Cantera  2.1.2
Public Member Functions | Public Attributes | Protected Attributes | Private Member Functions | List of all members
DebyeHuckel Class Reference

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

#include <DebyeHuckel.h>

Inheritance diagram for DebyeHuckel:
[legend]
Collaboration diagram for DebyeHuckel:
[legend]

Public Member Functions

 DebyeHuckel ()
 Default Constructor. More...
 
 DebyeHuckel (const DebyeHuckel &)
 Copy constructor. More...
 
DebyeHuckeloperator= (const DebyeHuckel &)
 Assignment operator. More...
 
 DebyeHuckel (const std::string &inputFile, const std::string &id="")
 Full constructor for creating the phase. More...
 
 DebyeHuckel (XML_Node &phaseRef, const std::string &id="")
 Full constructor for creating the phase. More...
 
virtual ~DebyeHuckel ()
 Destructor. More...
 
ThermoPhaseduplMyselfAsThermoPhase () const
 Duplicator from the ThermoPhase parent class. More...
 
virtual void setParameters (int n, doublereal *const c)
 Set the equation of state parameters. More...
 
virtual void getParameters (int &n, doublereal *const c) const
 Get the equation of state parameters in a vector. More...
 
virtual void setParametersFromXML (const XML_Node &eosdata)
 Set equation of state parameter values from XML entries. More...
 
virtual void initThermo ()
 Initialize the object's internal lengths after species are set. More...
 
virtual void initThermoXML (XML_Node &phaseNode, const std::string &id)
 Process the XML file after species are set up. More...
 
virtual double A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const
 Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol)) More...
 
virtual double dA_DebyedT_TP (double temperature=-1.0, double pressure=-1.0) const
 Value of the derivative of the Debye Huckel constant with respect to temperature. More...
 
virtual double d2A_DebyedT2_TP (double temperature=-1.0, double pressure=-1.0) const
 Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More...
 
virtual double dA_DebyedP_TP (double temperature=-1.0, double pressure=-1.0) const
 Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure. More...
 
double AionicRadius (int k=0) const
 Reports the ionic radius of the kth species. More...
 
int formDH () const
 Returns the form of the Debye-Huckel parameterization used. More...
 
Array2Dget_Beta_ij ()
 Returns a reference to M_Beta_ij. More...
 
Utilities
virtual int eosType () const
 Equation of state type flag. More...
 
Molar Thermodynamic Properties of the Solution
virtual doublereal enthalpy_mole () const
 Molar enthalpy of the solution. Units: J/kmol. More...
 
virtual doublereal intEnergy_mole () const
 Molar internal energy of the solution. Units: J/kmol. More...
 
virtual doublereal entropy_mole () const
 Molar entropy. Units: J/kmol/K. More...
 
virtual doublereal gibbs_mole () const
 Molar Gibbs function. Units: J/kmol. More...
 
virtual doublereal cp_mole () const
 Molar heat capacity at constant pressure. Units: J/kmol/K. More...
 
virtual doublereal cv_mole () const
 Molar heat capacity at constant volume. Units: J/kmol/K. More...
 
Activities, Standard States, and Activity Concentrations

The activity \(a_k\) of a species in solution is related to the chemical potential by

\[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \]

The quantity \(\mu_k^0(T,P)\) is the chemical potential at unit activity, which depends only on temperature and the pressure.

Activity is assumed to be molality-based here.

virtual void getActivityConcentrations (doublereal *c) const
 This method returns an array of generalized concentrations. More...
 
virtual doublereal standardConcentration (size_t k=0) const
 Return the standard concentration for the kth species. More...
 
virtual doublereal logStandardConc (size_t k=0) const
 Natural logarithm of the standard concentration of the kth species. More...
 
virtual void getUnitsStandardConc (double *uA, int k=0, int sizeUA=6) const
 Returns the units of the standard and generalized concentrations. More...
 
virtual void getActivities (doublereal *ac) const
 Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration. More...
 
virtual void getMolalityActivityCoefficients (doublereal *acMolality) const
 Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration. More...
 
