Cantera 2.6.0

Public Member Functions | Public Attributes | Private Member Functions | Private Attributes | List of all members
HMWSoln Class Reference
Models of Phases of Matter » Thermodynamic Properties

Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality. More...

`#include <HMWSoln.h>`

Inheritance diagram for HMWSoln:
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Collaboration diagram for HMWSoln:
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## Public Member Functions
| HMWSoln (const std::string &inputFile="", const std::string &id="")
| Construct and initialize an HMWSoln ThermoPhase object directly from an ASCII input file. More...
| HMWSoln (XML_Node &phaseRef, const std::string &id="")
| Construct and initialize an HMWSoln ThermoPhase object directly from an XML database. More...
virtual doublereal | satPressure (doublereal T)
| Get the saturation pressure for a given temperature. More...
void | setBinarySalt (const std::string &sp1, const std::string &sp2, size_t nParams, double *beta0, double *beta1, double *beta2, double *Cphi, double alpha1, double alpha2)
void | setTheta (const std::string &sp1, const std::string &sp2, size_t nParams, double *theta)
void | setPsi (const std::string &sp1, const std::string &sp2, const std::string &sp3, size_t nParams, double *psi)
void | setLambda (const std::string &sp1, const std::string &sp2, size_t nParams, double *lambda)
void | setMunnn (const std::string &sp, size_t nParams, double *munnn)
void | setZeta (const std::string &sp1, const std::string &sp2, const std::string &sp3, size_t nParams, double *psi)
void | setPitzerTempModel (const std::string &model)
void | setPitzerRefTemperature (double Tref)
void | setA_Debye (double A)
| Set the A_Debye parameter. More...
void | setMaxIonicStrength (double Imax)
void | setCroppingCoefficients (double ln_gamma_k_min, double ln_gamma_k_max, double ln_gamma_o_min, double ln_gamma_o_max)
virtual void | initThermo ()
virtual void | getParameters (AnyMap &phaseNode) const
| Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newPhase(AnyMap&) function. More...
virtual void | initThermoXML (XML_Node &phaseNode, const std::string &id)
| Initialize the phase parameters from an XML file. More...
virtual double | A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const
| Value of the Debye Huckel constant as a function of temperature and pressure. 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 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 | ADebye_L (double temperature=-1.0, double pressure=-1.0) const
| Return Pitzer's definition of A_L. More...
double | ADebye_J (double temperature=-1.0, double pressure=-1.0) const
| Return Pitzer's definition of A_J. More...
double | ADebye_V (double temperature=-1.0, double pressure=-1.0) const
| Return Pitzer's definition of A_V. 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...
void | printCoeffs () const
| Print out all of the input Pitzer coefficients. More...
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...
Utilities
virtual std::string | type () const
| String indicating the thermodynamic model implemented. More...
Molar Thermodynamic Properties of the Solution
virtual doublereal | enthalpy_mole () const
| Molar enthalpy. Units: J/kmol. More...
virtual doublereal | relative_enthalpy () const
| Excess molar enthalpy of the solution from the mixing process. More...
virtual doublereal | relative_molal_enthalpy () const
| Excess molar enthalpy of the solution from the mixing process on a molality basis. 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 activity concentrations. More...
virtual doublereal | standardConcentration (size_t k=0) const
| Return the standard concentration for the kth species. More...
virtual void | getActivities (doublereal *ac) const
| Get the array of non-dimensional activities 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 | getPartialMolarVolumes (doublereal *vbar) const
| Return an array of partial molar volumes for the species in the mixture. More...
virtual void | getPartialMolarCp (doublereal *cpbar) const
| Return an array of partial molar heat capacities for the species in the mixture. More...
Public Member Functions inherited from MolalityVPSSTP
| MolalityVPSSTP ()
| Default Constructor. 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, const 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 | setState (const AnyMap &state)
| Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model. 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, doublereal threshold=1e-14) const
| returns a summary of the state of the phase as a string More...
virtual std::string | phaseOfMatter () const
| String indicating the mechanical phase of the matter in this Phase. 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 | 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 (const 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
| We set the convention to molality here. More...
virtual void | getActivityCoefficients (doublereal *ac) const
| Get the array of non-dimensional activity coefficients 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...
virtual double | osmoticCoefficient () const
| Calculate the osmotic coefficient. More...
virtual bool | addSpecies (shared_ptr< Species > spec)
Public Member Functions inherited from VPStandardStateTP
virtual void | setTemperature (const doublereal temp)
| Set the temperature of the phase. More...
virtual void | setPressure (doublereal p)
| Set the internally stored pressure (Pa) at constant temperature and composition. More...
virtual void | setState_TP (doublereal T, doublereal pres)
| Set the temperature and pressure at the same time. More...
virtual 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 double | minTemp (size_t k=npos) const
| Minimum temperature for which the thermodynamic data for the species or phase are valid. More...
virtual double | maxTemp (size_t k=npos) const
| Maximum temperature for which the thermodynamic data for the species are valid. More...
PDSS * | providePDSS (size_t k)
const PDSS * | providePDSS (size_t k) const
| VPStandardStateTP ()
| Constructor. More...
virtual | ~VPStandardStateTP ()
virtual bool | isCompressible () const
| Return whether phase represents a compressible substance. 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 species mole number derivatives of the log activity coefficients. More...
virtual 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 for the species at their standard states at the current T and P of the solution. 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 Entropy 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 in their standard states at the current T and P of the solution. More...
virtual void | getPureGibbs (doublereal *gpure) const
| Get the Gibbs functions for the standard state of the species at the current T and P of the solution. More...
virtual void | getIntEnergy_RT (doublereal *urt) const
| Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution. More...
virtual void | getCp_R (doublereal *cpr) const
| Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution. More...
virtual void | getStandardVolumes (doublereal *vol) const
| Get the molar volumes of the species standard states at the current T and P of the solution. More...
virtual const vector_fp & | getStandardVolumes () const
virtual void | getSpeciesParameters (const std::string &name, AnyMap &speciesNode) const
| Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase. More...
void | installPDSS (size_t k, std::unique_ptr< PDSS > &&pdss)
| Install a PDSS object for species k More...
virtual bool | addSpecies (shared_ptr< Species > spec)
| Add a Species to this Phase. More...
virtual void | getEnthalpy_RT_ref (doublereal *hrt) const
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
| Returns the vector of the Gibbs function of the reference state at the current temperature of the solution and the reference pressure for the species. More...
virtual void | getEntropy_R_ref (doublereal *er) const
| Returns the vector of nondimensional entropies of the reference state at the current temperature of the solution and the reference pressure for each species. More...
virtual void | getCp_R_ref (doublereal *cprt) const
| Returns the vector of nondimensional constant pressure heat capacities of the reference state at the current temperature of the solution and reference pressure for each species. More...
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...
Public Member Functions inherited from ThermoPhase
| ThermoPhase ()
| Constructor. More...
doublereal | RT () const
| Return the Gas Constant multiplied by the current temperature. More...
double | equivalenceRatio () const
| Compute the equivalence ratio for the current mixture from available oxygen and required oxygen. More...
virtual bool | isIdeal () const
| Boolean indicating whether phase is ideal. More...
virtual doublereal | refPressure () const
| Returns the reference pressure in Pa. More...
doublereal | Hf298SS (const size_t k) const
| Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...
virtual void | modifyOneHf298SS (const size_t 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 void | resetHf298 (const size_t k=npos)
| Restore the original heat of formation of one or more species. More...
bool | chargeNeutralityNecessary () const
| Returns the chargeNeutralityNecessity boolean. More...
virtual doublereal | intEnergy_mole () const
| Molar internal energy. Units: J/kmol. More...
virtual doublereal | isothermalCompressibility () const
| Returns the isothermal compressibility. Units: 1/Pa. More...
virtual doublereal | thermalExpansionCoeff () const
| Return the volumetric thermal expansion coefficient. Units: 1/K. More...
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 Units | standardConcentrationUnits () const
| Returns the units of the "standard concentration" for this phase. More...
virtual doublereal | logStandardConc (size_t k=0) const
| Natural logarithm of the standard concentration of the kth species. 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 | 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...
doublereal | enthalpy_mass () const
| Specific enthalpy. Units: J/kg. More...
doublereal | intEnergy_mass () const
| Specific internal energy. Units: J/kg. More...
doublereal | entropy_mass () const
| Specific entropy. Units: J/kg/K. More...
doublereal | gibbs_mass () const
| Specific Gibbs function. Units: J/kg. More...
doublereal | cp_mass () const
| Specific heat at constant pressure. Units: J/kg/K. More...
doublereal | cv_mass () const
| Specific heat at constant volume. Units: J/kg/K. 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, const 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, const 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 (double h, double p, double tol=1e-9)
| Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More...
virtual void | setState_UV (double u, double v, double tol=1e-9)
| Set the specific internal energy (J/kg) and specific volume (m^3/kg). More...
virtual void | setState_SP (double s, double p, double tol=1e-9)
| Set the specific entropy (J/kg/K) and pressure (Pa). More...
virtual void | setState_SV (double s, double v, double tol=1e-9)
| Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More...
virtual void | setState_ST (double s, double t, double tol=1e-9)
| Set the specific entropy (J/kg/K) and temperature (K). More...
virtual void | setState_TV (double t, double v, double tol=1e-9)
| Set the temperature (K) and specific volume (m^3/kg). More...
virtual void | setState_PV (double p, double v, double tol=1e-9)
| Set the pressure (Pa) and specific volume (m^3/kg). More...
virtual void | setState_UP (double u, double p, double tol=1e-9)
| Set the specific internal energy (J/kg) and pressure (Pa). More...
virtual void | setState_VH (double v, double h, double tol=1e-9)
| Set the specific volume (m^3/kg) and the specific enthalpy (J/kg) More...
virtual void | setState_TH (double t, double h, double tol=1e-9)
| Set the temperature (K) and the specific enthalpy (J/kg) More...
virtual void | setState_SH (double s, double h, double tol=1e-9)
| Set the specific entropy (J/kg/K) and the specific enthalpy (J/kg) More...
virtual void | setState_RP (doublereal rho, doublereal p)
| Set the density (kg/m**3) and pressure (Pa) at constant composition. More...
virtual void | setState_RPX (doublereal rho, doublereal p, const doublereal *x)
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More...
virtual void | setState_RPX (doublereal rho, doublereal p, const compositionMap &x)
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More...
virtual void | setState_RPX (doublereal rho, doublereal p, const std::string &x)
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More...
virtual void | setState_RPY (doublereal rho, doublereal p, const doublereal *y)
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More...
virtual void | setState_RPY (doublereal rho, doublereal p, const compositionMap &y)
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More...
virtual void | setState_RPY (doublereal rho, doublereal p, const std::string &y)
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More...
void | setMixtureFraction (double mixFrac, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
void | setMixtureFraction (double mixFrac, const std::string &fuelComp, const std::string &oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
void | setMixtureFraction (double mixFrac, const compositionMap &fuelComp, const compositionMap &oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More...
double | mixtureFraction (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar, const std::string &element="Bilger") const
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
double | mixtureFraction (const std::string &fuelComp, const std::string &oxComp, ThermoBasis basis=ThermoBasis::molar, const std::string &element="Bilger") const
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
double | mixtureFraction (const compositionMap &fuelComp, const compositionMap &oxComp, ThermoBasis basis=ThermoBasis::molar, const std::string &element="Bilger") const
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More...
void | setEquivalenceRatio (double phi, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the equivalence ratio. More...
void | setEquivalenceRatio (double phi, const std::string &fuelComp, const std::string &oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the equivalence ratio. More...
void | setEquivalenceRatio (double phi, const compositionMap &fuelComp, const compositionMap &oxComp, ThermoBasis basis=ThermoBasis::molar)
| Set the mixture composition according to the equivalence ratio. More...
double | equivalenceRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
double | equivalenceRatio (const std::string &fuelComp, const std::string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
double | equivalenceRatio (const compositionMap &fuelComp, const compositionMap &oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More...
double | stoichAirFuelRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
double | stoichAirFuelRatio (const std::string &fuelComp, const std::string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
double | stoichAirFuelRatio (const compositionMap &fuelComp, const compositionMap &oxComp, ThermoBasis basis=ThermoBasis::molar) const
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More...
void | equilibrate (const std::string &XY, const std::string &solver="auto", double rtol=1e-9, int max_steps=50000, int max_iter=100, int estimate_equil=0, int log_level=0)
| Equilibrate a ThermoPhase object. More...
virtual void | setToEquilState (const doublereal *mu_RT)
| This method is used by the ChemEquil equilibrium solver. More...
virtual bool | compatibleWithMultiPhase () const
| Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations. More...
virtual doublereal | critTemperature () const
| Critical temperature (K). More...
virtual doublereal | critPressure () const
| Critical pressure (Pa). More...
virtual doublereal | critVolume () const
| Critical volume (m3/kmol). More...
virtual doublereal | critCompressibility () const
| Critical compressibility (unitless). More...
virtual doublereal | critDensity () const
| Critical density (kg/m3). More...
virtual doublereal | satTemperature (doublereal p) const
| Return the saturation temperature given the pressure. 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...
void | setState_TPQ (double T, double P, double Q)
| Set the temperature, pressure, and vapor fraction (quality). More...
virtual void | modifySpecies (size_t k, shared_ptr< Species > spec)
| Modify the thermodynamic data associated with a species. 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...
virtual MultiSpeciesThermo & | speciesThermo (int k=-1)
| Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More...
virtual const MultiSpeciesThermo & | speciesThermo (int k=-1) const
void | initThermoFile (const std::string &inputFile, const std::string &id)
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 | setParameters (const AnyMap &phaseNode, const AnyMap &rootNode=AnyMap())
| Set equation of state parameters from an AnyMap phase description. More...
AnyMap | parameters (bool withInput=true) const
| Returns the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newPhase(AnyMap&) function. More...
const AnyMap & | input () const
| Access input data associated with the phase description. More...
AnyMap & | input ()
virtual void | setParametersFromXML (const XML_Node &eosdata)
| Set equation of state parameter values from XML entries. 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...
Public Member Functions inherited from Phase
| Phase ()
| Default constructor. More...
| Phase (const Phase &)=delete
Phase & | operator= (const Phase &)=delete
XML_Node & | xml () const
| Returns a const reference to the XML_Node that describes the phase. More...
void | setXMLdata (XML_Node &xmlPhase)
| Stores the XML tree information for the current phase. More...
virtual bool | isPure () const
| Return whether phase represents a pure (single species) substance. More...
virtual bool | hasPhaseTransition () const
| Return whether phase represents a substance with phase transitions. More...
virtual bool | isCompressible () const
| Return whether phase represents a compressible substance. More...
virtual std::map< std::string, size_t > | nativeState () const
| Return a map of properties defining the native state of a substance. More...
virtual std::vector< std::string > | fullStates () const
| Return a vector containing full states defining a phase. More...
virtual std::vector< std::string > | partialStates () const
| Return a vector of settable partial property sets within a phase. More...
virtual size_t | stateSize () const
| Return size of vector defining internal state of the phase. More...
void | saveState (vector_fp &state) const
| Save the current internal state of the phase. More...
virtual 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...
virtual 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...
void | getCharges (double *charges) const
| Copy the vector of species charges into array charges. More...
doublereal | elementalMassFraction (const size_t m) const
| Elemental mass fraction of element m. More...
doublereal | elementalMoleFraction (const size_t m) const
| Elemental mole fraction of element m. More...
const double * | moleFractdivMMW () const
| Returns a const pointer to the start of the moleFraction/MW array. 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 bool | ready () const
| Returns a bool indicating whether the object is ready for use. More...
int | stateMFNumber () const
| Return the State Mole Fraction Number. More...
virtual void | invalidateCache ()
| Invalidate any cached values which are normally updated only when a change in state is detected. More...
bool | caseSensitiveSpecies () const
| Returns `true` if case sensitive species names are enforced. More...
void | setCaseSensitiveSpecies (bool cflag=true)
| Set flag that determines whether case sensitive species are enforced in look-up operations, for example speciesIndex. More...
virtual void | setRoot (std::shared_ptr< Solution > root)
| Set root Solution holding all phase information. More...
vector_fp | getCompositionFromMap (const compositionMap &comp) const
| Converts a compositionMap to a vector with entries for each species Species that are not specified are set to zero in the vector. More...
void | massFractionsToMoleFractions (const double *Y, double *X) const
| Converts a mixture composition from mole fractions to mass fractions. More...
void | moleFractionsToMassFractions (const double *X, double *Y) const
| Converts a mixture composition from mass fractions to mole fractions. 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. More...
void | checkElementArraySize (size_t mm) const
| Check that an array size is at least 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. More...
void | checkSpeciesArraySize (size_t kk) const
| Check that an array size is at least nSpecies(). More...
void | setMoleFractionsByName (const 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 (const 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, const 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, const 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...
compositionMap | getMoleFractionsByName (double threshold=0.0) const
| Get the mole fractions by name. More...
double | moleFraction (size_t k) const
| Return the mole fraction of a single species. More...
double | moleFraction (const std::string &name) const
| Return the mole fraction of a single species. More...
compositionMap | getMassFractionsByName (double threshold=0.0) const
| Get the mass fractions by name. More...
double | massFraction (size_t k) const
| Return the mass fraction of a single species. More...
double | massFraction (const std::string &name) const
| Return the mass fraction of a single species. More...
void | getMoleFractions (double *const x) const
| Get the species mole fraction vector. More...
virtual void | setMoleFractions (const double *const x)
| Set the mole fractions to the specified values. More...
virtual void | setMoleFractions_NoNorm (const double *const x)
| Set the mole fractions to the specified values without normalizing. More...
void | getMassFractions (double *const y) const
| Get the species mass fractions. More...
const double * | massFractions () const
| Return a const pointer to the mass fraction array. More...
virtual void | setMassFractions (const double *const y)
| Set the mass fractions to the specified values and normalize them. More...
virtual void | setMassFractions_NoNorm (const double *const y)
| Set the mass fractions to the specified values without normalizing. More...
void | getConcentrations (double *const c) const
| Get the species concentrations (kmol/m^3). More...
double | concentration (const size_t k) const
| Concentration of species k. More...
virtual void | setConcentrations (const double *const conc)
| Set the concentrations to the specified values within the phase. More...
virtual void | setConcentrationsNoNorm (const double *const conc)
| Set the concentrations without ignoring negative concentrations. More...
doublereal | temperature () const
| Temperature (K). More...
virtual double | electronTemperature () const
| Electron Temperature (K) More...
virtual double | density () const
| Density (kg/m^3). More...
double | molarDensity () const
| Molar density (kmol/m^3). More...
double | molarVolume () const
| Molar volume (m^3/kmol). More...
virtual void | setDensity (const double density_)
| Set the internally stored density (kg/m^3) of the phase. More...
virtual void | setMolarDensity (const double molarDensity)
| Set the internally stored molar density (kmol/m^3) of the phase. More...
virtual void | setElectronTemperature (double etemp)
| Set the internally stored electron temperature of the phase (K). More...
doublereal | mean_X (const doublereal *const Q) const
| Evaluate the mole-fraction-weighted mean of an array Q. More...
doublereal | mean_X (const vector_fp &Q) const
| Evaluate the mole-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...
size_t | addElement (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. More...
void | addSpeciesAlias (const std::string &name, const std::string &alias)
| Add a species alias (that is, a user-defined alternative species name). More...
virtual std::vector< std::string > | findIsomers (const compositionMap &compMap) const
| Return a vector with isomers names matching a given composition map. More...
virtual std::vector< std::string > | findIsomers (const std::string &comp) const
| Return a vector with isomers names matching a given composition string. More...
shared_ptr< Species > | species (const std::string &name) const
| Return the Species object for the named species. More...
shared_ptr< Species > | species (size_t k) const
| Return the Species object for species whose index is k. More...
void | ignoreUndefinedElements ()
| Set behavior when adding a species containing undefined elements to just skip the species. More...
void | addUndefinedElements ()
| Set behavior when adding a species containing undefined elements to add those elements to the phase. More...
void | throwUndefinedElements ()
| Set the behavior when adding a species containing undefined elements to throw an exception. More...

