const

virtual

Molar enthalpy of the solution. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 201 of file DebyeHuckel.cpp.

References DATA_PTR, DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::m_tmpV, and Phase::mean_X().

Referenced by DebyeHuckel::intEnergy_mole().

doublereal intEnergy_mole ( ) const

virtual

Molar internal energy of the solution. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 207 of file DebyeHuckel.cpp.

References DebyeHuckel::enthalpy_mole(), Phase::molarDensity(), and DebyeHuckel::pressure().

doublereal entropy_mole ( ) const

virtual

Molar entropy. Units: J/kmol/K.

For an ideal, constant partial molar volume solution mixture with pure species phases which exhibit zero volume expansivity:

\[ \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k log(X_k) \]

The reference-state pure-species entropies \( \hat s^0_k(T,p_{ref}) \) are computed by the species thermodynamic property manager. The pure species entropies are independent of temperature since the volume expansivities are equal to zero.

See Also

SpeciesThermo

Reimplemented from ThermoPhase.

Definition at line 216 of file DebyeHuckel.cpp.

References DATA_PTR, DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::m_tmpV, and Phase::mean_X().

doublereal gibbs_mole ( ) const

virtual

Molar Gibbs function. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 222 of file DebyeHuckel.cpp.

References DATA_PTR, DebyeHuckel::getChemPotentials(), DebyeHuckel::m_tmpV, and Phase::mean_X().

doublereal cp_mole ( ) const

virtual

Molar heat capacity at constant pressure. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 228 of file DebyeHuckel.cpp.

References DATA_PTR, DebyeHuckel::getPartialMolarCp(), DebyeHuckel::m_tmpV, and Phase::mean_X().

doublereal cv_mole ( ) const

virtual

Molar heat capacity at constant volume. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 234 of file DebyeHuckel.cpp.

References DebyeHuckel::err().

doublereal pressure ( ) const

virtual

Return the thermodynamic pressure (Pa).

For this incompressible system, we return the internally stored independent value of the pressure.

Reimplemented from ThermoPhase.

Definition at line 246 of file DebyeHuckel.cpp.

References VPStandardStateTP::m_Pcurrent.

Referenced by DebyeHuckel::A_Debye_TP(), DebyeHuckel::d2A_DebyedT2_TP(), DebyeHuckel::dA_DebyedP_TP(), DebyeHuckel::dA_DebyedT_TP(), and DebyeHuckel::intEnergy_mole().

void setPressure ( doublereal  p )

virtual

Set the internally stored pressure (Pa) at constant temperature and composition.

This method sets the pressure within the object. The water model is a completely compressible model. Also, the dielectric constant is pressure dependent.

Parameters

p	input Pressure (Pa)

Todo:

Implement a variable pressure capability

Reimplemented from VPStandardStateTP.

Definition at line 251 of file DebyeHuckel.cpp.

References DebyeHuckel::setState_TP(), and Phase::temperature().

void calcDensity ( )

protectedvirtual

Calculate the density of the mixture using the partial molar volumes and mole fractions as input.

The formula for this is

\[ \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} \]

where \(X_k\) are the mole fractions, \(W_k\) are the molecular weights, and \(V_k\) are the pure species molar volumes.

Note, the basis behind this formula is that in an ideal solution the partial molar volumes are equal to the pure species molar volumes. We have additionally specified in this class that the pure species molar volumes are independent of temperature and pressure.

Reimplemented from VPStandardStateTP.

Definition at line 278 of file DebyeHuckel.cpp.

References PDSS_Water::density(), Phase::getMoleFractions(), DebyeHuckel::getPartialMolarVolumes(), DebyeHuckel::m_densWaterSS, Phase::m_kk, DebyeHuckel::m_pp, DebyeHuckel::m_tmpV, DebyeHuckel::m_waterSS, Phase::meanMolecularWeight(), and Phase::setDensity().

Referenced by DebyeHuckel::setState_TP().

void setDensity ( const doublereal  rho )

virtual

Set the internally stored density (gm/m^3) of the phase.

Overwritten setDensity() function is necessary because the density is not an independent variable.

This function will now throw an error condition

May have to adjust the strategy here to make the eos for these materials slightly compressible, in order to create a condition where the density is a function of the pressure.

This function will now throw an error condition if the input isn't exactly equal to the current density.

Todo:

Now have a compressible ss equation for liquid water. Therefore, this phase is compressible. May still want to change the independent variable however.

Parameters

rho	Input density (kg/m^3).

Reimplemented from Phase.

Definition at line 315 of file DebyeHuckel.cpp.

References Phase::density().

void setMolarDensity ( const doublereal  conc )

virtual

Set the internally stored molar density (kmol/m^3) of the phase.

Overwritten setMolarDensity() function is necessary because the density is not an independent variable.

This function will now throw an error condition if the input isn't exactly equal to the current molar density.

Parameters

conc	Input molar density (kmol/m^3).

Reimplemented from Phase.

Definition at line 324 of file DebyeHuckel.cpp.