Partial Molar Properties of the Solution
virtual void getChemPotentials (doublereal *mu) const
 Get the species chemical potentials. Units: J/kmol. More...
 
virtual void getPartialMolarEnthalpies (doublereal *hbar) const
 Returns an array of partial molar enthalpies for the species in the mixture. More...
 
virtual void getPartialMolarEntropies (doublereal *sbar) const
 Returns an array of partial molar entropies of the species in the solution. More...
 
virtual void getPartialMolarCp (doublereal *cpbar) const
 Return an array of partial molar heat capacities for the species in the mixture. More...
 
virtual void getPartialMolarVolumes (doublereal *vbar) const
 Return an array of partial molar volumes for the species in the mixture. More...
 
Chemical Equilibrium
virtual void setToEquilState (const doublereal *lambda_RT)
 This method is used by the ChemEquil equilibrium solver. More...
 
Saturation properties.

These methods are only implemented by subclasses that implement full liquid-vapor equations of state.

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

Public Attributes

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

Protected Attributes

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

Private Member Functions

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

Mechanical Equation of State Properties

In this equation of state implementation, the density is a function only of the mole fractions.

Therefore, it can't be an independent variable. Instead, the pressure is used as the independent variable. Functions which try to set the thermodynamic state by calling setDensity() may cause an exception to be thrown.

virtual doublereal pressure () const
 Return the thermodynamic pressure (Pa). More...
 
virtual void setPressure (doublereal p)
 Set the internally stored pressure (Pa) at constant temperature and composition. More...
 
void setDensity (const doublereal rho)
 Set the internally stored density (gm/m^3) of the phase. More...
 
virtual void setMolarDensity (const doublereal conc)
 Set the internally stored molar density (kmol/m^3) of the phase. More...
 
virtual void setTemperature (const doublereal temp)
 Set the temperature (K) More...
 
virtual void setState_TP (doublereal t, doublereal p)
 Set the temperature (K) and pressure (Pa) More...
 
virtual doublereal isothermalCompressibility () const
 The isothermal compressibility. More...
 
virtual doublereal thermalExpansionCoeff () const
 The thermal expansion coefficient. More...
 
virtual void calcDensity ()
 Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...
 

Additional Inherited Members

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

Detailed Description

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

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


Specification of Species Standard State Properties


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

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

For an incompressible,

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

The enthalpy function is given by the following relation.

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

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

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

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

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

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


Specification of Solution Thermodynamic Properties


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

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

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

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

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

<H3> Ionic Strength </H3>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

DHFORM_DILUTE_LIMIT = 0

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

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

where \( I\) is the ionic strength

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

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

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

<H3> Bdot Formulation </H3>

  DHFORM_BDOT_AK       = 1

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

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

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

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

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

where

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

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

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

DHFORM_BDOT_AUNIFORM = 2

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

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

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

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

<H3> Beta_IJ formulation </H3>

DHFORM_BETAIJ        = 3

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

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

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

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

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

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

An example activityCoefficients XML block for this formulation is supplied below

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

Pitzer Beta_IJ formulation

DHFORM_PITZER_BETAIJ = 4

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

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

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

Specification of the Debye Huckel Constants

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

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

where

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

Therefore:

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

where

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

An example of a fixed value implementation is given below.

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

An example of a variable value implementation is given below.

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

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


Application within Kinetics Managers


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

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

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

where

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

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

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

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

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

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

where

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

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

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


Instantiation of the Class


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

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

or

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

or by the following call to importPhase():

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

XML Example


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

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

Definition at line 600 of file DebyeHuckel.h.

Constructor & Destructor Documentation

Default Constructor.

Definition at line 31 of file DebyeHuckel.cpp.

References DebyeHuckel::m_npActCoeff.

Referenced by DebyeHuckel::duplMyselfAsThermoPhase().

DebyeHuckel ( const DebyeHuckel b)

Copy constructor.

Definition at line 98 of file DebyeHuckel.cpp.

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

Full constructor for creating the phase.

Parameters
inputFileFile name containing the XML description of the phase
idid attribute containing the name of the phase.

Definition at line 53 of file DebyeHuckel.cpp.

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

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

Full constructor for creating the phase.

Parameters
phaseRefXML phase node containing the description of the phase
idid attribute containing the name of the phase.

Definition at line 76 of file DebyeHuckel.cpp.

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

~DebyeHuckel ( )
virtual

Destructor.

Definition at line 165 of file DebyeHuckel.cpp.