## Public Attributes
int | m_form_A_Debye
| Form of the constant outside the Debye-Huckel term called A. More...

## Protected Member Functions
Mechanical Equation of State Properties
void | calcDensity ()
| Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...
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 | calcDensity ()
| Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...
virtual void | _updateStandardStateThermo () const
| Updates the standard state thermodynamic functions at the current T and P of the solution. More...
virtual void | invalidateCache ()
| Invalidate any cached values which are normally updated only when a change in state is detected. More...
const vector_fp & | Gibbs_RT_ref () const
virtual void | getParameters (AnyMap &phaseNode) const
| Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newPhase(AnyMap&) function. More...
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...
Protected Member Functions inherited from Phase
void | assertCompressible (const std::string &setter) const
| Ensure that phase is compressible. More...
void | assignDensity (const double density_)
| Set the internally stored constant density (kg/m^3) of the phase. More...
void | setMolecularWeight (const int k, const double mw)
| Set the molecular weight of a single species to a given value. More...
virtual void | compositionChanged ()
| Apply changes to the state which are needed after the composition changes. More...

## Private Member Functions
void | s_updateScaling_pHScaling () const
| Apply the current phScale to a set of activity Coefficients. More...
void | s_updateScaling_pHScaling_dT () const
| Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature. More...
void | s_updateScaling_pHScaling_dT2 () const
| Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature. More...
void | s_updateScaling_pHScaling_dP () const
| Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure. More...
doublereal | s_NBS_CLM_lnMolalityActCoeff () const
| Calculate the Chlorine activity coefficient on the NBS scale. More...
doublereal | s_NBS_CLM_dlnMolalityActCoeff_dT () const
| Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale. More...
doublereal | s_NBS_CLM_d2lnMolalityActCoeff_dT2 () const
| Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale. More...
doublereal | s_NBS_CLM_dlnMolalityActCoeff_dP () const
| Calculate the pressure derivative of the Chlorine activity coefficient. More...
void | initLengths ()
| Initialize all of the species-dependent lengths in the object. More...
virtual void | applyphScale (doublereal *acMolality) const
| Apply the current phScale to a set of activity Coefficients or activities. More...
void | s_update_lnMolalityActCoeff () const
void | s_update_dlnMolalityActCoeff_dT () const
| This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More...
void | s_update_d2lnMolalityActCoeff_dT2 () const
| This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More...
void | s_update_dlnMolalityActCoeff_dP () const
| This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients. More...
void | s_updateIMS_lnMolalityActCoeff () const
| This function will be called to update the internally stored natural logarithm of the molality activity coefficients. More...
void | s_updatePitzer_lnMolalityActCoeff () const
| Calculate the Pitzer portion of the activity coefficients. More...
void | s_updatePitzer_dlnMolalityActCoeff_dT () const
| Calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More...
void | s_updatePitzer_d2lnMolalityActCoeff_dT2 () const
| This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More...
void | s_updatePitzer_dlnMolalityActCoeff_dP () const
| Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients. More...
void | s_updatePitzer_CoeffWRTemp (int doDerivs=2) const
| Calculates the Pitzer coefficients' dependence on the temperature. More...
void | calc_lambdas (double is) const
| Calculate the lambda interactions. More...
void | calc_thetas (int z1, int z2, double *etheta, double *etheta_prime) const
| Calculate etheta and etheta_prime. More...
void | counterIJ_setup () const
| Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species. More...
void | calcMolalitiesCropped () const
| Calculate the cropped molalities. More...
void | readXMLBinarySalt (XML_Node &BinSalt)
| Process an XML node called "binarySaltParameters". More...
void | readXMLTheta (XML_Node &BinSalt)
| Process an XML node called "thetaAnion" or "thetaCation". More...
void | readXMLPsi (XML_Node &BinSalt)
| Process an XML node called "psiCommonAnion" or "psiCommonCation". More...
void | readXMLLambdaNeutral (XML_Node &BinSalt)
| Process an XML node called "lambdaNeutral". More...
void | readXMLMunnnNeutral (XML_Node &BinSalt)
| Process an XML node called "MunnnNeutral". More...
void | readXMLZetaCation (const XML_Node &BinSalt)
| Process an XML node called "zetaCation". More...
void | calcIMSCutoffParams_ ()
| Precalculate the IMS Cutoff parameters for typeCutoff = 2. More...
void | calcMCCutoffParams_ ()
| Calculate molality cut-off parameters. More...

## Private Attributes
int | m_formPitzerTemp
| This is the form of the temperature dependence of Pitzer parameterization used in the model. More...
double | m_IionicMolality
| Current value of the ionic strength on the molality scale Associated Salts, if present in the mechanism, don't contribute to the value of the ionic strength in this version of the Ionic strength. More...
double | m_maxIionicStrength
| Maximum value of the ionic strength allowed in the calculation of the activity coefficients. More...
double | m_TempPitzerRef
| Reference Temperature for the Pitzer formulations. More...
double | m_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. More...
PDSS * | m_waterSS
| Water standard state calculator. More...
std::unique_ptr< WaterProps > | m_waterProps
| Pointer to the water property calculator. More...
vector_fp | m_tmpV
| vector of size m_kk, used as a temporary holding area. More...
vector_fp | m_Beta0MX_ij
| Array of 2D data used in the Pitzer/HMW formulation. More...
vector_fp | m_Beta0MX_ij_L
| Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ. More...
vector_fp | m_Beta0MX_ij_LL
| Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ. More...
vector_fp | m_Beta0MX_ij_P
| Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ. More...
Array2D | m_Beta0MX_ij_coeff
| Array of coefficients for Beta0, a variable in Pitzer's papers. More...
vector_fp | m_Beta1MX_ij
| Array of 2D data used in the Pitzer/HMW formulation. More...
vector_fp | m_Beta1MX_ij_L
| Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ. More...
vector_fp | m_Beta1MX_ij_LL
| Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ. More...
vector_fp | m_Beta1MX_ij_P
| Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ. More...
Array2D | m_Beta1MX_ij_coeff
| Array of coefficients for Beta1, a variable in Pitzer's papers. More...
vector_fp | m_Beta2MX_ij
| Array of 2D data used in the Pitzer/HMW formulation. More...
vector_fp | m_Beta2MX_ij_L
| Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ. More...
vector_fp | m_Beta2MX_ij_LL
| Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ. More...
vector_fp | m_Beta2MX_ij_P
| Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ. More...
Array2D | m_Beta2MX_ij_coeff
| Array of coefficients for Beta2, a variable in Pitzer's papers. More...
vector_fp | m_Alpha1MX_ij
vector_fp | m_Alpha2MX_ij
| Array of 2D data used in the Pitzer/HMW formulation. More...
vector_fp | m_CphiMX_ij
| Array of 2D data used in the Pitzer/HMW formulation. More...
vector_fp | m_CphiMX_ij_L
| Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ. More...
vector_fp | m_CphiMX_ij_LL
| Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ. More...
vector_fp | m_CphiMX_ij_P
| Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ. More...
Array2D | m_CphiMX_ij_coeff
| Array of coefficients for CphiMX, a parameter in the activity coefficient formulation. More...
vector_fp | m_Theta_ij
| Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation. More...
vector_fp | m_Theta_ij_L
| Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ. More...
vector_fp | m_Theta_ij_LL
| Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ. More...
vector_fp | m_Theta_ij_P
| Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ. More...
Array2D | m_Theta_ij_coeff
| Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation. More...
vector_fp | m_Psi_ijk
| Array of 3D data used in the Pitzer/HMW formulation. More...
vector_fp | m_Psi_ijk_L
| Derivative of Psi_ijk[n] wrt T. More...
vector_fp | m_Psi_ijk_LL
| Derivative of Psi_ijk[n] wrt TT. More...
vector_fp | m_Psi_ijk_P
| Derivative of Psi_ijk[n] wrt P. More...
Array2D | m_Psi_ijk_coeff
| Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation. More...
Array2D | m_Lambda_nj
| Lambda coefficient for the ij interaction. More...
Array2D | m_Lambda_nj_L
| Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij. More...
Array2D | m_Lambda_nj_LL
| Derivative of Lambda_nj[i][j] wrt TT. More...
Array2D | m_Lambda_nj_P
| Derivative of Lambda_nj[i][j] wrt P. More...
Array2D | m_Lambda_nj_coeff
| Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation. More...
vector_fp | m_Mu_nnn
| Mu coefficient for the self-ternary neutral coefficient. More...
vector_fp | m_Mu_nnn_L
| Mu coefficient temperature derivative for the self-ternary neutral coefficient. More...
vector_fp | m_Mu_nnn_LL
| Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient. More...
vector_fp | m_Mu_nnn_P
| Mu coefficient pressure derivative for the self-ternary neutral coefficient. More...
Array2D | m_Mu_nnn_coeff
| Array of coefficients form_Mu_nnn term. More...
vector_fp | m_lnActCoeffMolal_Scaled
| Logarithm of the activity coefficients on the molality scale. More...
vector_fp | m_lnActCoeffMolal_Unscaled
| Logarithm of the activity coefficients on the molality scale. More...
vector_fp | m_dlnActCoeffMolaldT_Scaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More...
vector_fp | m_dlnActCoeffMolaldT_Unscaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More...
vector_fp | m_d2lnActCoeffMolaldT2_Scaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More...
vector_fp | m_d2lnActCoeffMolaldT2_Unscaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More...
vector_fp | m_dlnActCoeffMolaldP_Scaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More...
vector_fp | m_dlnActCoeffMolaldP_Unscaled
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More...
vector_fp | m_molalitiesCropped
| Cropped and modified values of the molalities used in activity coefficient calculations. More...
bool | m_molalitiesAreCropped
| Boolean indicating whether the molalities are cropped or are modified. More...
vector_int | m_CounterIJ
| a counter variable for keeping track of symmetric binary interactions amongst the solute species. More...
double | elambda [17]
| This is elambda, MEC. More...
double | elambda1 [17]
| This is elambda1, MEC. More...
vector_fp | m_gfunc_IJ
| Various temporary arrays used in the calculation of the Pitzer activity coefficients. More...
vector_fp | m_g2func_IJ
| This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ. More...
vector_fp | m_hfunc_IJ
| hfunc, was called gprime in Pitzer's paper. More...
vector_fp | m_h2func_IJ
| hfunc2, was called gprime in Pitzer's paper. More...
vector_fp | m_BMX_IJ
| Intermediate variable called BMX in Pitzer's paper. More...
vector_fp | m_BMX_IJ_L
| Derivative of BMX_IJ wrt T. Vector index is counterIJ. More...
vector_fp | m_BMX_IJ_LL
| Derivative of BMX_IJ wrt TT. Vector index is counterIJ. More...
vector_fp | m_BMX_IJ_P
| Derivative of BMX_IJ wrt P. Vector index is counterIJ. More...
vector_fp | m_BprimeMX_IJ
| Intermediate variable called BprimeMX in Pitzer's paper. More...
vector_fp | m_BprimeMX_IJ_L
| Derivative of BprimeMX wrt T. Vector index is counterIJ. More...
vector_fp | m_BprimeMX_IJ_LL
| Derivative of BprimeMX wrt TT. Vector index is counterIJ. More...
vector_fp | m_BprimeMX_IJ_P
| Derivative of BprimeMX wrt P. Vector index is counterIJ. More...
vector_fp | m_BphiMX_IJ
| Intermediate variable called BphiMX in Pitzer's paper. More...
vector_fp | m_BphiMX_IJ_L
| Derivative of BphiMX_IJ wrt T. Vector index is counterIJ. More...
vector_fp | m_BphiMX_IJ_LL
| Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ. More...
vector_fp | m_BphiMX_IJ_P
| Derivative of BphiMX_IJ wrt P. Vector index is counterIJ. More...
vector_fp | m_Phi_IJ
| Intermediate variable called Phi in Pitzer's paper. More...
vector_fp | m_Phi_IJ_L
| Derivative of m_Phi_IJ wrt T. Vector index is counterIJ. More...
vector_fp | m_Phi_IJ_LL
| Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ. More...
vector_fp | m_Phi_IJ_P
| Derivative of m_Phi_IJ wrt P. Vector index is counterIJ. More...
vector_fp | m_Phiprime_IJ
| Intermediate variable called Phiprime in Pitzer's paper. More...
vector_fp | m_PhiPhi_IJ
| Intermediate variable called PhiPhi in Pitzer's paper. More...
vector_fp | m_PhiPhi_IJ_L
| Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ. More...
vector_fp | m_PhiPhi_IJ_LL
| Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ. More...
vector_fp | m_PhiPhi_IJ_P
| Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ. More...
vector_fp | m_CMX_IJ
| Intermediate variable called CMX in Pitzer's paper. More...
vector_fp | m_CMX_IJ_L
| Derivative of m_CMX_IJ wrt T. Vector index is counterIJ. More...
vector_fp | m_CMX_IJ_LL
| Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ. More...
vector_fp | m_CMX_IJ_P
| Derivative of m_CMX_IJ wrt P. Vector index is counterIJ. More...
vector_fp | m_gamma_tmp
| Intermediate storage of the activity coefficient itself. More...
vector_fp | IMS_lnActCoeffMolal_
| Logarithm of the molal activity coefficients. More...
doublereal | IMS_X_o_cutoff_
| value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process; More...
doublereal | IMS_cCut_
| Parameter in the polyExp cutoff treatment having to do with rate of exp decay. More...
doublereal | IMS_slopegCut_
| Parameter in the polyExp cutoff treatment. More...
doublereal | MC_X_o_cutoff_
| value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process; More...
doublereal | m_last_is
Parameters in the polyExp cutoff treatment having to do with rate of exp decay
doublereal | IMS_dfCut_
doublereal | IMS_efCut_
doublereal | IMS_afCut_
doublereal | IMS_bfCut_
doublereal | IMS_dgCut_
doublereal | IMS_egCut_
doublereal | IMS_agCut_
doublereal | IMS_bgCut_
Parameters in the Molality Exp cutoff treatment
doublereal | MC_dpCut_
doublereal | MC_epCut_
doublereal | MC_apCut_
doublereal | MC_bpCut_
doublereal | MC_cpCut_
doublereal | CROP_ln_gamma_o_min
doublereal | CROP_ln_gamma_o_max
doublereal | CROP_ln_gamma_k_min
doublereal | CROP_ln_gamma_k_max
vector_int | CROP_speciesCropped_
| This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime. More...