References Phase::molarDensity().

void setTemperature ( const doublereal  temp )

virtual

Set the temperature (K)

This function sets the temperature, and makes sure that the value propagates to underlying objects, such as the water standard state model.

Parameters

temp	Temperature in kelvin

Reimplemented from VPStandardStateTP.

Definition at line 333 of file DebyeHuckel.cpp.

References VPStandardStateTP::m_Pcurrent, and DebyeHuckel::setState_TP().

void setState_TP ( doublereal  t, doublereal  p  )

virtual

Set the temperature (K) and pressure (Pa)

Set the temperature and pressure.

Parameters

t	Temperature (K)
p	Pressure (Pa)

Reimplemented from VPStandardStateTP.

Definition at line 256 of file DebyeHuckel.cpp.

References VPStandardStateTP::_updateStandardStateThermo(), DebyeHuckel::calcDensity(), VPStandardStateTP::m_Pcurrent, and Phase::setTemperature().

Referenced by DebyeHuckel::setPressure(), and DebyeHuckel::setTemperature().

doublereal isothermalCompressibility ( ) const

virtual

The isothermal compressibility.

Units: 1/Pa. The isothermal compressibility is defined as

\[ \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T \]

It's equal to zero for this model, since the molar volume doesn't change with pressure or temperature.

Reimplemented from ThermoPhase.

Definition at line 301 of file DebyeHuckel.cpp.

doublereal thermalExpansionCoeff ( ) const

virtual

The thermal expansion coefficient.

Units: 1/K. The thermal expansion coefficient is defined as

\[ \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P \]

It's equal to zero for this model, since the molar volume doesn't change with pressure or temperature.

Reimplemented from ThermoPhase.

Definition at line 308 of file DebyeHuckel.cpp.

void getActivityConcentrations ( doublereal *  c ) const

virtual

This method returns an array of generalized concentrations.

\( C_k\) that are defined such that \( a_k = C_k / C^0_k, \) where \( C^0_k \) is a standard concentration defined below. These generalized concentrations are used by kinetics manager classes to compute the forward and reverse rates of elementary reactions.

Parameters

c	Array of generalized concentrations. The units depend upon the implementation of the reaction rate expressions within the phase.

Reimplemented from MolalityVPSSTP.

Definition at line 342 of file DebyeHuckel.cpp.

References DebyeHuckel::getActivities(), Phase::m_kk, and DebyeHuckel::standardConcentration().

doublereal standardConcentration ( size_t  k = 0 ) const

virtual

Return the standard concentration for the kth species.

The standard concentration \( C^0_k \) used to normalize the activity (i.e., generalized) concentration in kinetics calculations.

For the time being, we will use the concentration of pure solvent for the the standard concentration of all species. This has the effect of making reaction rates based on the molality of species proportional to the molality of the species.

Parameters

k	Optional parameter indicating the species. The default is to assume this refers to species 0.

Returns

Returns the standard Concentration in units of m³ kmol^-1.

Reimplemented from MolalityVPSSTP.

Definition at line 351 of file DebyeHuckel.cpp.

References MolalityVPSSTP::m_indexSolvent, and Phase::m_speciesSize.

Referenced by DebyeHuckel::getActivityConcentrations(), and DebyeHuckel::logStandardConc().

doublereal logStandardConc ( size_t  k = 0 ) const

virtual

Natural logarithm of the standard concentration of the kth species.

Parameters

k	index of the species (defaults to zero)

Reimplemented from MolalityVPSSTP.

Definition at line 357 of file DebyeHuckel.cpp.

References DebyeHuckel::standardConcentration().

void getUnitsStandardConc ( double *  uA, int  k = 0, int  sizeUA = 6  ) const

virtual

Returns the units of the standard and generalized concentrations.

Note they have the same units, as their ratio is defined to be equal to the activity of the kth species in the solution, which is unitless.

This routine is used in print out applications where the units are needed. Usually, MKS units are assumed throughout the program and in the XML input files.

The base ThermoPhase class assigns the default quantities of (kmol/m3) for all species. Inherited classes are responsible for overriding the default values if necessary.

On return uA contains the powers of the units (MKS assumed) of the standard concentrations and generalized concentrations for the kth species.

Parameters

uA	Output vector containing the units uA[0] = kmol units - default = 1 uA[1] = m units - default = -nDim(), the number of spatial dimensions in the Phase class. uA[2] = kg units - default = 0; uA[3] = Pa(pressure) units - default = 0; uA[4] = Temperature units - default = 0; uA[5] = time units - default = 0
k	species index. Defaults to 0.
sizeUA	output int containing the size of the vector. Currently, this is equal to 6.

Deprecated:

Reimplemented from MolalityVPSSTP.

Definition at line 363 of file DebyeHuckel.cpp.

References Phase::nDim().

void getActivities ( doublereal *  ac ) const

virtual

Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.

We resolve this function at this level by calling on the activityConcentration function. However, derived classes may want to override this default implementation.

(note solvent activity coefficient is on molar scale).