References DebyeHuckel::m_waterProps.

Member Function Documentation

DebyeHuckel & operator= ( const DebyeHuckel b)
ThermoPhase * duplMyselfAsThermoPhase ( ) const
virtual

Duplicator from the ThermoPhase parent class.

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

Returns
returns a pointer to a ThermoPhase

Reimplemented from MolalityVPSSTP.

Definition at line 173 of file DebyeHuckel.cpp.

References DebyeHuckel::DebyeHuckel().

int eosType ( ) const
virtual

Equation of state type flag.

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

Reimplemented from MolalityVPSSTP.

Definition at line 178 of file DebyeHuckel.cpp.

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

doublereal enthalpy_mole ( ) const
virtual

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

Reimplemented from ThermoPhase.

Definition at line 201 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::intEnergy_mole().

doublereal intEnergy_mole ( ) const
virtual

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

Reimplemented from ThermoPhase.

Definition at line 207 of file DebyeHuckel.cpp.

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

doublereal entropy_mole ( ) const
virtual

Molar entropy. Units: J/kmol/K.

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

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

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

See Also
SpeciesThermo

Reimplemented from ThermoPhase.

Definition at line 216 of file DebyeHuckel.cpp.

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

doublereal gibbs_mole ( ) const
virtual

Molar Gibbs function. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 222 of file DebyeHuckel.cpp.

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

doublereal cp_mole ( ) const
virtual

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

Reimplemented from ThermoPhase.

Definition at line 228 of file DebyeHuckel.cpp.

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

doublereal cv_mole ( ) const
virtual

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

Reimplemented from ThermoPhase.

Definition at line 234 of file DebyeHuckel.cpp.

References DebyeHuckel::err().

doublereal pressure ( ) const
virtual

Return the thermodynamic pressure (Pa).

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

Reimplemented from ThermoPhase.

Definition at line 246 of file DebyeHuckel.cpp.

References VPStandardStateTP::m_Pcurrent.

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

void setPressure ( doublereal  p)
virtual

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

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

Parameters
pinput Pressure (Pa)
Todo:
Implement a variable pressure capability

Reimplemented from VPStandardStateTP.

Definition at line 251 of file DebyeHuckel.cpp.

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

void calcDensity ( )
protectedvirtual

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

The formula for this is

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

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

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

Reimplemented from VPStandardStateTP.

Definition at line 278 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::setState_TP().

void setDensity ( const doublereal  rho)
virtual

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

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

This function will now throw an error condition

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

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

Todo:
Now have a compressible ss equation for liquid water. Therefore, this phase is compressible. May still want to change the independent variable however.
Parameters
rhoInput density (kg/m^3).

Reimplemented from Phase.

Definition at line 315 of file DebyeHuckel.cpp.

References Phase::density().

void setMolarDensity ( const doublereal  conc)
virtual

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

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

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

Parameters
concInput molar density (kmol/m^3).

Reimplemented from Phase.

Definition at line 324 of file DebyeHuckel.cpp.

References Phase::molarDensity().

void setTemperature ( const doublereal  temp)
virtual

Set the temperature (K)

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

Parameters
tempTemperature in kelvin

Reimplemented from VPStandardStateTP.

Definition at line 333 of file DebyeHuckel.cpp.

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

void setState_TP ( doublereal  t,
doublereal  p 
)
virtual

Set the temperature (K) and pressure (Pa)

Set the temperature and pressure.

Parameters
tTemperature (K)
pPressure (Pa)

Reimplemented from VPStandardStateTP.

Definition at line 256 of file DebyeHuckel.cpp.

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

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

doublereal isothermalCompressibility ( ) const
virtual

The isothermal compressibility.

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

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

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

Reimplemented from ThermoPhase.

Definition at line 301 of file DebyeHuckel.cpp.

doublereal thermalExpansionCoeff ( ) const
virtual

The thermal expansion coefficient.

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

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

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

Reimplemented from ThermoPhase.

Definition at line 308 of file DebyeHuckel.cpp.

void getActivityConcentrations ( doublereal *  c) const
virtual

This method returns an array of generalized concentrations.

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

Parameters
cArray of generalized concentrations. The units depend upon the implementation of the reaction rate expressions within the phase.