## Additional Inherited Members
Protected Attributes inherited from MolalityVPSSTP
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...
double | m_minTemp
| The minimum temperature at which data for all species is valid. More...
double | m_maxTemp
| The maximum temperature at which data for all species is valid. More...
doublereal | m_Tlast_ss
| The last temperature at which the standard state thermodynamic properties were calculated at. More...
doublereal | m_Plast_ss
| The last pressure at which the Standard State thermodynamic properties were calculated at. More...
std::vector< std::unique_ptr< PDSS > > | m_PDSS_storage
| Storage for the PDSS objects for the species. More...
vector_fp | m_h0_RT
| Vector containing the species reference enthalpies at T = m_tlast and P = p_ref. More...
vector_fp | m_cp0_R
| Vector containing the species reference constant pressure heat capacities at T = m_tlast and P = p_ref. More...
vector_fp | m_g0_RT
| Vector containing the species reference Gibbs functions at T = m_tlast and P = p_ref. More...
vector_fp | m_s0_R
| Vector containing the species reference entropies at T = m_tlast and P = p_ref. More...
vector_fp | m_V0
| Vector containing the species reference molar volumes. More...
vector_fp | m_hss_RT
| Vector containing the species Standard State enthalpies at T = m_tlast and P = m_plast. More...
vector_fp | m_cpss_R
| Vector containing the species Standard State constant pressure heat capacities at T = m_tlast and P = m_plast. More...
vector_fp | m_gss_RT
| Vector containing the species Standard State Gibbs functions at T = m_tlast and P = m_plast. More...
vector_fp | m_sss_R
| Vector containing the species Standard State entropies at T = m_tlast and P = m_plast. More...
vector_fp | m_Vss
| Vector containing the species standard state volumes at T = m_tlast and P = m_plast. More...
Protected Attributes inherited from ThermoPhase
MultiSpeciesThermo | m_spthermo
| Pointer to the calculation manager for species reference-state thermodynamic properties. More...
AnyMap | m_input
| Data supplied via setParameters. 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. Units are Volts. More...
bool | m_chargeNeutralityNecessary
| Boolean indicating whether a charge neutrality condition is a necessity. More...
int | m_ssConvention
| Contains the standard state convention. More...
doublereal | m_tlast
| last value of the temperature processed by reference state More...
Protected Attributes inherited from Phase
ValueCache | m_cache
| Cached for saved calculations within each ThermoPhase. More...
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_speciesCharge
| Vector of species charges. length m_kk. More...
std::map< std::string, shared_ptr< Species > > | m_species
UndefElement::behavior | m_undefinedElementBehavior
| Flag determining behavior when adding species with an undefined element. More...
bool | m_caseSensitiveSpecies
| Flag determining whether case sensitive species names are enforced. More...

## Detailed Description

Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality.

As a prerequisite to the specification of thermodynamic quantities, The concentrations of the ionic species are assumed to obey the electroneutrality condition.

## Specification of Species Standard State Properties

The solvent is assumed to be liquid water. A real model for liquid water (IAPWS 1995 formulation) is used as its standard state. All standard state properties for the solvent are based on this real model for water, and involve function calls to the object that handles the real water model, Cantera::WaterPropsIAPWS.

The standard states for solutes 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 solutes that rely on ThermoPhase::m_spthermo, are assumed to have an incompressible standard state mechanical property. In other words, the molar volumes are independent of temperature and pressure.

For these incompressible, standard states, 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.

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

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.

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

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

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, that is, 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. This problem leads to a redundancy in the evaluation of species standard state properties. The redundancy issue is resolved by setting the standard state chemical potential enthalpy, entropy, and volume for the hydrogen ion, H+, to zero, for every temperature and pressure. After this convention is applied, all other standard state properties of ionic species contain meaningful information.

### Ionic Strength

Most of the parameterizations within the model use the ionic strength as a key variable. The ionic strength, \( I\) 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).

### Specification of the Excess Gibbs Free Energy

Pitzer's formulation may best be represented as a specification of the excess Gibbs free energy, \( G^{ex} \), defined as the deviation of the total Gibbs free energy from that of an ideal molal solution.

\[ G = G^{id} + G^{ex} \]

The ideal molal solution contribution, not equal to an ideal solution contribution and in fact containing a singularity at the zero solvent mole fraction limit, is given below.

\[ G^{id} = n_o \mu^o_o + \sum_{k\ne o} n_k \mu_k^{\triangle} + \tilde{M}_o n_o ( RT (\sum{m_i(\ln(m_i)-1)})) \]

From the excess Gibbs free energy formulation, the activity coefficient expression and the osmotic coefficient expression for the solvent may be defined, by taking the appropriate derivatives. Using this approach guarantees that the entire system will obey the Gibbs-Duhem relations.

Pitzer employs the following general expression for the excess Gibbs free energy

\[ \begin{array}{cclc} \frac{G^{ex}}{\tilde{M}_o n_o RT} &= & \left( \frac{4A_{Debye}I}{3b} \right) \ln(1 + b \sqrt{I}) + 2 \sum_c \sum_a m_c m_a B_{ca} + \sum_c \sum_a m_c m_a Z C_{ca} \\&& + \sum_{c < c'} \sum m_c m_{c'} \left[ 2 \Phi_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ 2 \Phi_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&& + 2 \sum_n \sum_c m_n m_c \lambda_{nc} + 2 \sum_n \sum_a m_n m_a \lambda_{na} + 2 \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \sum_n m^2_n \lambda_{nn} \end{array} \]

a is a subscript over all anions, c is a subscript extending over all cations, and i is a subscript that extends over all anions and cations. n is a subscript that extends only over neutral solute molecules. The second line contains cross terms where cations affect cations and/or cation/anion pairs, and anions affect anions or cation/anion pairs. Note part of the coefficients, \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) stem from the theory of unsymmetrical mixing of electrolytes with different charges. This theory depends on the total ionic strength of the solution, and therefore, \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) will depend on I, the ionic strength. \( B_{ca}\) is a strong function of the total ionic strength, I, of the electrolyte. The rest of the coefficients are assumed to be independent of the molalities or ionic strengths. However, all coefficients are potentially functions of the temperature and pressure of the solution.

A is the Debye-Huckel constant. Its specification is described in its own section below.

\( I\) is the ionic strength of the solution, and is given by:

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

In contrast to several other Debye-Huckel implementations (see DebyeHuckel), the parameter \( b\) in the above equation is a constant that does not vary with respect to ion identity. This is an important simplification as it avoids troubles with satisfaction of the Gibbs-Duhem analysis.

The function \( Z \) is given by

\[ Z = \sum_i m_i \left| z_i \right| \]

The value of \( B_{ca}\) is given by the following function

\[ B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I}) + \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \]

where

\[ g(x) = 2 \frac{(1 - (1 + x)\exp[-x])}{x^2} \]

The formulation for \( B_{ca}\) combined with the formulation of the Debye- Huckel term in the eqn. for the excess Gibbs free energy stems essentially from an empirical fit to the ionic strength dependent data based over a wide sampling of binary electrolyte systems. \( C_{ca} \), \( \lambda_{nc} \), \( \lambda_{na} \), \( \lambda_{nn} \), \( \Psi_{c{c'}a} \), \( \Psi_{a{a'}c} \) are experimentally derived coefficients that may have pressure and/or temperature dependencies.

The \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) formulations are slightly more complicated. \( b \) is a universal constant defined to be equal to \( 1.2\ kg^{1/2}\ gmol^{-1/2} \). The exponential coefficient \( \alpha^{(1)}_{ca} \) is usually fixed at \( \alpha^{(1)}_{ca} = 2.0\ kg^{1/2} gmol^{-1/2}\) except for 2-2 electrolytes, while other parameters were fit to experimental data. For 2-2 electrolytes, \( \alpha^{(1)}_{ca} = 1.4\ kg^{1/2}\ gmol^{-1/2}\) is used in combination with either \( \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}\) or \( \alpha^{(2)}_{ca} = k A_\psi \), where k is a constant. For electrolytes other than 2-2 electrolytes the \( \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \) term is not used in the fitting procedure; it is only used for divalent metal solfates and other high-valence electrolytes which exhibit significant association at low ionic strengths.

The \( \beta^{(0)}_{ca} \), \( \beta^{(1)}_{ca}\), \( \beta^{(2)}_{ca} \), and \( C_{ca} \) binary coefficients are referred to as ion- interaction or Pitzer parameters. These Pitzer parameters may vary with temperature and pressure but they do not depend on the ionic strength. Their values and temperature derivatives of their values have been tabulated for a range of electrolytes

The \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) contributions, which capture cation-cation and anion-anion interactions, also have an ionic strength dependence.

Ternary contributions \( \Psi_{c{c'}a} \) and \( \Psi_{a{a'}c} \) have been measured also for some systems. The success of the Pitzer method lies in its ability to model nonlinear activity coefficients of complex multicomponent systems with just binary and minor ternary contributions, which can be independently measured in binary or ternary subsystems.

### Multicomponent Activity Coefficients for Solutes

The formulas for activity coefficients of solutes may be obtained by taking the following derivative of the excess Gibbs Free Energy formulation described above:

\[ \ln(\gamma_k^\triangle) = \frac{d\left( \frac{G^{ex}}{M_o n_o RT} \right)}{d(m_k)}\Bigg|_{n_i} \]

In the formulas below the following conventions are used. The subscript M refers to a particular cation. The subscript X refers to a particular anion, whose activity is being currently evaluated. the subscript a refers to a summation over all anions in the solution, while the subscript c refers to a summation over all cations in the solutions.

The activity coefficient for a particular cation M is given by

\[ \ln(\gamma_M^\triangle) = -z_M^2(F) + \sum_a m_a \left( 2 B_{Ma} + Z C_{Ma} \right) + z_M \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_c m_c \left[ 2 \Phi_{Mc} + \sum_a m_a \Psi_{Mca} \right] + \sum_{a < a'} \sum m_a m_{a'} \Psi_{Ma{a'}} + 2 \sum_n m_n \lambda_{nM} \]

The activity coefficient for a particular anion X is given by

\[ \ln(\gamma_X^\triangle) = -z_X^2(F) + \sum_a m_c \left( 2 B_{cX} + Z C_{cX} \right) + \left|z_X \right| \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_a m_a \left[ 2 \Phi_{Xa} + \sum_c m_c \Psi_{cXa} \right] + \sum_{c < c'} \sum m_c m_{c'} \Psi_{c{c'}X} + 2 \sum_n m_n \lambda_{nM} \]

where the function \( F \) is given by

\[ F = - A_{\phi} \left[ \frac{\sqrt{I}}{1 + b \sqrt{I}} + \frac{2}{b} \ln{\left(1 + b\sqrt{I}\right)} \right] + \sum_a \sum_c m_a m_c B'_{ca} + \sum_{c < c'} \sum m_c m_{c'} \Phi'_{c{c'}} + \sum_{a < a'} \sum m_a m_{a'} \Phi'_{a{a'}} \]

We have employed the definition of \( A_{\phi} \), also used by Pitzer which is equal to

\[ A_{\phi} = \frac{A_{Debye}}{3} \]

In the above formulas, \( \Phi'_{c{c'}} \) and \( \Phi'_{a{a'}} \) are the ionic strength derivatives of \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \), respectively.