Parameters

ac	Output vector of activities. Length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 387 of file DebyeHuckel.cpp.

References VPStandardStateTP::_updateStandardStateThermo(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), and DebyeHuckel::s_update_lnMolalityActCoeff().

Referenced by DebyeHuckel::getActivityConcentrations().

void getMolalityActivityCoefficients ( doublereal *  acMolality ) const

virtual

Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration.

note solvent is on molar scale. The solvent molar based activity coefficient is returned.

Note, most of the work is done in an internal private routine

Parameters

acMolality

Vector of Molality-based activity coefficients Length: m_kk

Reimplemented from MolalityVPSSTP.

Definition at line 406 of file DebyeHuckel.cpp.

References VPStandardStateTP::_updateStandardStateThermo(), DebyeHuckel::A_Debye_TP(), Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, and DebyeHuckel::s_update_lnMolalityActCoeff().

void getChemPotentials ( doublereal *  mu ) const

virtual

Get the species chemical potentials. Units: J/kmol.

This function returns a vector of chemical potentials of the species in solution.

\[ \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} m_k) \]

Parameters

mu	Output vector of species chemical potentials. Length: m_kk. Units: J/kmol

Reimplemented from ThermoPhase.

Definition at line 420 of file DebyeHuckel.cpp.

References Cantera::GasConstant, VPStandardStateTP::getStandardChemPotentials(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), DebyeHuckel::s_update_lnMolalityActCoeff(), Cantera::SmallNumber, and Phase::temperature().

Referenced by DebyeHuckel::gibbs_mole().

void getPartialMolarEnthalpies ( doublereal *  hbar ) const

virtual

Returns an array of partial molar enthalpies for the species in the mixture.

Units (J/kmol)

For this phase, the partial molar enthalpies are equal to the standard state enthalpies modified by the derivative of the molality-based activity coefficient wrt temperature

\[ \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT} \]

The solvent partial molar enthalpy is equal to

\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o}{dT} \]

The temperature dependence of the activity coefficients currently only occurs through the temperature dependence of the Debye constant.

Parameters

hbar	Output vector of species partial molar enthalpies. Length: m_kk. units are J/kmol.

Reimplemented from ThermoPhase.

Definition at line 448 of file DebyeHuckel.cpp.

References DebyeHuckel::dA_DebyedT_TP(), Cantera::GasConstant, VPStandardStateTP::getEnthalpy_RT(), DebyeHuckel::m_dlnActCoeffMolaldT, Phase::m_kk, DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Phase::temperature().

Referenced by DebyeHuckel::enthalpy_mole().

void getPartialMolarEntropies ( doublereal *  sbar ) const

virtual

Returns an array of partial molar entropies of the species in the solution.

Units: J/kmol/K. Maxwell's equations provide an insight in how to calculate this (p.215 Smith and Van Ness)

\[ \frac{d\mu_i}{dT} = -\bar{s}_i \]

For this phase, the partial molar entropies are equal to the SS species entropies plus the ideal solution contribution.following contribution:

\[ \bar s_k(T,P) = \hat s^0_k(T) - R log(M0 * molality[k]) \]

\[ \bar s_{solvent}(T,P) = \hat s^0_{solvent}(T) - R ((xmolSolvent - 1.0) / xmolSolvent) \]

The reference-state pure-species entropies, \( \hat s^0_k(T) \), at the reference pressure, \( P_{ref} \), are computed by the species thermodynamic property manager. They are polynomial functions of temperature.

See Also

SpeciesThermo

Parameters

sbar	Output vector of species partial molar entropies. Length = m_kk. units are J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 483 of file DebyeHuckel.cpp.

References DebyeHuckel::dA_DebyedT_TP(), Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), DebyeHuckel::m_dlnActCoeffMolaldT, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), Cantera::SmallNumber, and Phase::temperature().

Referenced by DebyeHuckel::entropy_mole().

void getPartialMolarCp ( doublereal *  cpbar ) const

virtual

Return an array of partial molar heat capacities for the species in the mixture.

Units: J/kmol/K

Parameters

cpbar

Output vector of species partial molar heat capacities at constant pressure. Length = m_kk. units are J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 546 of file DebyeHuckel.cpp.

References DebyeHuckel::dA_DebyedT_TP(), Cantera::GasConstant, VPStandardStateTP::getCp_R(), DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_dlnActCoeffMolaldT, Phase::m_kk, DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Phase::temperature().

Referenced by DebyeHuckel::cp_mole().

void getPartialMolarVolumes ( doublereal *  vbar ) const

virtual

Return an array of partial molar volumes for the species in the mixture.

Units: m^3/kmol.

For this solution, the partial molar volumes are normally equal to theconstant species molar volumes, except when the activity coefficients depend on pressure.

The general relation is

  vbar_i = d(chemPot_i)/dP at const T, n
         = V0_i + d(Gex)/dP)_T,M
         = V0_i + RT d(lnActCoeffi)dP _T,M

Parameters

vbar	Output vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.

Reimplemented from ThermoPhase.