Reimplemented from MolalityVPSSTP.

Definition at line 342 of file DebyeHuckel.cpp.

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

doublereal standardConcentration ( size_t  k = 0) const
virtual

Return the standard concentration for the kth species.

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

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

Parameters
kOptional parameter indicating the species. The default is to assume this refers to species 0.
Returns
Returns the standard Concentration in units of m3 kmol-1.

Reimplemented from MolalityVPSSTP.

Definition at line 351 of file DebyeHuckel.cpp.

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

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

doublereal logStandardConc ( size_t  k = 0) const
virtual

Natural logarithm of the standard concentration of the kth species.

Parameters
kindex of the species (defaults to zero)

Reimplemented from MolalityVPSSTP.

Definition at line 357 of file DebyeHuckel.cpp.

References DebyeHuckel::standardConcentration().

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

Returns the units of the standard and generalized concentrations.

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

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

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

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

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

Reimplemented from MolalityVPSSTP.

Definition at line 363 of file DebyeHuckel.cpp.

References Phase::nDim().

void getActivities ( doublereal *  ac) const
virtual

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

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

(note solvent activity coefficient is on molar scale).

Parameters
acOutput vector of activities. Length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 387 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::getActivityConcentrations().

void getMolalityActivityCoefficients ( doublereal *  acMolality) const
virtual

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

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

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

Parameters
acMolalityVector of Molality-based activity coefficients Length: m_kk

Reimplemented from MolalityVPSSTP.

Definition at line 406 of file DebyeHuckel.cpp.

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

void getChemPotentials ( doublereal *  mu) const
virtual

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

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

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

Parameters
muOutput vector of species chemical potentials. Length: m_kk. Units: J/kmol

Reimplemented from ThermoPhase.

Definition at line 420 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::gibbs_mole().

void getPartialMolarEnthalpies ( doublereal *  hbar) const
virtual

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

Units (J/kmol)

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

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

The solvent partial molar enthalpy is equal to

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

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

Parameters
hbarOutput vector of species partial molar enthalpies. Length: m_kk. units are J/kmol.

Reimplemented from ThermoPhase.

Definition at line 448 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::enthalpy_mole().

void getPartialMolarEntropies ( doublereal *  sbar) const
virtual

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

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

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

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

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

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

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

See Also
SpeciesThermo
Parameters
sbarOutput vector of species partial molar entropies. Length = m_kk. units are J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 483 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::entropy_mole().

void getPartialMolarCp ( doublereal *  cpbar) const
virtual

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

Units: J/kmol/K

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

Reimplemented from ThermoPhase.

Definition at line 546 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::cp_mole().

void getPartialMolarVolumes ( doublereal *  vbar) const
virtual

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

Units: m^3/kmol.

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

The general relation is

  vbar_i = d(chemPot_i)/dP at const T, n
         = V0_i + d(Gex)/dP)_T,M
         = V0_i + RT d(lnActCoeffi)dP _T,M
Parameters
vbarOutput vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.

Reimplemented from ThermoPhase.

Definition at line 531 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::calcDensity().

virtual void setToEquilState ( const doublereal *  lambda_RT)
inlinevirtual

This method is used by the ChemEquil equilibrium solver.

It sets the state such that the chemical potentials satisfy

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

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

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

Reimplemented from MolalityVPSSTP.

Definition at line 1064 of file DebyeHuckel.h.

References DebyeHuckel::err().

void setParameters ( int  n,
doublereal *const  c 
)
virtual

Set the equation of state parameters.

The number and meaning of these depends on the subclass.

Parameters
nnumber of parameters
carray of n coefficients
Deprecated:
Unimplemented

Reimplemented from ThermoPhase.

Definition at line 1127 of file DebyeHuckel.cpp.

References Cantera::warn_deprecated().

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

Get the equation of state parameters in a vector.

The number and meaning of these depends on the subclass.

Parameters
nnumber of parameters
carray of n coefficients
Deprecated:
Unimplemented

Reimplemented from ThermoPhase.

Definition at line 1132 of file DebyeHuckel.cpp.

References Cantera::warn_deprecated().

void setParametersFromXML ( const XML_Node eosdata)
virtual

Set equation of state parameter values from XML entries.