The function \( B'_{MX} \) is defined as:

\[ B'_{MX} = \left( \frac{\beta^{(1)}_{MX} h(\alpha^{(1)}_{MX} \sqrt{I})}{I} \right) \left( \frac{\beta^{(2)}_{MX} h(\alpha^{(2)}_{MX} \sqrt{I})}{I} \right) \]

where \( h(x) \) is defined as

\[ h(x) = g'(x) \frac{x}{2} = \frac{2\left(1 - \left(1 + x + \frac{x^2}{2} \right)\exp(-x) \right)}{x^2} \]

The activity coefficient for neutral species N is given by

\[ \ln(\gamma_N^\triangle) = 2 \left( \sum_i m_i \lambda_{iN}\right) \]

### Activity of the Water Solvent

The activity for the solvent water, \( a_o \), is not independent and must be determined either from the Gibbs-Duhem relation or from taking the appropriate derivative of the same excess Gibbs free energy function as was used to formulate the solvent activity coefficients. Pitzer's description follows the later approach to derive a formula for the osmotic coefficient, \( \phi \).

\[ \phi - 1 = - \left( \frac{d\left(\frac{G^{ex}}{RT} \right)}{d(\tilde{M}_o n_o)} \right) \frac{1}{\sum_{i \ne 0} m_i} \]

The osmotic coefficient may be related to the water activity by the following relation:

\[ \phi = - \frac{1}{\tilde{M}_o \sum_{i \neq o} m_i} \ln(a_o) = - \frac{n_o}{\sum_{i \neq o}n_i} \ln(a_o) \]

The result is the following

\[ \begin{array}{ccclc} \phi - 1 &= & \frac{2}{\sum_{i \ne 0} m_i} \bigg[ & - A_{\phi} \frac{I^{3/2}}{1 + b \sqrt{I}} + \sum_c \sum_a m_c m_a \left( B^{\phi}_{ca} + Z C_{ca}\right) \\&&& + \sum_{c < c'} \sum m_c m_{c'} \left[ \Phi^{\phi}_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ \Phi^{\phi}_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&&& + \sum_n \sum_c m_n m_c \lambda_{nc} + \sum_n \sum_a m_n m_a \lambda_{na} + \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \frac{1}{2} \left( \sum_n m^2_n \lambda_{nn}\right) \bigg] \end{array} \]

It can be shown that the expression

\[ B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{ca} \sqrt{I})} + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I} )} \]

is consistent with the expression \( B_{ca} \) in the \( G^{ex} \) expression after carrying out the derivative wrt \( m_M \).

Also taking into account that \( {\Phi}_{c{c'}} \) and \( {\Phi}_{a{a'}} \) has an ionic strength dependence.

\[ \Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI} \]

\[ \Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI} \]

### Temperature and Pressure Dependence of the Pitzer Parameters

In general most of the coefficients introduced in the previous section may have a temperature and pressure dependence. The temperature and pressure dependence of these coefficients strongly influence the value of the excess Enthalpy and excess Volumes of Pitzer solutions. Therefore, these are readily measurable quantities. HMWSoln provides several different methods for putting these dependencies into the coefficients. HMWSoln has an implementation described by Silverter and Pitzer (1977), which was used to fit experimental data for NaCl over an extensive range, below the critical temperature of water. They found a temperature functional form for fitting the 3 following coefficients that describe the Pitzer parameterization for a single salt to be adequate to describe how the excess Gibbs free energy values for the binary salt changes with respect to temperature. The following functional form was used to fit the temperature dependence of the Pitzer Coefficients for each cation - anion pair, M X.

\[ \beta^{(0)}_{MX} = q^{b0}_0 + q^{b0}_1 \left( T - T_r \right) + q^{b0}_2 \left( T^2 - T_r^2 \right) + q^{b0}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{b0}_4 \ln \left( \frac{T}{T_r} \right) \]

\[ \beta^{(1)}_{MX} = q^{b1}_0 + q^{b1}_1 \left( T - T_r \right) + q^{b1}_{2} \left( T^2 - T_r^2 \right) \]

\[ C^{\phi}_{MX} = q^{Cphi}_0 + q^{Cphi}_1 \left( T - T_r \right) + q^{Cphi}_2 \left( T^2 - T_r^2 \right) + q^{Cphi}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{Cphi}_4 \ln \left( \frac{T}{T_r} \right) \]

where

\[ C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX} \]

In later papers, Pitzer has added additional temperature dependencies to all of the other remaining second and third order virial coefficients. Some of these dependencies are justified and motivated by theory. Therefore, a formalism wherein all of the coefficients in the base theory have temperature dependencies associated with them has been implemented within the HMWSoln object. Much of the formalism, however, has been unexercised.

In the HMWSoln object, the temperature dependence of the Pitzer parameters are specified in the following way.

- PIZTER_TEMP_CONSTANT - string name "CONSTANT"
  - Assumes that all coefficients are independent of temperature and pressure
- PIZTER_TEMP_COMPLEX1 - string name "COMPLEX" or "COMPLEX1"
  - Uses the full temperature dependence for the \(\beta^{(0)}_{MX} \) (5 coeffs), the \(\beta^{(1)}_{MX} \) (3 coeffs), and \( C^{\phi}_{MX} \) (5 coeffs) parameters described above.
- PITZER_TEMP_LINEAR - string name "LINEAR"
  - Uses just the temperature dependence for the \(\beta^{(0)}_{MX} \), the \(\beta^{(1)}_{MX} \), and \( C^{\phi}_{MX} \) coefficients described above. There are 2 coefficients for each term.

The temperature dependence is specified in an attributes field in the `activityCoefficients` XML block, called `TempModel`. Permissible values for that attribute are `CONSTANT`, `COMPLEX1`, and `LINEAR`.

The specification of the binary interaction between a cation and an anion is given by the coefficients, \( B_{MX}\) and \( C_{MX}\) The specification of \( B_{MX}\) is a function of \(\beta^{(0)}_{MX} \), \(\beta^{(1)}_{MX} \), \(\beta^{(2)}_{MX} \), \(\alpha^{(1)}_{MX} \), and \(\alpha^{(2)}_{MX} \). \( C_{MX}\) is calculated from \(C^{\phi}_{MX} \) from the formula above. All of the underlying coefficients are specified in the XML element block `binarySaltParameters`, which has the attribute `cation` and `anion` to identify the interaction. XML elements named `beta0, beta1, beta2, Cphi, Alpha1, Alpha2` within each `binarySaltParameters` block specify the parameters. Within each of these blocks multiple parameters describing temperature or pressure dependence are serially listed in the order that they appear in the equation in this document. An example of the `beta0` block that fits the `COMPLEX1` temperature dependence given above is

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<binarySaltParameters cation="Na+" anion="OH-">
<beta0> q0, q1, q2, q3, q4 </beta0>
</binarySaltParameters>

The parameters for \( \beta^{(0)}\) fit the following equation:

\[ \beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right) + q_2^{{\beta}0} \left( T^2 - T_r^2 \right) + q_3^{{\beta}0} \left( \frac{1}{T} - \frac{1}{T_r} \right) + q_4^{{\beta}0} \ln \left( \frac{T}{T_r} \right) \]

This same `COMPLEX1` temperature dependence given above is used for the following parameters: \( \beta^{(0)}_{MX} \), \( \beta^{(1)}_{MX} \), \( \beta^{(2)}_{MX} \), \( \Theta_{cc'} \), \(\Theta_{aa'} \), \( \Psi_{c{c'}a} \) and \( \Psi_{ca{a'}} \).

### Like-Charged Binary Ion Parameters and the Mixing Parameters

The previous section contained the functions, \( \Phi_{c{c'}} \), \( \Phi_{a{a'}} \) and their derivatives wrt the ionic strength, \( \Phi'_{c{c'}} \) and \( \Phi'_{a{a'}} \). Part of these terms come from theory.

Since like charged ions repel each other and are generally not near each other, the virial coefficients for same-charged ions are small. However, Pitzer doesn't ignore these in his formulation. Relatively larger and longer range terms between like-charged ions exist however, which appear only for unsymmetrical mixing of same-sign charged ions with different charges. \( \Phi_{ij} \), where \( ij \) is either \( a{a'} \) or \( c{c'} \) is given by

\[ {\Phi}_{ij} = \Theta_{ij} + \,^E \Theta_{ij}(I) \]

\( \Theta_{ij} \) is the small virial coefficient expansion term. Dependent in general on temperature and pressure, its ionic strength dependence is ignored in Pitzer's approach. \( \,^E\Theta_{ij}(I) \) accounts for the electrostatic unsymmetrical mixing effects and is dependent only on the charges of the ions i, j, the total ionic strength and on the dielectric constant and density of the solvent. This seems to be a relatively well- documented part of the theory. They theory below comes from Pitzer summation (Pitzer) in the appendix. It's also mentioned in Bethke's book (Bethke), and the equations are summarized in Harvie & Weare (1980). Within the code, \( \,^E\Theta_{ij}(I) \) is evaluated according to the algorithm described in Appendix B [Pitzer] as

\[ \,^E\Theta_{ij}(I) = \left( \frac{z_i z_j}{4I} \right) \left( J(x_{ij}) - \frac{1}{2} J(x_{ii}) - \frac{1}{2} J(x_{jj}) \right) \]

where \( x_{ij} = 6 z_i z_j A_{\phi} \sqrt{I} \) and

\[ J(x) = \frac{1}{x} \int_0^{\infty}{\left( 1 + q + \frac{1}{2} q^2 - e^q \right) y^2 dy} \]

and \( q = - (\frac{x}{y}) e^{-y} \). \( J(x) \) is evaluated by numerical integration.

The \( \Theta_{ij} \) term is a constant that is specified by the XML element `thetaCation` and `thetaAnion`, which has the attribute `cation1`, `cation2` and `anion1`, `anion2` respectively to identify the interaction. No temperature or pressure dependence of this parameter is currently allowed. An example of the block is presented below.

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
</thetaCation>

### Ternary Pitzer Parameters

The \( \Psi_{c{c'}a} \) and \( \Psi_{ca{a'}} \) terms represent ternary interactions between two cations and an anion and two anions and a cation, respectively. In Pitzer's implementation these terms are usually small in absolute size. Currently these parameters do not have any dependence on temperature, pressure, or ionic strength.

Their values are input using the XML element `psiCommonCation` and `psiCommonAnion`. The species id's are specified in attribute fields in the XML element. The fields `cation`, `anion1`, and `anion2` are used for `psiCommonCation`. The fields `anion`, `cation1` and `cation2` are used for `psiCommonAnion`. An example block is given below. The `Theta` field below is a duplicate of the `thetaAnion` field mentioned above. The two fields are input into the same block for convenience, and because their data are highly correlated, in practice. It is an error for the two blocks to specify different information about thetaAnion (or thetaCation) in different blocks. It's ok to specify duplicate but consistent information in multiple blocks.

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>

### Treatment of Neutral Species

Binary virial-coefficient-like interactions between two neutral species may be specified in the \( \lambda_{mn} \) terms that appear in the formulas above. Currently these interactions are independent of temperature, pressure, and ionic strength. Also, currently, the neutrality of the species are not checked. Therefore, this interaction may involve charged species in the solution as well. The identity of the species is specified by the `species1` and `species2` attributes to the XML `lambdaNeutral` node. These terms are symmetrical; `species1` and `species2` may be reversed and the term will be the same. An example is given below.

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<lambdaNeutral species1="CO2" species2="CH4">
<lambda> 0.05 </lambda>
</lambdaNeutral>

## Example of the Specification of Parameters for the Activity Coefficients

An example is given below.

An example `activityCoefficients` XML block for this formulation is supplied below

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<activityCoefficients model="Pitzer" TempModel="complex1">
<!-- Pitzer Coefficients
These coefficients are from Pitzer's main
paper, in his book.
-->
<A_Debye model="water" />
<ionicRadius default="3.042843" units="Angstroms">
</ionicRadius>
<binarySaltParameters cation="Na+" anion="Cl-">
<beta0> 0.0765, 0.008946, -3.3158E-6,
-777.03, -4.4706
</beta0>
<beta1> 0.2664, 6.1608E-5, 1.0715E-6, 0.0, 0.0 </beta1>
<beta2> 0.0, 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.00127, -4.655E-5, 0.0,
33.317, 0.09421
</Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="H+" anion="Cl-">
<beta0> 0.1775, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.2945, 0.0, 0.0, 0.0, 0.0 </beta1>
<beta2> 0.0, 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.0008, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="Na+" anion="OH-">
<beta0> 0.0864, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.253, 0.0, 0.0 0.0, 0.0 </beta1>
<beta2> 0.0 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.0044, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<thetaAnion anion1="Cl-" anion2="OH-">
<Theta> -0.05, 0.0, 0.0, 0.0, 0.0 </Theta>
</thetaAnion>
<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05, 0.0, 0.0, 0.0, 0.0 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>
<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036, 0.0, 0.0, 0.0, 0.0 </Theta>
</thetaCation>
<psiCommonAnion anion="Cl-" cation1="Na+" cation2="H+">
<Theta> 0.036, 0.0, 0.0, 0.0, 0.0 </Theta>
<Psi> -0.004 </Psi>
</psiCommonAnion>
</activityCoefficients>

### Specification of the Debye-Huckel Constant

In the equations above, the formula for \( A_{Debye} \) is needed. The HMWSoln 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 and creates nontrivial entries for the excess heat capacity, enthalpy, and excess volumes of solution.

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

where

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

Therefore:

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

Units = sqrt(kg/gmol)

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

An example of a fixed value implementation is given below.

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<activityCoefficients model="Pitzer">
<!-- A_Debye units = sqrt(kg/gmol) -->
<A_Debye> 1.172576 </A_Debye>
<!-- object description continues -->
</activityCoefficients>

An example of a variable value implementation within the HMWSoln object is given below. The model attribute, "water", triggers the full implementation.

Note: The XML input format is deprecated and will be removed in Cantera 3.0

<activityCoefficients model="Pitzer">
<!-- A_Debye units = sqrt(kg/gmol) -->
<A_Debye model="water" />
<!-- object description continues -->
</activityCoefficients>

### Temperature and Pressure Dependence of the Activity Coefficients

Temperature dependence of the activity coefficients leads to nonzero terms for the excess enthalpy and entropy of solution. This means that the partial molar enthalpies, entropies, and heat capacities are all non-trivial to compute. The following formulas are used.