Definition at line 531 of file DebyeHuckel.cpp.

References Cantera::GasConstant, VPStandardStateTP::getStandardVolumes(), DebyeHuckel::m_dlnActCoeffMolaldP, Phase::m_kk, DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Phase::temperature().

Referenced by DebyeHuckel::calcDensity().

virtual void setToEquilState ( const doublereal *  lambda_RT )

inlinevirtual

This method is used by the ChemEquil equilibrium solver.

It sets the state such that the chemical potentials satisfy

\[ \frac{\mu_k}{\hat R T} = \sum_m A_{k,m} \left(\frac{\lambda_m} {\hat R T}\right) \]

where \( \lambda_m \) is the element potential of element m. The temperature is unchanged. Any phase (ideal or not) that implements this method can be equilibrated by ChemEquil.

Parameters

lambda_RT

Input vector of dimensionless element potentials The length is equal to nElements().

Reimplemented from MolalityVPSSTP.

Definition at line 1064 of file DebyeHuckel.h.

References DebyeHuckel::err().

void setParameters ( int  n, doublereal *const  c  )

virtual

Set the equation of state parameters.

The number and meaning of these depends on the subclass.

Parameters

n	number of parameters
c	array of n coefficients

Deprecated:

Unimplemented

Reimplemented from ThermoPhase.

Definition at line 1127 of file DebyeHuckel.cpp.

References Cantera::warn_deprecated().

void getParameters ( int &  n, doublereal *const  c  ) const

virtual

Get the equation of state parameters in a vector.

The number and meaning of these depends on the subclass.

Parameters

n	number of parameters
c	array of n coefficients

Deprecated:

Unimplemented

Reimplemented from ThermoPhase.

Definition at line 1132 of file DebyeHuckel.cpp.

References Cantera::warn_deprecated().

void setParametersFromXML ( const XML_Node &  eosdata )

virtual

Set equation of state parameter values from XML entries.

This method is called by function importPhase() in file importCTML.cpp when processing a phase definition in an input file. It should be overloaded in subclasses to set any parameters that are specific to that particular phase model. Note, this method is called before the phase is initialized with elements and/or species.

HKM -> Right now, the parameters are set elsewhere (initThermoXML) It just didn't seem to fit.

Parameters

eosdata

An XML_Node object corresponding to the "thermo" entry for this phase in the input file.

Reimplemented from VPStandardStateTP.

Definition at line 1137 of file DebyeHuckel.cpp.

virtual doublereal satTemperature ( doublereal  p ) const

inlinevirtual

Return the saturation temperature given the pressure.

Parameters

p	Pressure (Pa)

Reimplemented from ThermoPhase.

Definition at line 1114 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual doublereal satPressure ( doublereal  T )

inlinevirtual

Get the saturation pressure for a given temperature.

Note the limitations of this function. Stability considerations concerning multiphase equilibrium are ignored in this calculation. Therefore, the call is made directly to the SS of water underneath. The object is put back into its original state at the end of the call.

Todo:

This is probably not implemented correctly. The stability of the salt should be added into this calculation. The underlying water model may be called to get the stability of the pure water solution, if needed.

Parameters

T	Temperature (kelvin)

Reimplemented from ThermoPhase.

Definition at line 1134 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual doublereal vaporFraction ( ) const

inlinevirtual

Return the fraction of vapor at the current conditions.

Reimplemented from ThermoPhase.

Definition at line 1139 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual void setState_Tsat ( doublereal  t, doublereal  x  )

inlinevirtual

Set the state to a saturated system at a particular temperature.

Parameters

t	Temperature (kelvin)
x	Fraction of vapor

Reimplemented from ThermoPhase.

Definition at line 1144 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual void setState_Psat ( doublereal  p, doublereal  x  )

inlinevirtual

Set the state to a saturated system at a particular pressure.

Parameters

p	Pressure (Pa)
x	Fraction of vapor

Reimplemented from ThermoPhase.

Definition at line 1148 of file DebyeHuckel.h.

References DebyeHuckel::err().

void initThermo ( )

virtual

Initialize the object's internal lengths after species are set.

Initialize. This method is provided to allow subclasses to perform any initialization required after all species have been added. For example, it might be used to resize internal work arrays that must have an entry for each species. The base class implementation does nothing, and subclasses that do not require initialization do not need to overload this method. When importing a CTML phase description, this method is called just prior to returning from function importPhase().

Cascading call sequence downwards starting with Parent.

See Also

importCTML.cpp

Reimplemented from MolalityVPSSTP.

Definition at line 586 of file DebyeHuckel.cpp.

References DebyeHuckel::initLengths(), and MolalityVPSSTP::initThermo().

Referenced by DebyeHuckel::initThermoXML().

void initThermoXML ( XML_Node &  phaseNode, const std::string &  id  )

virtual

Process the XML file after species are set up.

This gets called from importPhase(). It processes the XML file after the species are set up. This is the main routine for reading in activity coefficient parameters.