The partial molar enthalpy, \( \bar s_k(T,P) \):

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

The solvent partial molar enthalpy is equal to

\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT} = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT}) \]

The partial molar entropy, \( \bar s_k(T,P) \):

\[ \bar s_k(T,P) = s^{\triangle}_k(T,P) - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}})) - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT} \]

\[ \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o) - R T \frac{d \ln(a_o)}{dT} \]

The partial molar heat capacity, \( C_{p,k}(T,P)\):

\[ \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT} - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2} \]

\[ \bar C_{p,o}(T,P) = C^o_{p,o}(T,P) - 2 R T \frac{d \ln(a_o)}{dT} - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2} \]

The pressure dependence of the activity coefficients leads to non-zero terms for the excess Volume of the solution. Therefore, the partial molar volumes are functions of the pressure derivatives of the activity coefficients.

\[ \bar V_k(T,P) = V^{\triangle}_k(T,P) + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP} \]

\[ \bar V_o(T,P) = V^o_o(T,P) + R T \frac{d \ln(a_o)}{dP} \]

The majority of work for these functions take place in the internal routines that calculate the first and second derivatives of the log of the activity coefficients wrt temperature, s_update_dlnMolalityActCoeff_dT(), s_update_d2lnMolalityActCoeff_dT2(), and the first derivative of the log activity coefficients wrt pressure, s_update_dlnMolalityActCoeff_dP().

## %Application within Kinetics Managers

For the time being, we have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.

This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.

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

\[ R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k) \]

where

\[ C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k \]

\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C^o_o \) is the concentration of water at 298 K and 1 atm. \( \tilde{M}_o \) has units of kg solvent per gmol solvent and is equal to

\[ \tilde{M}_o = \frac{M_o}{1000} \]

\( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.

\[ a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} \]

\(k^1 \) has units of m^3/kmol/s.

Therefore the generalized activity concentration of a solute species has the following form

\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]

The generalized activity concentration of the solvent has the same units, but it's a simpler form

\[ C_o^a = C^o_o a_o \]

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.

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

where

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

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

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

## XML Example

Note: The XML input format is deprecated and will be removed in Cantera 3.0

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-
</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
</soluteMolalities>
</state>
<!-- thermo model identifies the inherited class
from ThermoPhase that will handle the thermodynamics.
-->
<thermo model="HMW">
<standardConc model="solvent_volume" />
<activityCoefficients model="Pitzer" TempModel="complex1">
<!-- Pitzer Coefficients
These coefficients are from Pitzer's main
paper, in his book.
-->
<A_Debye model="water" />
<ionicRadius default="3.042843" units="Angstroms">
</ionicRadius>
<binarySaltParameters cation="Na+" anion="Cl-">
<beta0> 0.0765, 0.008946, -3.3158E-6,
-777.03, -4.4706
</beta0>
<beta1> 0.2664, 6.1608E-5, 1.0715E-6 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.00127, -4.655E-5, 0.0,
33.317, 0.09421
</Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="H+" anion="Cl-">
<beta0> 0.1775, 0.0, 0.0, 0.0, 0.0</beta0>
<beta1> 0.2945, 0.0, 0.0 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.0008, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="Na+" anion="OH-">
<beta0> 0.0864, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.253, 0.0, 0.0 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.0044, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<thetaAnion anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
</thetaAnion>
<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>
<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
</thetaCation>
<psiCommonAnion anion="Cl-" cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
<Psi> -0.004 </Psi>
</psiCommonAnion>
</activityCoefficients>
<solvent> H2O(L) </solvent>
</thermo>
<elementArray datasrc="elements.xml"> O H Na Cl </elementArray>
<kinetics model="none" >
</kinetics>
</phase>
Cantera::Phase::temperature
doublereal temperature() const
Temperature (K).
Definition: Phase.h:654
Cantera::ThermoPhase
Base class for a phase with thermodynamic properties.
Definition: ThermoPhase.h:102
Cantera::VPStandardStateTP::pressure
virtual doublereal pressure() const
Returns the current pressure of the phase.
Definition: VPStandardStateTP.h:140

Definition at line 1024 of file HMWSoln.h.

## Constructor & Destructor Documentation

## ◆ ~HMWSoln()

~HMWSoln | ( |  | ) |

Definition at line 39 of file HMWSoln.cpp.

## ◆ HMWSoln() [1/2]

HMWSoln | ( | const std::string & | inputFile = `""`,
|  | const std::string & | id = `""`
| ) |  |
| explicit

Construct and initialize an HMWSoln ThermoPhase object directly from an ASCII input file.

This constructor is a shell that calls the routine initThermo(), with a reference to the parsed input file to get the info for the phase.

Parameters

  inputFile | Name of the input file containing the phase definition to set up the object. If blank, an empty phase will be created.
  id | ID of the phase in the input file. Defaults to the empty string.

Definition at line 43 of file HMWSoln.cpp.

## ◆ HMWSoln() [2/2]

HMWSoln | ( | XML_Node & | phaseRef,
|  | const std::string & | id = `""`
| ) |  |

Construct and initialize an HMWSoln ThermoPhase object directly from an XML database.

Parameters

  phaseRef | XML phase node containing the description of the phase
  id | id attribute containing the name of the phase. (default is the empty string)

Deprecated:
  The XML input format is deprecated and will be removed in Cantera 3.0.

Definition at line 78 of file HMWSoln.cpp.

## Member Function Documentation

## ◆ type()

virtual std::string type | ( |  | ) | const
| inline virtual

String indicating the thermodynamic model implemented.

Usually corresponds to the name of the derived class, less any suffixes such as "Phase", TP", "VPSS", etc.

Reimplemented from ThermoPhase.

Definition at line 1058 of file HMWSoln.h.

## ◆ enthalpy_mole()

doublereal enthalpy_mole | ( |  | ) | const
| virtual

Molar enthalpy. Units: J/kmol.

Molar enthalpy of the solution. Units: J/kmol. (HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 115 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ relative_enthalpy()

doublereal relative_enthalpy | ( |  | ) | const
| virtual

Excess molar enthalpy of the solution from the mixing process.

Units: J/ kmol.

Note this is kmol of the total solution.

Definition at line 121 of file HMWSoln.cpp.

References VPStandardStateTP::getEnthalpy_RT(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_gamma_tmp, Phase::m_kk, HMWSoln::m_tmpV, Phase::mean_X(), and ThermoPhase::RT().

Referenced by HMWSoln::relative_molal_enthalpy().

## ◆ relative_molal_enthalpy()

doublereal relative_molal_enthalpy | ( |  | ) | const
| virtual

Excess molar enthalpy of the solution from the mixing process on a molality basis.

Units: J/ (kmol add salt).

Note this is kmol of the guessed at salt composition

Definition at line 133 of file HMWSoln.cpp.

References Phase::charge(), Phase::getMoleFractions(), Phase::m_kk, HMWSoln::m_tmpV, Cantera::npos, and HMWSoln::relative_enthalpy().

## ◆ entropy_mole()

doublereal entropy_mole | ( |  | ) | const
| virtual

Molar entropy. Units: J/kmol/K.

Molar entropy of the solution. 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
  MultiSpeciesThermo

       (HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 173 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarEntropies(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ gibbs_mole()

doublereal gibbs_mole | ( |  | ) | const
| virtual

Molar Gibbs function. Units: J/kmol.

(HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 179 of file HMWSoln.cpp.

References HMWSoln::getChemPotentials(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ cp_mole()

doublereal cp_mole | ( |  | ) | const
| virtual

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

Reimplemented from ThermoPhase.

Definition at line 185 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarCp(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ cv_mole()

doublereal cv_mole | ( |  | ) | const
| virtual

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

(HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 191 of file HMWSoln.cpp.

References ThermoPhase::isothermalCompressibility().

## ◆ calcDensity()

void calcDensity | ( |  | ) |
| protected virtual

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

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() will cause an exception to be thrown.

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.

NOTE: This is a non-virtual function, which is not a member of the ThermoPhase base class.

Reimplemented from VPStandardStateTP.

Definition at line 203 of file HMWSoln.cpp.

References Phase::assignDensity(), ValueCache::getId(), HMWSoln::getPartialMolarVolumes(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_tmpV, Phase::mean_X(), Phase::meanMolecularWeight(), VPStandardStateTP::pressure(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().

## ◆ getActivityConcentrations()

void getActivityConcentrations | ( | doublereal * | c | ) | const
| virtual

This method returns an array of generalized activity concentrations.

The generalized activity concentrations, \( C_k^a\), are defined such that \( a_k = C^a_k / C^0_k, \) 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.

The generalized activity concentration of a solute species has the following form

\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]

The generalized activity concentration of the solvent has the same units, but it's a simpler form

\[ C_o^a = C^o_o a_o \]

Parameters

  c | Array of generalized concentrations. The units are kmol m-3 for both the solvent and the solute species

Reimplemented from MolalityVPSSTP.

Definition at line 220 of file HMWSoln.cpp.

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

## ◆ 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 (that is, generalized) concentration for use

We have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.

\[ C_j^0 = C^o_o \tilde{M}_o \quad and C_o^0 = C^o_o \]

The consequence of this is that the standard concentrations have unequal units between the solvent and the solute. However, both the solvent and the solute activity concentrations will have the same units of kmol/kg^3.

This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.

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

\[ R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k) \]

where

\[ C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k \]

\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C^o_o \) is the concentration of water at 298 K and 1 atm. \( \tilde{M}_o \) has units of kg solvent per gmol solvent and is equal to

\[ \tilde{M}_o = \frac{M_o}{1000} \]

\( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.

\[ a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} \]

\(k^1 \) has units of m^3/kmol/s.

Therefore the generalized activity concentration of a solute species has the following form

\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]

The generalized activity concentration of the solvent has the same units, but it's a simpler form

\[ C_o^a = C^o_o a_o \]

Parameters

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

Returns
  the standard Concentration in units of m^3/kmol.

Reimplemented from MolalityVPSSTP.

Definition at line 233 of file HMWSoln.cpp.

References VPStandardStateTP::getStandardVolumes(), MolalityVPSSTP::m_Mnaught, and HMWSoln::m_tmpV.

Referenced by HMWSoln::getActivityConcentrations().

## ◆ getActivities()

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 is on molar scale).

Parameters

  ac | Output vector of activities. Length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 243 of file HMWSoln.cpp.

References Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), and VPStandardStateTP::updateStandardStateThermo().

Referenced by HMWSoln::getActivityConcentrations().

## ◆ getChemPotentials()

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 272 of file HMWSoln.cpp.

References VPStandardStateTP::getStandardChemPotentials(), Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), and Cantera::SmallNumber.

Referenced by HMWSoln::gibbs_mole().

## ◆ getPartialMolarEnthalpies()

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

\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT} = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT}) \]

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 292 of file HMWSoln.cpp.

References VPStandardStateTP::getEnthalpy_RT(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, ThermoPhase::RT(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().

Referenced by HMWSoln::enthalpy_mole(), and HMWSoln::relative_enthalpy().

## ◆ getPartialMolarEntropies()

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 answer for how calculate this (p.215 Smith and Van Ness)

d(chemPot_i)/dT = -sbar_i

For this phase, the partial molar entropies are equal to the SS species entropies plus the ideal solution contribution plus complicated functions of the temperature derivative of the activity coefficients.

\[ \bar s_k(T,P) = s^{\triangle}_k(T,P) - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}})) - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT} \]

\[ \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o) - R T \frac{d \ln(a_o)}{dT} \]

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 311 of file HMWSoln.cpp.

References Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Cantera::SmallNumber.

Referenced by HMWSoln::entropy_mole().

## ◆ getPartialMolarVolumes()

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 functions of the pressure derivatives of the activity coefficients.

\[ \bar V_k(T,P) = V^{\triangle}_k(T,P) + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP} \]

\[ \bar V_o(T,P) = V^o_o(T,P) + R T \frac{d \ln(a_o)}{dP} \]

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 346 of file HMWSoln.cpp.

References VPStandardStateTP::getStandardVolumes(), HMWSoln::m_dlnActCoeffMolaldP_Scaled, Phase::m_kk, ThermoPhase::RT(), and HMWSoln::s_update_dlnMolalityActCoeff_dP().

Referenced by HMWSoln::calcDensity().

## ◆ getPartialMolarCp()

void getPartialMolarCp | ( | doublereal * | cpbar | ) | const
| virtual

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

Units: J/kmol/K

The following formulas are implemented within the code.

\[ \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT} - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2} \]

\[ \bar C_{p,o}(T,P) = C^o_{p,o}(T,P) - 2 R T \frac{d \ln(a_o)}{dT} - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2} \]

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 359 of file HMWSoln.cpp.

References Cantera::GasConstant, VPStandardStateTP::getCp_R(), HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, ThermoPhase::RT(), HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().

Referenced by HMWSoln::cp_mole().

## ◆ satPressure()

doublereal satPressure | ( | doublereal | T | ) |
| virtual

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 379 of file HMWSoln.cpp.

References HMWSoln::m_waterSS, VPStandardStateTP::pressure(), PDSS::satPressure(), PDSS::setState_TP(), and Phase::temperature().

## ◆ setBinarySalt()

void setBinarySalt | ( | const std::string & | sp1,
|  | const std::string & | sp2,
|  | size_t | nParams,
|  | double * | beta0,
|  | double * | beta1,
|  | double * | beta2,
|  | double * | Cphi,
|  | double | alpha1,
|  | double | alpha2
| ) |  |

Definition at line 405 of file HMWSoln.cpp.

## ◆ setTheta()

void setTheta | ( | const std::string & | sp1,
|  | const std::string & | sp2,
|  | size_t | nParams,
|  | double * | theta
| ) |  |

Definition at line 440 of file HMWSoln.cpp.

## ◆ setPsi()

void setPsi | ( | const std::string & | sp1,
|  | const std::string & | sp2,
|  | const std::string & | sp3,
|  | size_t | nParams,
|  | double * | psi
| ) |  |

Definition at line 463 of file HMWSoln.cpp.

## ◆ setLambda()

void setLambda | ( | const std::string & | sp1,
|  | const std::string & | sp2,
|  | size_t | nParams,
|  | double * | lambda
| ) |  |

Definition at line 499 of file HMWSoln.cpp.

## ◆ setMunnn()

void setMunnn | ( | const std::string & | sp,
|  | size_t | nParams,
|  | double * | munnn
| ) |  |

Definition at line 526 of file HMWSoln.cpp.

## ◆ setZeta()

void setZeta | ( | const std::string & | sp1,
|  | const std::string & | sp2,
|  | const std::string & | sp3,
|  | size_t | nParams,
|  | double * | psi
| ) |  |

Definition at line 544 of file HMWSoln.cpp.

## ◆ setPitzerTempModel()

void setPitzerTempModel | ( | const std::string & | model | ) |

Definition at line 587 of file HMWSoln.cpp.

## ◆ setPitzerRefTemperature()

void setPitzerRefTemperature | ( | double | Tref | ) |
| inline

Definition at line 1439 of file HMWSoln.h.

## ◆ setA_Debye()

void setA_Debye | ( | double | A | ) |

Set the A_Debye parameter.

If a negative value is provided, enables calculation of A_Debye using the detailed water equation of state.

Definition at line 601 of file HMWSoln.cpp.

Referenced by HMWSoln::initThermoXML().

## ◆ setMaxIonicStrength()

void setMaxIonicStrength | ( | double | Imax | ) |
| inline

Definition at line 1447 of file HMWSoln.h.

## ◆ setCroppingCoefficients()

void setCroppingCoefficients | ( | double | ln_gamma_k_min,
|  | double | ln_gamma_k_max,
|  | double | ln_gamma_o_min,
|  | double | ln_gamma_o_max
| ) |  |

Definition at line 611 of file HMWSoln.cpp.