Parameters

phaseNode	This object must be the phase node of a complete XML tree description of the phase, including all of the species data. In other words while "phase" must point to an XML phase object, it must have sibling nodes "speciesData" that describe the species in the phase.
id	ID of the phase. If nonnull, a check is done to see if phaseNode is pointing to the phase with the correct id.

Reimplemented from VPStandardStateTP.

Definition at line 622 of file DebyeHuckel.cpp.

References XML_Node::attrib(), Cantera::cEST_solvent, Phase::charge(), XML_Node::child(), PDSS_Water::density(), XML_Node::findByAttr(), XML_Node::findByName(), Cantera::fpValue(), Cantera::get_XML_NameID(), ctml::getChildValue(), ctml::getFloat(), ctml::getMap(), ctml::getMatrixValues(), ctml::getStringArray(), XML_Node::hasAttrib(), XML_Node::hasChild(), XML_Node::id(), DebyeHuckel::initThermo(), Cantera::interp_est(), Cantera::lowercase(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_B_Dot, DebyeHuckel::m_Beta_ij, DebyeHuckel::m_electrolyteSpeciesType, DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_formDH, DebyeHuckel::m_formGC, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_maxIionicStrength, Phase::m_speciesCharge, DebyeHuckel::m_speciesCharge_Stoich, Phase::m_speciesSize, DebyeHuckel::m_useHelgesonFixedForm, DebyeHuckel::m_waterProps, DebyeHuckel::m_waterSS, PDSS::molecularWeight(), Cantera::npos, Cantera::OneAtm, XML_Node::root(), PDSS_Water::setState_TP(), MolalityVPSSTP::setStateFromXML(), ThermoPhase::speciesData(), Phase::speciesIndex(), Phase::speciesName(), Phase::speciesNames(), and Cantera::toSI().

double A_Debye_TP ( double  temperature = -1.0, double  pressure = -1.0  ) const

virtual

Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol))

The default is to assume that it is constant, given in the initialization process, and stored in the member double, m_A_Debye. Optionally, a full water treatment may be employed that makes \( A_{Debye} \) a full function of T and P.

\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]

where

\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]

Therefore:

\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]

where

• Units = sqrt(kg/gmol)
• \( N_a \) is Avogadro's number
• \( \rho_w \) is the density of water
• \( e \) is the electronic charge
• \( \epsilon = K \epsilon_o \) is the permittivity of water
• \( K \) is the dielectric constant of water,
• \( \epsilon_o \) is the permittivity of free space.
• \( \rho_o \) is the density of the solvent in its standard state.

Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^1/2 based on:

• \( \epsilon / \epsilon_0 \) = 78.54 (water at 25C)
• T = 298.15 K
• B_Debye = 3.28640E9 (kg/gmol)^1/2 m^-1

Parameters

temperature	Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed.
pressure	Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.

Definition at line 1141 of file DebyeHuckel.cpp.

References WaterProps::ADebye(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_waterProps, DebyeHuckel::pressure(), and Phase::temperature().

Referenced by DebyeHuckel::getMolalityActivityCoefficients(), and DebyeHuckel::s_update_lnMolalityActCoeff().

double dA_DebyedT_TP ( double  temperature = -1.0, double  pressure = -1.0  ) const

virtual

Value of the derivative of the Debye Huckel constant with respect to temperature.

This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).

Units = sqrt(kg/gmol) K-1

Parameters

temperature	Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed.
pressure	Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.

Definition at line 1168 of file DebyeHuckel.cpp.

References WaterProps::ADebye(), DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_waterProps, DebyeHuckel::pressure(), and Phase::temperature().

Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dT().

double d2A_DebyedT2_TP ( double  temperature = -1.0, double  pressure = -1.0  ) const

virtual

Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure.

This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).

Units = sqrt(kg/gmol) K-2

Parameters

temperature	Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed.
pressure	Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.

Definition at line 1193 of file DebyeHuckel.cpp.

References WaterProps::ADebye(), DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_waterProps, DebyeHuckel::pressure(), and Phase::temperature().

Referenced by DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2().

double dA_DebyedP_TP ( double  temperature = -1.0, double  pressure = -1.0  ) const

virtual

Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure.

This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).

Units = sqrt(kg/gmol) Pa-1

Parameters

temperature	Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed.
pressure	Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.

Definition at line 1218 of file DebyeHuckel.cpp.

References WaterProps::ADebye(), DebyeHuckel::m_form_A_Debye, DebyeHuckel::m_waterProps, DebyeHuckel::pressure(), and Phase::temperature().

Referenced by DebyeHuckel::s_update_dlnMolalityActCoeff_dP().

double AionicRadius

(

int

k = 0

)

const

Reports the ionic radius of the kth species.

Parameters

k	species index.

Definition at line 1247 of file DebyeHuckel.cpp.

References DebyeHuckel::m_Aionic.

int formDH ( ) const

inline

Returns the form of the Debye-Huckel parameterization used.

Definition at line 1302 of file DebyeHuckel.h.

References DebyeHuckel::m_formDH.