## ◆ initThermo()

void initThermo | ( |  | ) |
| virtual

The following methods are used in the process of constructing the phase and setting its parameters from a specification in an input file. They are not normally used in application programs. To see how they are used, see importPhase().

Reimplemented from MolalityVPSSTP.

Definition at line 638 of file HMWSoln.cpp.

References AnyMap::hasKey(), HMWSoln::initLengths(), MolalityVPSSTP::initThermo(), HMWSoln::m_formPitzerTemp, and ThermoPhase::m_input.

## ◆ getParameters()

void getParameters | ( | AnyMap & | phaseNode | ) | const
| virtual

Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newPhase(AnyMap&) function.

This does not include user-defined fields available in input().

Reimplemented from ThermoPhase.

Definition at line 814 of file HMWSoln.cpp.

References ThermoPhase::getParameters(), and HMWSoln::m_formPitzerTemp.

## ◆ initThermoXML()

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

Initialize the phase parameters from an XML file.

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.

Deprecated:
  The XML input format is deprecated and will be removed in Cantera 3.0.

Reimplemented from ThermoPhase.

Definition at line 1044 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::caseInsensitiveEquals(), XML_Node::child(), XML_Node::children(), Cantera::fpValueCheck(), Cantera::getFloat(), XML_Node::hasChild(), XML_Node::id(), HMWSoln::initLengths(), ThermoPhase::initThermoXML(), HMWSoln::readXMLBinarySalt(), HMWSoln::readXMLLambdaNeutral(), HMWSoln::readXMLPsi(), HMWSoln::readXMLTheta(), HMWSoln::readXMLZetaCation(), and HMWSoln::setA_Debye().

## ◆ A_Debye_TP()

double A_Debye_TP | ( | double | temperature = `-1.0`,
|  | double | pressure = `-1.0`
| ) |  | const
| virtual

Value of the Debye Huckel constant as a function of temperature and pressure.

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

           Units = sqrt(kg/gmol)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1143 of file HMWSoln.cpp.

Referenced by HMWSoln::getUnscaledMolalityActivityCoefficients(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ dA_DebyedT_TP()

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 as a function of temperature and pressure.

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

           Units = sqrt(kg/gmol)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1175 of file HMWSoln.cpp.

Referenced by HMWSoln::ADebye_L(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ dA_DebyedP_TP()

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.

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

Units = sqrt(kg/gmol)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1199 of file HMWSoln.cpp.

Referenced by HMWSoln::ADebye_V(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ ADebye_L()

double ADebye_L | ( | double | temperature = `-1.0`,
|  | double | pressure = `-1.0`
| ) |  | const

Return Pitzer's definition of A_L.

This is basically the derivative of the A_phi multiplied by 4 R T**2

           A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
           dA_phidT = d(A_Debye)/dT / 3.0
           A_L = dA_phidT * (4 * R * T * T)

           Units = sqrt(kg/gmol) (RT)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1231 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedT_TP().

## ◆ ADebye_J()

double ADebye_J | ( | double | temperature = `-1.0`,
|  | double | pressure = `-1.0`
| ) |  | const

Return Pitzer's definition of A_J.

This is basically the temperature derivative of A_L, and the second derivative of A_phi

           A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
           dA_phidT = d(A_Debye)/dT / 3.0
           A_J = 2 A_L/T + 4 * R * T * T * d2(A_phi)/dT2

           Units = sqrt(kg/gmol) (R)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1253 of file HMWSoln.cpp.

## ◆ ADebye_V()

double ADebye_V | ( | double | temperature = `-1.0`,
|  | double | pressure = `-1.0`
| ) |  | const

Return Pitzer's definition of A_V.

This is the derivative wrt pressure of A_phi multiplied by - 4 R T

           A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
           dA_phidT = d(A_Debye)/dP / 3.0
           A_V = - dA_phidP * (4 * R * T)

           Units = sqrt(kg/gmol) (RT) / Pascal

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1242 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedP_TP().

## ◆ d2A_DebyedT2_TP()

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.

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

           Units = sqrt(kg/gmol)

Parameters

  temperature | Temperature of the derivative calculation or -1 to indicate the current temperature
  pressure | Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1265 of file HMWSoln.cpp.

Referenced by HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ printCoeffs()

void printCoeffs | ( |  | ) | const

Print out all of the input Pitzer coefficients.

Definition at line 4349 of file HMWSoln.cpp.

References MolalityVPSSTP::calcMolalities(), Phase::charge(), Phase::getMoleFractions(), HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta2MX_ij, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, Phase::m_kk, HMWSoln::m_molalitiesCropped, HMWSoln::m_Psi_ijk, HMWSoln::m_Theta_ij, HMWSoln::m_tmpV, HMWSoln::s_updatePitzer_CoeffWRTemp(), Phase::speciesName(), Cantera::writelog(), and Cantera::writelogf().

## ◆ getUnscaledMolalityActivityCoefficients()

void getUnscaledMolalityActivityCoefficients | ( | doublereal * | acMolality | ) | const
| virtual

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

See Denbigh p. 278 for a thorough discussion. This class must be overridden in classes which derive from MolalityVPSSTP. This function takes over from the molar-based activity coefficient calculation, getActivityCoefficients(), in derived classes.

Parameters

  acMolality | Output vector containing the molality based activity coefficients. length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 259 of file HMWSoln.cpp.

References HMWSoln::A_Debye_TP(), Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Unscaled, and VPStandardStateTP::updateStandardStateThermo().

## ◆ s_updateScaling_pHScaling()

void s_updateScaling_pHScaling | ( |  | ) | const
| private

Apply the current phScale to a set of activity Coefficients.

See the Eq3/6 Manual for a thorough discussion.

Definition at line 4407 of file HMWSoln.cpp.

References AssertTrace, Phase::charge(), MolalityVPSSTP::m_indexCLM, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, HMWSoln::m_lnActCoeffMolal_Unscaled, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_lnMolalityActCoeff().

## ◆ s_updateScaling_pHScaling_dT()

void s_updateScaling_pHScaling_dT | ( |  | ) | const
| private

Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature.

See the Eq3/6 Manual for a thorough discussion of the need

Definition at line 4422 of file HMWSoln.cpp.

References AssertTrace, Phase::charge(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT().

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().

## ◆ s_updateScaling_pHScaling_dT2()

void s_updateScaling_pHScaling_dT2 | ( |  | ) | const
| private

Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature.

See the Eq3/6 Manual for a thorough discussion of the need

Definition at line 4437 of file HMWSoln.cpp.

References AssertTrace, Phase::charge(), HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2().

Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().

## ◆ s_updateScaling_pHScaling_dP()

void s_updateScaling_pHScaling_dP | ( |  | ) | const
| private

Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure.

See the Eq3/6 Manual for a thorough discussion of the need

Definition at line 4452 of file HMWSoln.cpp.

References AssertTrace, Phase::charge(), HMWSoln::m_dlnActCoeffMolaldP_Scaled, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP().

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().

## ◆ s_NBS_CLM_lnMolalityActCoeff()

doublereal s_NBS_CLM_lnMolalityActCoeff | ( |  | ) | const
| private

Calculate the Chlorine activity coefficient on the NBS scale.

We assume here that the m_IionicMolality variable is up to date.

Definition at line 4467 of file HMWSoln.cpp.

References HMWSoln::m_IionicMolality.

Referenced by HMWSoln::applyphScale(), and HMWSoln::s_updateScaling_pHScaling().

## ◆ s_NBS_CLM_dlnMolalityActCoeff_dT()

doublereal s_NBS_CLM_dlnMolalityActCoeff_dT | ( |  | ) | const
| private

Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale.

We assume here that the m_IionicMolality variable is up to date.

Definition at line 4475 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedT_TP(), and HMWSoln::m_IionicMolality.

Referenced by HMWSoln::s_updateScaling_pHScaling_dT().

## ◆ s_NBS_CLM_d2lnMolalityActCoeff_dT2()

doublereal s_NBS_CLM_d2lnMolalityActCoeff_dT2 | ( |  | ) | const
| private

Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale.

We assume here that the m_IionicMolality variable is up to date.

Definition at line 4482 of file HMWSoln.cpp.

References HMWSoln::d2A_DebyedT2_TP(), and HMWSoln::m_IionicMolality.

Referenced by HMWSoln::s_updateScaling_pHScaling_dT2().

## ◆ s_NBS_CLM_dlnMolalityActCoeff_dP()

doublereal s_NBS_CLM_dlnMolalityActCoeff_dP | ( |  | ) | const
| private

Calculate the pressure derivative of the Chlorine activity coefficient.

We assume here that the m_IionicMolality variable is up to date.

Definition at line 4489 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedP_TP(), and HMWSoln::m_IionicMolality.

Referenced by HMWSoln::s_updateScaling_pHScaling_dP().

## ◆ initLengths()

void initLengths | ( |  | ) |
| private

Initialize all of the species-dependent lengths in the object.

Definition at line 1293 of file HMWSoln.cpp.

References HMWSoln::m_formPitzerTemp, Phase::m_kk, HMWSoln::m_molalitiesCropped, and HMWSoln::m_tmpV.

Referenced by HMWSoln::initThermo(), and HMWSoln::initThermoXML().

## ◆ applyphScale()

void applyphScale | ( | doublereal * | acMolality | ) | const
| private virtual

Apply the current phScale to a set of activity Coefficients or activities.

See the Eq3/6 Manual for a thorough discussion.

Parameters

  acMolality | input/Output vector containing the molality based activity coefficients. length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 4393 of file HMWSoln.cpp.

References AssertTrace, Phase::charge(), MolalityVPSSTP::m_indexCLM, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Unscaled, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_lnMolalityActCoeff().

## ◆ s_update_lnMolalityActCoeff()

void s_update_lnMolalityActCoeff | ( |  | ) | const
| private

Definition at line 1406 of file HMWSoln.cpp.

## ◆ s_update_dlnMolalityActCoeff_dT()

void s_update_dlnMolalityActCoeff_dT | ( |  | ) | const
| private

This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients.

This function does all of the direct work. The solvent activity coefficient is on the molality scale. It's derivative is too.

Definition at line 2697 of file HMWSoln.cpp.

References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), HMWSoln::s_updateScaling_pHScaling_dT(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().

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

## ◆ s_update_d2lnMolalityActCoeff_dT2()

void s_update_d2lnMolalityActCoeff_dT2 | ( |  | ) | const
| private

This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.

Definition at line 3216 of file HMWSoln.cpp.

References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updateScaling_pHScaling_dT2(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().

Referenced by HMWSoln::getPartialMolarCp().

## ◆ s_update_dlnMolalityActCoeff_dP()

void s_update_dlnMolalityActCoeff_dP | ( |  | ) | const
| private

This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients.

Assumes that the activity coefficients are current.

Definition at line 3727 of file HMWSoln.cpp.

References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updateScaling_pHScaling_dP(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().

Referenced by HMWSoln::getPartialMolarVolumes().

## ◆ s_updateIMS_lnMolalityActCoeff()

void s_updateIMS_lnMolalityActCoeff | ( |  | ) | const
| private

This function will be called to update the internally stored natural logarithm of the molality activity coefficients.

Definition at line 4306 of file HMWSoln.cpp.

References MolalityVPSSTP::calcMolalities(), HMWSoln::IMS_cCut_, HMWSoln::IMS_lnActCoeffMolal_, HMWSoln::IMS_X_o_cutoff_, Phase::m_kk, MolalityVPSSTP::m_xmolSolventMIN, and Phase::moleFraction().

## ◆ s_updatePitzer_lnMolalityActCoeff()

void s_updatePitzer_lnMolalityActCoeff | ( |  | ) | const
| private

Calculate the Pitzer portion of the activity coefficients.

This is the main routine in the whole module. It calculates the molality based activity coefficients for the solutes, and the activity of water.

Definition at line 2194 of file HMWSoln.cpp.

References HMWSoln::A_Debye_TP(), HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta2MX_ij, HMWSoln::m_BMX_IJ, HMWSoln::m_BphiMX_IJ, HMWSoln::m_BprimeMX_IJ, HMWSoln::m_CMX_IJ, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, Phase::m_kk, MolalityVPSSTP::m_molalities, HMWSoln::m_molalitiesCropped, HMWSoln::m_Phi_IJ, HMWSoln::m_PhiPhi_IJ, HMWSoln::m_Phiprime_IJ, and HMWSoln::m_Theta_ij.

## ◆ s_updatePitzer_dlnMolalityActCoeff_dT()

void s_updatePitzer_dlnMolalityActCoeff_dT | ( |  | ) | const
| private

Calculates the temperature derivative of the natural logarithm of the molality activity coefficients.

Public function makes sure that all dependent data is up to date, before calling a private function

Definition at line 2725 of file HMWSoln.cpp.

References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::dA_DebyedT_TP(), HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_L, HMWSoln::m_Beta1MX_ij_L, HMWSoln::m_Beta2MX_ij_L, HMWSoln::m_BMX_IJ_L, HMWSoln::m_BphiMX_IJ_L, HMWSoln::m_BprimeMX_IJ_L, HMWSoln::m_CMX_IJ_L, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_L, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, Phase::m_kk, HMWSoln::m_Lambda_nj_L, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_L, HMWSoln::m_Phi_IJ_L, HMWSoln::m_PhiPhi_IJ_L, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_L, HMWSoln::m_Theta_ij_L, and MolalityVPSSTP::m_weightSolvent.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().

## ◆ s_updatePitzer_d2lnMolalityActCoeff_dT2()

void s_updatePitzer_d2lnMolalityActCoeff_dT2 | ( |  | ) | const
| private

This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.

It is assumed that the Pitzer activity coefficient and first derivative routine are called immediately preceding the call to this routine.

Definition at line 3244 of file HMWSoln.cpp.

References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::d2A_DebyedT2_TP(), HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_LL, HMWSoln::m_Beta1MX_ij_LL, HMWSoln::m_Beta2MX_ij_LL, HMWSoln::m_BMX_IJ_LL, HMWSoln::m_BphiMX_IJ_LL, HMWSoln::m_BprimeMX_IJ_LL, HMWSoln::m_CMX_IJ_LL, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_LL, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, HMWSoln::m_g2func_IJ, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, Phase::m_kk, HMWSoln::m_Lambda_nj_LL, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_LL, HMWSoln::m_Phi_IJ_LL, HMWSoln::m_PhiPhi_IJ_LL, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_LL, HMWSoln::m_Theta_ij_LL, and MolalityVPSSTP::m_weightSolvent.

Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().

## ◆ s_updatePitzer_dlnMolalityActCoeff_dP()

void s_updatePitzer_dlnMolalityActCoeff_dP | ( |  | ) | const
| private

Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients.

It is assumed that the Pitzer activity coefficient and first derivative routine are called immediately preceding the calling of this routine.

Definition at line 3751 of file HMWSoln.cpp.