Array2D& get_Beta_ij ( )

inline

Returns a reference to M_Beta_ij.

Definition at line 1307 of file DebyeHuckel.h.

References DebyeHuckel::m_Beta_ij.

double _nonpolarActCoeff ( double  IionicMolality ) const

private

Static function that implements the non-polar species salt-out modifications.

Returns the calculated activity coefficients.

Parameters

IionicMolality

Value of the ionic molality (sqrt(gmol/kg))

Definition at line 1287 of file DebyeHuckel.cpp.

References DebyeHuckel::m_npActCoeff.

Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().

double _osmoticCoeffHelgesonFixedForm ( ) const

private

Formula for the osmotic coefficient that occurs in the GWB.

It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.

Definition at line 1297 of file DebyeHuckel.cpp.

References DebyeHuckel::m_A_Debye, and DebyeHuckel::m_IionicMolalityStoich.

Referenced by DebyeHuckel::_lnactivityWaterHelgesonFixedForm().

double _lnactivityWaterHelgesonFixedForm ( ) const

private

Formula for the log of the water activity that occurs in the GWB.

It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.

Definition at line 1316 of file DebyeHuckel.cpp.

References DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), MolalityVPSSTP::calcMolalities(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_maxIionicStrength, MolalityVPSSTP::m_Mnaught, and MolalityVPSSTP::m_molalities.

Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().

doublereal err ( const std::string &  msg ) const

private

Bail out of functions with an error exit if they are not implemented.

Definition at line 1256 of file DebyeHuckel.cpp.

Referenced by DebyeHuckel::cv_mole(), DebyeHuckel::satPressure(), DebyeHuckel::satTemperature(), DebyeHuckel::setState_Psat(), DebyeHuckel::setState_Tsat(), DebyeHuckel::setToEquilState(), and DebyeHuckel::vaporFraction().

void initLengths ( )

private

Initialize the internal lengths.

This internal function adjusts the lengths of arrays based on the number of species.

Definition at line 1263 of file DebyeHuckel.cpp.

References DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Dot, DebyeHuckel::m_Beta_ij, DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_dlnActCoeffMolaldP, DebyeHuckel::m_dlnActCoeffMolaldT, DebyeHuckel::m_electrolyteSpeciesType, DebyeHuckel::m_formDH, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, DebyeHuckel::m_pp, Phase::m_speciesSize, DebyeHuckel::m_tmpV, Phase::nSpecies(), and Array2D::resize().

Referenced by DebyeHuckel::initThermo().

void s_update_lnMolalityActCoeff ( ) const

private

Calculate the log activity coefficients.

This function updates the internally stored natural logarithm of the molality activity coefficients. This is the main routine for implementing the activity coefficient formulation.

Definition at line 1335 of file DebyeHuckel.cpp.

References DebyeHuckel::_lnactivityWaterHelgesonFixedForm(), DebyeHuckel::_nonpolarActCoeff(), DebyeHuckel::A_Debye_TP(), MolalityVPSSTP::calcMolalities(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_B_Dot, DebyeHuckel::m_Beta_ij, DebyeHuckel::m_electrolyteSpeciesType, DebyeHuckel::m_formDH, DebyeHuckel::m_IionicMolality, DebyeHuckel::m_IionicMolalityStoich, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, DebyeHuckel::m_maxIionicStrength, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, Phase::m_speciesCharge, DebyeHuckel::m_speciesCharge_Stoich, DebyeHuckel::m_useHelgesonFixedForm, Phase::moleFraction(), and Array2D::value().

Referenced by DebyeHuckel::getActivities(), DebyeHuckel::getChemPotentials(), DebyeHuckel::getMolalityActivityCoefficients(), DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), and DebyeHuckel::getPartialMolarVolumes().

void s_update_dlnMolalityActCoeff_dT ( ) const

private

Calculation of temperature derivative of activity coefficient.

Using internally stored values, this function calculates the temperature derivative of the logarithm of the activity coefficient for all species in the mechanism.

We assume that the activity coefficients are current in this routine

The solvent activity coefficient is on the molality scale. Its derivative is too.

Definition at line 1593 of file DebyeHuckel.cpp.

References DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_dlnActCoeffMolaldT, DebyeHuckel::m_formDH, DebyeHuckel::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, Phase::m_speciesCharge, and Phase::moleFraction().

Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), and DebyeHuckel::getPartialMolarEntropies().

void s_update_d2lnMolalityActCoeff_dT2 ( ) const

private

Calculate the temperature 2nd derivative of the activity coefficient.

Using internally stored values, this function calculates the temperature 2nd derivative of the logarithm of the activity coefficient for all species in the mechanism.

We assume that the activity coefficients are current in this routine

solvent activity coefficient is on the molality scale. Its derivatives are too.

Definition at line 1720 of file DebyeHuckel.cpp.

References DebyeHuckel::d2A_DebyedT2_TP(), DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_formDH, DebyeHuckel::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, Phase::m_speciesCharge, and Phase::moleFraction().