References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::dA_DebyedP_TP(), HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_P, HMWSoln::m_Beta1MX_ij_P, HMWSoln::m_Beta2MX_ij_P, HMWSoln::m_BMX_IJ_P, HMWSoln::m_BphiMX_IJ_P, HMWSoln::m_BprimeMX_IJ_P, HMWSoln::m_CMX_IJ_P, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_P, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, HMWSoln::m_g2func_IJ, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, Phase::m_kk, HMWSoln::m_Lambda_nj_P, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_P, HMWSoln::m_Phi_IJ_P, HMWSoln::m_PhiPhi_IJ_P, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_P, HMWSoln::m_Theta_ij_P, MolalityVPSSTP::m_weightSolvent, VPStandardStateTP::pressure(), and Phase::temperature().

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().

## ◆ s_updatePitzer_CoeffWRTemp()

void s_updatePitzer_CoeffWRTemp | ( | int | doDerivs = `2` | ) | const
| private

Calculates the Pitzer coefficients' dependence on the temperature.

It will also calculate the temperature derivatives of the coefficients, as they are important in the calculation of the latent heats and the heat capacities of the mixtures.

Parameters

  doDerivs | If >= 1, then the routine will calculate the first derivative. If >= 2, the routine will calculate the first and second temperature derivative. default = 2

Definition at line 1948 of file HMWSoln.cpp.

Referenced by HMWSoln::printCoeffs().

## ◆ calc_lambdas()

void calc_lambdas | ( | double | is | ) | const
| private

Calculate the lambda interactions.

Calculate E-lambda terms for charge combinations of like sign, using method of Pitzer (1975). This implementation is based on Bethke, Appendix 2.

Parameters

  is | Ionic strength

Definition at line 4236 of file HMWSoln.cpp.

References HMWSoln::elambda, and HMWSoln::elambda1.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ calc_thetas()

void calc_thetas | ( | int | z1,
|  | int | z2,
|  | double * | etheta,
|  | double * | etheta_prime
| ) |  | const
| private

Calculate etheta and etheta_prime.

This interaction accounts for the mixing effects of like-signed ions with different charges. This interaction will be nonzero for species with the same charge. this routine is not to be called for neutral species; it core dumps or error exits.

MEC implementation routine.

Parameters

  z1 | charge of the first molecule
  z2 | charge of the second molecule
  etheta | return pointer containing etheta
  etheta_prime | Return pointer containing etheta_prime.

This routine uses the internal variables, elambda[] and elambda1[].

Definition at line 4280 of file HMWSoln.cpp.

References AssertThrowMsg, HMWSoln::elambda, and HMWSoln::elambda1.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ counterIJ_setup()

void counterIJ_setup | ( |  | ) | const
| private

Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species.

The purpose of this is to squeeze the ij parameters into a compressed single counter.

n = m_kk*i + j m_Counter[n] = counter

Definition at line 1611 of file HMWSoln.cpp.

References HMWSoln::m_CounterIJ, and Phase::m_kk.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ calcMolalitiesCropped()

void calcMolalitiesCropped | ( |  | ) | const
| private

Calculate the cropped molalities.

This is an internal routine that calculates values of m_molalitiesCropped from m_molalities

Definition at line 1470 of file HMWSoln.cpp.

References Phase::charge(), Phase::getMoleFractions(), HMWSoln::m_gamma_tmp, Phase::m_kk, HMWSoln::m_maxIionicStrength, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, HMWSoln::m_molalitiesAreCropped, HMWSoln::m_molalitiesCropped, HMWSoln::MC_X_o_cutoff_, and Cantera::npos.

## ◆ readXMLBinarySalt()

void readXMLBinarySalt | ( | XML_Node & | BinSalt | ) |
| private

Process an XML node called "binarySaltParameters".

This node contains all of the parameters necessary to describe the Pitzer model for that particular binary salt. This function reads the XML file and writes the coefficients it finds to an internal data structures.

Parameters

  BinSalt | reference to the XML_Node named binarySaltParameters containing the anion - cation interaction

Definition at line 1634 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

Referenced by HMWSoln::initThermoXML().

## ◆ readXMLTheta()

void readXMLTheta | ( | XML_Node & | BinSalt | ) |
| private

Process an XML node called "thetaAnion" or "thetaCation".

This node contains all of the parameters necessary to describe the binary interactions between two anions or two cations.

Parameters

  BinSalt | reference to the XML_Node named thetaAnion containing the anion - anion interaction

Definition at line 1680 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

Referenced by HMWSoln::initThermoXML().

## ◆ readXMLPsi()

void readXMLPsi | ( | XML_Node & | BinSalt | ) |
| private

Process an XML node called "psiCommonAnion" or "psiCommonCation".

This node contains all of the parameters necessary to describe the ternary interactions between one anion and two cations or two anions and one cation.

Parameters

  BinSalt | reference to the XML_Node named psiCommonAnion containing the anion - cation1 - cation2 interaction

Definition at line 1720 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

Referenced by HMWSoln::initThermoXML().

## ◆ readXMLLambdaNeutral()

void readXMLLambdaNeutral | ( | XML_Node & | BinSalt | ) |
| private

Process an XML node called "lambdaNeutral".

This node contains all of the parameters necessary to describe the binary interactions between one neutral species and any other species (neutral or otherwise) in the mechanism.

Parameters

  BinSalt | reference to the XML_Node named lambdaNeutral containing multiple Neutral - species interactions

Definition at line 1769 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

Referenced by HMWSoln::initThermoXML().

## ◆ readXMLMunnnNeutral()

void readXMLMunnnNeutral | ( | XML_Node & | BinSalt | ) |
| private

Process an XML node called "MunnnNeutral".

This node contains all of the parameters necessary to describe the self-ternary interactions for one neutral species.

Parameters

  BinSalt | reference to the XML_Node named Munnn containing the self-ternary interaction

Definition at line 1799 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

## ◆ readXMLZetaCation()

void readXMLZetaCation | ( | const XML_Node & | BinSalt | ) |
| private

Process an XML node called "zetaCation".

This node contains all of the parameters necessary to describe the ternary interactions between one neutral, one cation, and one anion.

Parameters

  BinSalt | reference to the XML_Node named psiCommonCation containing the neutral - cation - anion interaction

Definition at line 1824 of file HMWSoln.cpp.

References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().

Referenced by HMWSoln::initThermoXML().

## ◆ calcIMSCutoffParams_()

void calcIMSCutoffParams_ | ( |  | ) |
| private

Precalculate the IMS Cutoff parameters for typeCutoff = 2.

Definition at line 1859 of file HMWSoln.cpp.

References HMWSoln::IMS_cCut_, HMWSoln::IMS_slopegCut_, and HMWSoln::IMS_X_o_cutoff_.

## ◆ calcMCCutoffParams_()

void calcMCCutoffParams_ | ( |  | ) |
| private

Calculate molality cut-off parameters.

Definition at line 1912 of file HMWSoln.cpp.

References HMWSoln::MC_X_o_cutoff_.

## Member Data Documentation

## ◆ m_formPitzerTemp

int m_formPitzerTemp
| private

This is the form of the temperature dependence of Pitzer parameterization used in the model.

      PITZER_TEMP_CONSTANT   0
      PITZER_TEMP_LINEAR     1
      PITZER_TEMP_COMPLEX1   2

Definition at line 1671 of file HMWSoln.h.

Referenced by HMWSoln::getParameters(), HMWSoln::initLengths(), HMWSoln::initThermo(), HMWSoln::readXMLBinarySalt(), HMWSoln::readXMLLambdaNeutral(), HMWSoln::readXMLMunnnNeutral(), HMWSoln::readXMLPsi(), HMWSoln::readXMLTheta(), and HMWSoln::readXMLZetaCation().

## ◆ m_IionicMolality

double m_IionicMolality
| mutable private

Current value of the ionic strength on the molality scale Associated Salts, if present in the mechanism, don't contribute to the value of the ionic strength in this version of the Ionic strength.

Definition at line 1676 of file HMWSoln.h.

Referenced by HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT(), HMWSoln::s_NBS_CLM_lnMolalityActCoeff(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_maxIionicStrength

double m_maxIionicStrength
| private

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

Definition at line 1680 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped().

## ◆ m_TempPitzerRef

double m_TempPitzerRef
| private

Reference Temperature for the Pitzer formulations.

Definition at line 1683 of file HMWSoln.h.

## ◆ m_form_A_Debye

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 1700 of file HMWSoln.h.

## ◆ m_A_Debye

double m_A_Debye
| mutable private

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

And, therefore, most be recalculated whenever T or P changes. This variable is a local copy of the calculation.

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

     where B_Debye = F / sqrt(epsilon R T/2)
                     (dw/1000)^(1/2)

A_Debye = (1/ (8 Pi)) (2 Na * dw/1000)^(1/2) (e * e / (epsilon * kb * T))^(3/2)

Units = sqrt(kg/gmol)

Nominal value = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) epsilon_0 = 8.854187817E-12 C2 N-1 m-2 e = 1.60217653 E-19 C F = 9.6485309E7 C kmol-1 R = 8.314472E3 kg m2 s-2 kmol-1 K-1 T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m dw = C_0 * M_0 (density of water) (kg/m3) = 1.0E3 at 25C

Definition at line 1732 of file HMWSoln.h.

## ◆ m_waterSS

PDSS* m_waterSS
| private

Water standard state calculator.

derived from the equation of state for water.

Definition at line 1738 of file HMWSoln.h.

Referenced by HMWSoln::satPressure().

## ◆ m_waterProps

std::unique_ptr<WaterProps> m_waterProps
| private

Pointer to the water property calculator.

Definition at line 1741 of file HMWSoln.h.

## ◆ m_tmpV

vector_fp m_tmpV
| mutable private

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

Definition at line 1744 of file HMWSoln.h.

Referenced by HMWSoln::calcDensity(), HMWSoln::cp_mole(), HMWSoln::enthalpy_mole(), HMWSoln::entropy_mole(), HMWSoln::gibbs_mole(), HMWSoln::initLengths(), HMWSoln::printCoeffs(), HMWSoln::relative_enthalpy(), HMWSoln::relative_molal_enthalpy(), and HMWSoln::standardConcentration().

## ◆ m_Beta0MX_ij

vector_fp m_Beta0MX_ij
| mutable private

Array of 2D data used in the Pitzer/HMW formulation.

Beta0_ij[i][j] is the value of the Beta0 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 1753 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_Beta0MX_ij_L

vector_fp m_Beta0MX_ij_L
| mutable private

Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 1756 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Beta0MX_ij_LL

vector_fp m_Beta0MX_ij_LL
| mutable private

Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 1759 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Beta0MX_ij_P

vector_fp m_Beta0MX_ij_P
| mutable private

Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 1762 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Beta0MX_ij_coeff

Array2D m_Beta0MX_ij_coeff
| mutable private

Array of coefficients for Beta0, a variable in Pitzer's papers.

Column index is counterIJ. m_Beta0MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.

Definition at line 1770 of file HMWSoln.h.

## ◆ m_Beta1MX_ij

vector_fp m_Beta1MX_ij
| mutable private

Array of 2D data used in the Pitzer/HMW formulation.

Beta1_ij[i][j] is the value of the Beta1 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 1777 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_Beta1MX_ij_L

vector_fp m_Beta1MX_ij_L
| mutable private

Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 1780 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Beta1MX_ij_LL

vector_fp m_Beta1MX_ij_LL
| mutable private

Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 1783 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Beta1MX_ij_P

vector_fp m_Beta1MX_ij_P
| mutable private

Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 1786 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Beta1MX_ij_coeff

Array2D m_Beta1MX_ij_coeff
| mutable private

Array of coefficients for Beta1, a variable in Pitzer's papers.

Column index is counterIJ. m_Beta1MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.

Definition at line 1794 of file HMWSoln.h.

## ◆ m_Beta2MX_ij

vector_fp m_Beta2MX_ij
| mutable private

Array of 2D data used in the Pitzer/HMW formulation.

Beta2_ij[i][j] is the value of the Beta2 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 1801 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_Beta2MX_ij_L

vector_fp m_Beta2MX_ij_L
| mutable private

Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 1804 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Beta2MX_ij_LL

vector_fp m_Beta2MX_ij_LL
| mutable private

Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 1807 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Beta2MX_ij_P

vector_fp m_Beta2MX_ij_P
| mutable private

Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 1810 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Beta2MX_ij_coeff

Array2D m_Beta2MX_ij_coeff
| mutable private

Array of coefficients for Beta2, a variable in Pitzer's papers.

column index is counterIJ. m_Beta2MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction. This was added for the YMP database version of the code since it contains temperature-dependent parameters for some 2-2 electrolytes.

Definition at line 1820 of file HMWSoln.h.

## ◆ m_Alpha1MX_ij

vector_fp m_Alpha1MX_ij
| private

Definition at line 1827 of file HMWSoln.h.

## ◆ m_Alpha2MX_ij

vector_fp m_Alpha2MX_ij
| private

Array of 2D data used in the Pitzer/HMW formulation.

Alpha2MX_ij[i][j] is the value of the alpha2 coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more, usually. It is symmetric wrt i, j. counterIJ, where counterIJ = m_counterIJ[i][j], is used to access this array.

Definition at line 1835 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_CphiMX_ij

vector_fp m_CphiMX_ij
| mutable private

Array of 2D data used in the Pitzer/HMW formulation.

CphiMX_ij[i][j] is the value of the Cphi coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 1842 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_CphiMX_ij_L

vector_fp m_CphiMX_ij_L
| mutable private

Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 1845 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_CphiMX_ij_LL

vector_fp m_CphiMX_ij_LL
| mutable private

Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 1848 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_CphiMX_ij_P

vector_fp m_CphiMX_ij_P
| mutable private

Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 1851 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_CphiMX_ij_coeff

Array2D m_CphiMX_ij_coeff
| mutable private

Array of coefficients for CphiMX, a parameter in the activity coefficient formulation.

Column index is counterIJ. m_CphiMX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.

Definition at line 1860 of file HMWSoln.h.

## ◆ m_Theta_ij

vector_fp m_Theta_ij
| mutable private

Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation.

Array of 2D data used in the Pitzer/HMW formulation. Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

HKM Recent Pitzer papers have used a functional form for Theta_ij, which depends on the ionic strength.

Definition at line 1872 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_Theta_ij_L

vector_fp m_Theta_ij_L
| mutable private

Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 1875 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Theta_ij_LL

vector_fp m_Theta_ij_LL
| mutable private

Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 1878 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Theta_ij_P

vector_fp m_Theta_ij_P
| mutable private

Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 1881 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Theta_ij_coeff

Array2D m_Theta_ij_coeff
| private

Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation.

Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. Column index is counterIJ. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

m_Theta_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.

Definition at line 1893 of file HMWSoln.h.

## ◆ m_Psi_ijk

vector_fp m_Psi_ijk
| mutable private

Array of 3D data used in the Pitzer/HMW formulation.

Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where

n = k + j * m_kk + i * m_kk * m_kk;

It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.

Definition at line 1906 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Psi_ijk_L

vector_fp m_Psi_ijk_L
| mutable private

Derivative of Psi_ijk[n] wrt T.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 1910 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Psi_ijk_LL

vector_fp m_Psi_ijk_LL
| mutable private

Derivative of Psi_ijk[n] wrt TT.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 1914 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Psi_ijk_P

vector_fp m_Psi_ijk_P
| mutable private

Derivative of Psi_ijk[n] wrt P.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 1918 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Psi_ijk_coeff

Array2D m_Psi_ijk_coeff
| private

Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation.

Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where

n = k + j * m_kk + i * m_kk * m_kk;

It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.

m_Psi_ijk_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the n interaction.

Definition at line 1934 of file HMWSoln.h.

## ◆ m_Lambda_nj

Array2D m_Lambda_nj
| mutable private

Lambda coefficient for the ij interaction.

Array of 2D data used in the Pitzer/HMW formulation. Lambda_nj[n][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, that is, n. The charged species occupy the j coordinate. neutral, neutral interactions are also included here.

Definition at line 1944 of file HMWSoln.h.

## ◆ m_Lambda_nj_L

Array2D m_Lambda_nj_L
| mutable private

Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij.

Definition at line 1947 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Lambda_nj_LL

Array2D m_Lambda_nj_LL
| mutable private

Derivative of Lambda_nj[i][j] wrt TT.

Definition at line 1950 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Lambda_nj_P

Array2D m_Lambda_nj_P
| mutable private

Derivative of Lambda_nj[i][j] wrt P.

Definition at line 1953 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Lambda_nj_coeff

Array2D m_Lambda_nj_coeff
| private

Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation.

Array of 2D data used in the Pitzer/HMW formulation. Lambda_ij[i][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, that is, i. The charged species occupy the j coordinate. Neutral, neutral interactions are also included here.

    n = j + m_kk * i

m_Lambda_ij_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the (i,j) interaction.

Definition at line 1968 of file HMWSoln.h.

## ◆ m_Mu_nnn

vector_fp m_Mu_nnn
| mutable private

Mu coefficient for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn[i] represents the Mu coefficient for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 1976 of file HMWSoln.h.

## ◆ m_Mu_nnn_L

vector_fp m_Mu_nnn_L
| mutable private

Mu coefficient temperature derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 1986 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Mu_nnn_LL

vector_fp m_Mu_nnn_LL
| mutable private

Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient 2nd temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 1996 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Mu_nnn_P

vector_fp m_Mu_nnn_P
| mutable private

Mu coefficient pressure derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient pressure derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 2006 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Mu_nnn_coeff

Array2D m_Mu_nnn_coeff
| private

Array of coefficients form_Mu_nnn term.

Definition at line 2009 of file HMWSoln.h.

## ◆ m_lnActCoeffMolal_Scaled

vector_fp m_lnActCoeffMolal_Scaled
| mutable private

Logarithm of the activity coefficients on the molality scale.

mutable because we change this if the composition or temperature or pressure changes. Index is the species index

Definition at line 2016 of file HMWSoln.h.

Referenced by HMWSoln::getActivities(), HMWSoln::getChemPotentials(), HMWSoln::getPartialMolarEntropies(), and HMWSoln::s_updateScaling_pHScaling().

## ◆ m_lnActCoeffMolal_Unscaled

vector_fp m_lnActCoeffMolal_Unscaled
| mutable private

Logarithm of the activity coefficients on the molality scale.

mutable because we change this if the composition or temperature or pressure changes. Index is the species index

Definition at line 2023 of file HMWSoln.h.

Referenced by HMWSoln::applyphScale(), HMWSoln::getUnscaledMolalityActivityCoefficients(), and HMWSoln::s_updateScaling_pHScaling().

## ◆ m_dlnActCoeffMolaldT_Scaled

vector_fp m_dlnActCoeffMolaldT_Scaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.

Index is the species index

Definition at line 2027 of file HMWSoln.h.

Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::getPartialMolarEntropies(), and HMWSoln::s_updateScaling_pHScaling_dT().

## ◆ m_dlnActCoeffMolaldT_Unscaled

vector_fp m_dlnActCoeffMolaldT_Unscaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.

Index is the species index

Definition at line 2031 of file HMWSoln.h.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updateScaling_pHScaling_dT().

## ◆ m_d2lnActCoeffMolaldT2_Scaled

vector_fp m_d2lnActCoeffMolaldT2_Scaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.

Index is the species index.

Definition at line 2035 of file HMWSoln.h.

Referenced by HMWSoln::getPartialMolarCp(), and HMWSoln::s_updateScaling_pHScaling_dT2().

## ◆ m_d2lnActCoeffMolaldT2_Unscaled

vector_fp m_d2lnActCoeffMolaldT2_Unscaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.

Index is the species index

Definition at line 2039 of file HMWSoln.h.

Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updateScaling_pHScaling_dT2().

## ◆ m_dlnActCoeffMolaldP_Scaled

vector_fp m_dlnActCoeffMolaldP_Scaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.

Index is the species index

Definition at line 2043 of file HMWSoln.h.

Referenced by HMWSoln::getPartialMolarVolumes(), and HMWSoln::s_updateScaling_pHScaling_dP().

## ◆ m_dlnActCoeffMolaldP_Unscaled

vector_fp m_dlnActCoeffMolaldP_Unscaled
| mutable private

Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.

Index is the species index

Definition at line 2047 of file HMWSoln.h.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), and HMWSoln::s_updateScaling_pHScaling_dP().

## ◆ m_molalitiesCropped

vector_fp m_molalitiesCropped
| mutable private

Cropped and modified values of the molalities used in activity coefficient calculations.

Definition at line 2053 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped(), HMWSoln::initLengths(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_molalitiesAreCropped

bool m_molalitiesAreCropped
| mutable private

Boolean indicating whether the molalities are cropped or are modified.

Definition at line 2056 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped().

## ◆ m_CounterIJ

vector_int m_CounterIJ
| mutable private

a counter variable for keeping track of symmetric binary interactions amongst the solute species.

n = m_kk*i + j m_CounterIJ[n] = counterIJ

Definition at line 2064 of file HMWSoln.h.

Referenced by HMWSoln::counterIJ_setup(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ elambda

double elambda[17]
| mutable private

This is elambda, MEC.

Definition at line 2067 of file HMWSoln.h.

Referenced by HMWSoln::calc_lambdas(), and HMWSoln::calc_thetas().

## ◆ elambda1

double elambda1[17]
| mutable private

This is elambda1, MEC.

Definition at line 2070 of file HMWSoln.h.

Referenced by HMWSoln::calc_lambdas(), and HMWSoln::calc_thetas().

## ◆ m_gfunc_IJ

vector_fp m_gfunc_IJ
| mutable private

Various temporary arrays used in the calculation of the Pitzer activity coefficients.

The subscript, L, denotes the same quantity's derivative wrt temperature This is the value of g(x) in Pitzer's papers. Vector index is counterIJ

Definition at line 2079 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_g2func_IJ

vector_fp m_g2func_IJ
| mutable private

This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ.

Definition at line 2082 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_hfunc_IJ

vector_fp m_hfunc_IJ
| mutable private

hfunc, was called gprime in Pitzer's paper.

However, it's not the derivative of gfunc(x), so I renamed it. Vector index is counterIJ

Definition at line 2086 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_h2func_IJ

vector_fp m_h2func_IJ
| mutable private

hfunc2, was called gprime in Pitzer's paper.

However, it's not the derivative of gfunc(x), so I renamed it. Vector index is counterIJ

Definition at line 2090 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_BMX_IJ

vector_fp m_BMX_IJ
| mutable private

Intermediate variable called BMX in Pitzer's paper.

This is the basic cation - anion interaction. Vector index is counterIJ

Definition at line 2094 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_BMX_IJ_L

vector_fp m_BMX_IJ_L
| mutable private

Derivative of BMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2097 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_BMX_IJ_LL

vector_fp m_BMX_IJ_LL
| mutable private

Derivative of BMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2100 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_BMX_IJ_P

vector_fp m_BMX_IJ_P
| mutable private

Derivative of BMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2103 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_BprimeMX_IJ

vector_fp m_BprimeMX_IJ
| mutable private

Intermediate variable called BprimeMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2107 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_BprimeMX_IJ_L

vector_fp m_BprimeMX_IJ_L
| mutable private

Derivative of BprimeMX wrt T. Vector index is counterIJ.

Definition at line 2110 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_BprimeMX_IJ_LL

vector_fp m_BprimeMX_IJ_LL
| mutable private

Derivative of BprimeMX wrt TT. Vector index is counterIJ.

Definition at line 2113 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_BprimeMX_IJ_P

vector_fp m_BprimeMX_IJ_P
| mutable private

Derivative of BprimeMX wrt P. Vector index is counterIJ.

Definition at line 2116 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_BphiMX_IJ

vector_fp m_BphiMX_IJ
| mutable private

Intermediate variable called BphiMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2120 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_BphiMX_IJ_L

vector_fp m_BphiMX_IJ_L
| mutable private

Derivative of BphiMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2123 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_BphiMX_IJ_LL

vector_fp m_BphiMX_IJ_LL
| mutable private

Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2126 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_BphiMX_IJ_P

vector_fp m_BphiMX_IJ_P
| mutable private

Derivative of BphiMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2129 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Phi_IJ

vector_fp m_Phi_IJ
| mutable private

Intermediate variable called Phi in Pitzer's paper.

Vector index is counterIJ

Definition at line 2133 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_Phi_IJ_L

vector_fp m_Phi_IJ_L
| mutable private

Derivative of m_Phi_IJ wrt T. Vector index is counterIJ.

Definition at line 2136 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_Phi_IJ_LL

vector_fp m_Phi_IJ_LL
| mutable private

Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ.

Definition at line 2139 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_Phi_IJ_P

vector_fp m_Phi_IJ_P
| mutable private

Derivative of m_Phi_IJ wrt P. Vector index is counterIJ.

Definition at line 2142 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_Phiprime_IJ

vector_fp m_Phiprime_IJ
| mutable private

Intermediate variable called Phiprime in Pitzer's paper.

Vector index is counterIJ

Definition at line 2146 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_PhiPhi_IJ

vector_fp m_PhiPhi_IJ
| mutable private

Intermediate variable called PhiPhi in Pitzer's paper.

Vector index is counterIJ

Definition at line 2150 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_PhiPhi_IJ_L

vector_fp m_PhiPhi_IJ_L
| mutable private

Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ.

Definition at line 2153 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_PhiPhi_IJ_LL

vector_fp m_PhiPhi_IJ_LL
| mutable private

Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ.

Definition at line 2156 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_PhiPhi_IJ_P

vector_fp m_PhiPhi_IJ_P
| mutable private

Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ.

Definition at line 2159 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_CMX_IJ

vector_fp m_CMX_IJ
| mutable private

Intermediate variable called CMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2163 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ m_CMX_IJ_L

vector_fp m_CMX_IJ_L
| mutable private

Derivative of m_CMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2166 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().

## ◆ m_CMX_IJ_LL

vector_fp m_CMX_IJ_LL
| mutable private

Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2169 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().

## ◆ m_CMX_IJ_P

vector_fp m_CMX_IJ_P
| mutable private

Derivative of m_CMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2172 of file HMWSoln.h.

Referenced by HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().

## ◆ m_gamma_tmp

vector_fp m_gamma_tmp
| mutable private

Intermediate storage of the activity coefficient itself.

Vector index is the species index

Definition at line 2176 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped(), HMWSoln::relative_enthalpy(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().

## ◆ IMS_lnActCoeffMolal_

vector_fp IMS_lnActCoeffMolal_
| mutable private

Logarithm of the molal activity coefficients.

Normally these are all one. However, stability schemes will change that

Definition at line 2180 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_X_o_cutoff_

doublereal IMS_X_o_cutoff_
| private

value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process;

Definition at line 2184 of file HMWSoln.h.

Referenced by HMWSoln::calcIMSCutoffParams_(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_cCut_

doublereal IMS_cCut_
| private

Parameter in the polyExp cutoff treatment having to do with rate of exp decay.

Definition at line 2187 of file HMWSoln.h.

Referenced by HMWSoln::calcIMSCutoffParams_(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_slopegCut_

doublereal IMS_slopegCut_
| private

Parameter in the polyExp cutoff treatment.

This is the slope of the g function at the zero solvent point Default value is 0.0

Definition at line 2194 of file HMWSoln.h.

Referenced by HMWSoln::calcIMSCutoffParams_().

## ◆ IMS_dfCut_

doublereal IMS_dfCut_
| private

Definition at line 2198 of file HMWSoln.h.

## ◆ IMS_efCut_

doublereal IMS_efCut_
| private

Definition at line 2199 of file HMWSoln.h.

## ◆ IMS_afCut_

doublereal IMS_afCut_
| private

Definition at line 2200 of file HMWSoln.h.

## ◆ IMS_bfCut_

doublereal IMS_bfCut_
| private

Definition at line 2201 of file HMWSoln.h.

## ◆ IMS_dgCut_

doublereal IMS_dgCut_
| private

Definition at line 2202 of file HMWSoln.h.

## ◆ IMS_egCut_

doublereal IMS_egCut_
| private

Definition at line 2203 of file HMWSoln.h.

## ◆ IMS_agCut_

doublereal IMS_agCut_
| private

Definition at line 2204 of file HMWSoln.h.

## ◆ IMS_bgCut_

doublereal IMS_bgCut_
| private

Definition at line 2205 of file HMWSoln.h.

## ◆ MC_X_o_cutoff_

doublereal MC_X_o_cutoff_
| private

value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process;

Definition at line 2210 of file HMWSoln.h.

Referenced by HMWSoln::calcMCCutoffParams_(), and HMWSoln::calcMolalitiesCropped().

## ◆ MC_dpCut_

doublereal MC_dpCut_
| private

Definition at line 2214 of file HMWSoln.h.

## ◆ MC_epCut_

doublereal MC_epCut_
| private

Definition at line 2215 of file HMWSoln.h.

## ◆ MC_apCut_

doublereal MC_apCut_
| private

Definition at line 2216 of file HMWSoln.h.

## ◆ MC_bpCut_

doublereal MC_bpCut_
| private

Definition at line 2217 of file HMWSoln.h.

## ◆ MC_cpCut_

doublereal MC_cpCut_
| private

Definition at line 2218 of file HMWSoln.h.

## ◆ CROP_ln_gamma_o_min

doublereal CROP_ln_gamma_o_min
| private

Definition at line 2219 of file HMWSoln.h.

## ◆ CROP_ln_gamma_o_max

doublereal CROP_ln_gamma_o_max
| private

Definition at line 2220 of file HMWSoln.h.

## ◆ CROP_ln_gamma_k_min

doublereal CROP_ln_gamma_k_min
| private

Definition at line 2221 of file HMWSoln.h.

## ◆ CROP_ln_gamma_k_max

doublereal CROP_ln_gamma_k_max
| private

Definition at line 2222 of file HMWSoln.h.

## ◆ CROP_speciesCropped_

vector_int CROP_speciesCropped_
| mutable private

This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime.

- 0 = Not in cropped regime
- 1 = In a transition regime where it is altered but there still may be a temperature or pressure dependence
- 2 = In a cropped regime where there is no temperature or pressure dependence

Definition at line 2233 of file HMWSoln.h.

Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dP(), and HMWSoln::s_update_dlnMolalityActCoeff_dT().

## ◆ m_last_is

doublereal m_last_is
| mutable private

Definition at line 2344 of file HMWSoln.h.

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

- HMWSoln.h
- HMWSoln.cpp