Referenced by DebyeHuckel::getPartialMolarCp().

void s_update_dlnMolalityActCoeff_dP ( ) const

private

Calculate the pressure derivative of the activity coefficient.

Using internally stored values, this function calculates the pressure derivative of the logarithm of the activity coefficient for all species in the mechanism.

We assume that the activity coefficients, molalities, and A_Debye are current.

solvent activity coefficient is on the molality scale. Its derivatives are too.

Definition at line 1842 of file DebyeHuckel.cpp.

References DebyeHuckel::dA_DebyedP_TP(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Debye, DebyeHuckel::m_dlnActCoeffMolaldP, DebyeHuckel::m_electrolyteSpeciesType, DebyeHuckel::m_formDH, DebyeHuckel::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, Phase::m_speciesCharge, and Phase::moleFraction().

Referenced by DebyeHuckel::getPartialMolarVolumes().

Member Data Documentation

int m_formDH

protected

form of the Debye-Huckel parameterization used in the model.

The options are described at the top of this document, and in the general documentation. The list is repeated here:

DHFORM_DILUTE_LIMIT = 0 (default) DHFORM_BDOT_AK = 1 DHFORM_BDOT_AUNIFORM = 2 DHFORM_BETAIJ = 3 DHFORM_PITZER_BETAIJ = 4

Definition at line 1351 of file DebyeHuckel.h.

Referenced by DebyeHuckel::formDH(), DebyeHuckel::initLengths(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

int m_formGC

protected

Format for the generalized concentration:

0 = unity 1 = molar_volume 2 = solvent_volume (default)

The generalized concentrations can have three different forms depending on the value of the member attribute m_formGC, which is supplied in the constructor.

m_formGC	GeneralizedConc	StandardConc
0	X_k	1.0
1	X_k / V_k	1.0 / V_k
2	X_k / V_N	1.0 / V_N

The value and form of the generalized concentration will affect reaction rate constants involving species in this phase.

(HKM Note: Using option #1 may lead to spurious results and has been included only with warnings. The reason is that it molar volumes of electrolytes may often be negative. The molar volume of H+ is defined to be zero too. Either options 0 or 2 are the appropriate choice. Option 0 leads to bulk reaction rate constants which have units of s-1. Option 2 leads to bulk reaction rate constants for bimolecular rxns which have units of m-3 kmol-1 s-1.)

Definition at line 1382 of file DebyeHuckel.h.

Referenced by DebyeHuckel::eosType(), DebyeHuckel::initThermoXML(), and DebyeHuckel::operator=().

vector_int m_electrolyteSpeciesType

protected

Vector containing the electrolyte species type.

The possible types are:

• solvent
• Charged Species
• weakAcidAssociated
• strongAcidAssociated
• polarNeutral
• nonpolarNeutral

Definition at line 1395 of file DebyeHuckel.h.

Referenced by DebyeHuckel::initLengths(), DebyeHuckel::initThermoXML(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), and DebyeHuckel::s_update_lnMolalityActCoeff().

vector_fp m_Aionic

protected

a_k = Size of the ionic species in the DH formulation units = meters

Definition at line 1401 of file DebyeHuckel.h.

Referenced by DebyeHuckel::AionicRadius(), DebyeHuckel::initLengths(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

double m_IionicMolality

mutableprotected

Current value of the ionic strength on the molality scale.

Definition at line 1404 of file DebyeHuckel.h.

Referenced by DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

double m_maxIionicStrength

protected

Maximum value of the ionic strength allowed in the calculation of the activity coefficients.

Definition at line 1410 of file DebyeHuckel.h.

Referenced by DebyeHuckel::_lnactivityWaterHelgesonFixedForm(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

bool m_useHelgesonFixedForm

If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation.

This should be used with caution, and is really only included as a validation exercise.

Definition at line 1421 of file DebyeHuckel.h.

Referenced by DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

double m_IionicMolalityStoich

mutableprotected

Stoichiometric ionic strength on the molality scale.

Definition at line 1425 of file DebyeHuckel.h.

Referenced by DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

int m_form_A_Debye

Form of the constant outside the Debye-Huckel term called A.

It's normally a function of temperature and pressure. However, it can be set from the input file in order to aid in numerical comparisons. Acceptable forms:

  A_DEBYE_CONST  0
  A_DEBYE_WATER  1

The A_DEBYE_WATER form may be used for water solvents with needs to cover varying temperatures and pressures. Note, the dielectric constant of water is a relatively strong function of T, and its variability must be accounted for,

Definition at line 1445 of file DebyeHuckel.h.

Referenced by DebyeHuckel::A_Debye_TP(), DebyeHuckel::d2A_DebyedT2_TP(), DebyeHuckel::dA_DebyedP_TP(), DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::initThermoXML(), and DebyeHuckel::operator=().

double m_A_Debye

mutableprotected

Current value of the Debye Constant, A_Debye.

A_Debye -> this expression appears on the top of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature and pressure.

A_Debye = (F e B_Debye) / (8 Pi epsilon R T)

Units = sqrt(kg/gmol)

Nominal value(298K, atm) = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m

note in Pitzer's nomenclature, A_phi = A_Debye/3.0

Definition at line 1469 of file DebyeHuckel.h.

Referenced by DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), DebyeHuckel::A_Debye_TP(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

double m_B_Debye

protected

Current value of the constant that appears in the denominator.

B_Debye -> this expression appears on the bottom of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature

B_Bebye = F / sqrt( epsilon R T / 2 )

Units = sqrt(kg/gmol) / m

Nominal value = 3.28640E9 sqrt(kg/gmol) / m based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K

Definition at line 1488 of file DebyeHuckel.h.

Referenced by DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

vector_fp m_B_Dot

protected

Array of B_Dot values.

This expression is an extension of the Debye-Huckel expression used in some formulations to extend DH to higher molalities. B_dot is specific to the major ionic pair.

Definition at line 1496 of file DebyeHuckel.h.

Referenced by DebyeHuckel::initLengths(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

vector_fp m_npActCoeff

protected

These are coefficients to describe the increase in activity coeff for non-polar molecules due to the electrolyte becoming stronger (the so-called salt-out effect)

Definition at line 1503 of file DebyeHuckel.h.

Referenced by DebyeHuckel::_nonpolarActCoeff(), DebyeHuckel::DebyeHuckel(), and DebyeHuckel::operator=().

PDSS_Water* m_waterSS

protected

Pointer to the Water standard state object.

derived from the equation of state for water.

Definition at line 1510 of file DebyeHuckel.h.

Referenced by DebyeHuckel::calcDensity(), DebyeHuckel::initThermoXML(), and DebyeHuckel::operator=().

double m_densWaterSS

protected

Storage for the density of water's standard state.

Density depends on temperature and pressure.

Definition at line 1516 of file DebyeHuckel.h.

Referenced by DebyeHuckel::calcDensity(), and DebyeHuckel::operator=().

WaterProps* m_waterProps

protected

Pointer to the water property calculator.

Definition at line 1519 of file DebyeHuckel.h.

Referenced by DebyeHuckel::A_Debye_TP(), DebyeHuckel::d2A_DebyedT2_TP(), DebyeHuckel::dA_DebyedP_TP(), DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::~DebyeHuckel().

vector_fp m_pp

mutableprotected

Temporary array used in equilibrium calculations.

Definition at line 1522 of file DebyeHuckel.h.

Referenced by DebyeHuckel::calcDensity(), DebyeHuckel::initLengths(), and DebyeHuckel::operator=().

vector_fp m_tmpV

mutableprotected

vector of size m_kk, used as a temporary holding area.

Definition at line 1525 of file DebyeHuckel.h.

Referenced by DebyeHuckel::calcDensity(), DebyeHuckel::cp_mole(), DebyeHuckel::enthalpy_mole(), DebyeHuckel::entropy_mole(), DebyeHuckel::gibbs_mole(), DebyeHuckel::initLengths(), and DebyeHuckel::operator=().

vector_fp m_speciesCharge_Stoich

protected

Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules.

The Stoichiometric species charge is the charge of one of the ion that would occur if the species broke into two charged ion pairs. NaCl -> m_speciesCharge_Stoich = -1; HSO4- -> H+ + SO42- = -2 -> The other charge is calculated. For species that aren't ion pairs, it's equal to the m_speciesCharge[] value.

Definition at line 1539 of file DebyeHuckel.h.

Referenced by DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

Array2D m_Beta_ij

protected

Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species.

Definition at line 1547 of file DebyeHuckel.h.

Referenced by DebyeHuckel::get_Beta_ij(), DebyeHuckel::initLengths(), DebyeHuckel::initThermoXML(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_lnMolalityActCoeff().

vector_fp m_lnActCoeffMolal

mutableprotected

Logarithm of the activity coefficients on the molality scale.

mutable because we change this if the composition or temperature or pressure changes.

Definition at line 1554 of file DebyeHuckel.h.

Referenced by DebyeHuckel::getActivities(), DebyeHuckel::getChemPotentials(), DebyeHuckel::getMolalityActivityCoefficients(), DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::initLengths(), DebyeHuckel::operator=(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), and DebyeHuckel::s_update_lnMolalityActCoeff().

vector_fp m_dlnActCoeffMolaldT

mutableprotected

Derivative of log act coeff wrt T.

Definition at line 1557 of file DebyeHuckel.h.

Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::initLengths(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dT().

vector_fp m_d2lnActCoeffMolaldT2

mutableprotected

2nd Derivative of log act coeff wrt T

Definition at line 1560 of file DebyeHuckel.h.

Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::initLengths(), DebyeHuckel::operator=(), and DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2().

vector_fp m_dlnActCoeffMolaldP

mutableprotected

Derivative of log act coeff wrt P.

Definition at line 1563 of file DebyeHuckel.h.

Referenced by DebyeHuckel::getPartialMolarVolumes(), DebyeHuckel::initLengths(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dP().

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

• DebyeHuckel.h
• DebyeHuckel.cpp