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

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

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

Reimplemented from VPStandardStateTP.

Definition at line 1137 of file DebyeHuckel.cpp.

virtual doublereal satTemperature ( doublereal  p) const
inlinevirtual

Return the saturation temperature given the pressure.

Parameters
pPressure (Pa)

Reimplemented from ThermoPhase.

Definition at line 1114 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual doublereal satPressure ( doublereal  T)
inlinevirtual

Get the saturation pressure for a given temperature.

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

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

Reimplemented from ThermoPhase.

Definition at line 1134 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual doublereal vaporFraction ( ) const
inlinevirtual

Return the fraction of vapor at the current conditions.

Reimplemented from ThermoPhase.

Definition at line 1139 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual void setState_Tsat ( doublereal  t,
doublereal  x 
)
inlinevirtual

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

Parameters
tTemperature (kelvin)
xFraction of vapor

Reimplemented from ThermoPhase.

Definition at line 1144 of file DebyeHuckel.h.

References DebyeHuckel::err().

virtual void setState_Psat ( doublereal  p,
doublereal  x 
)
inlinevirtual

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

Parameters
pPressure (Pa)
xFraction of vapor

Reimplemented from ThermoPhase.

Definition at line 1148 of file DebyeHuckel.h.

References DebyeHuckel::err().

void initThermo ( )
virtual

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

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

Cascading call sequence downwards starting with Parent.

See Also
importCTML.cpp

Reimplemented from MolalityVPSSTP.

Definition at line 586 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::initThermoXML().

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

Process the XML file after species are set up.

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

Parameters
phaseNodeThis 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.
idID of the phase. If nonnull, a check is done to see if phaseNode is pointing to the phase with the correct id.

Reimplemented from VPStandardStateTP.

Definition at line 622 of file DebyeHuckel.cpp.

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

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

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

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

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

where

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

Therefore:

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

where

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

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

  • \( \epsilon / \epsilon_0 \) = 78.54 (water at 25C)
  • T = 298.15 K
  • B_Debye = 3.28640E9 (kg/gmol)1/2 m-1
Parameters
temperatureTemperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed.
pressurePressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.

Definition at line 1141 of file DebyeHuckel.cpp.

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

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

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

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

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

Units = sqrt(kg/gmol) K-1

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

Definition at line 1168 of file DebyeHuckel.cpp.

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

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

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

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

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

Units = sqrt(kg/gmol) K-2

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

Definition at line 1193 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2().

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

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

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

Units = sqrt(kg/gmol) Pa-1

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

Definition at line 1218 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::s_update_dlnMolalityActCoeff_dP().

double AionicRadius ( int  k = 0) const

Reports the ionic radius of the kth species.

Parameters
kspecies index.

Definition at line 1247 of file DebyeHuckel.cpp.

References DebyeHuckel::m_Aionic.

int formDH ( ) const
inline

Returns the form of the Debye-Huckel parameterization used.

Definition at line 1302 of file DebyeHuckel.h.

References DebyeHuckel::m_formDH.

Array2D& get_Beta_ij ( )
inline

Returns a reference to M_Beta_ij.

Definition at line 1307 of file DebyeHuckel.h.

References DebyeHuckel::m_Beta_ij.

double _nonpolarActCoeff ( double  IionicMolality) const
private

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

Returns the calculated activity coefficients.

Parameters
IionicMolalityValue of the ionic molality (sqrt(gmol/kg))

Definition at line 1287 of file DebyeHuckel.cpp.

References DebyeHuckel::m_npActCoeff.

Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().

double _osmoticCoeffHelgesonFixedForm ( ) const
private

Formula for the osmotic coefficient that occurs in the GWB.

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

Definition at line 1297 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::_lnactivityWaterHelgesonFixedForm().

double _lnactivityWaterHelgesonFixedForm ( ) const
private

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

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

Definition at line 1316 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().

doublereal err ( const std::string &  msg) const
private
void initLengths ( )
private
void s_update_lnMolalityActCoeff ( ) const
private
void s_update_dlnMolalityActCoeff_dT ( ) const
private

Calculation of temperature derivative of activity coefficient.

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

We assume that the activity coefficients are current in this routine

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

Definition at line 1593 of file DebyeHuckel.cpp.

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

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

void s_update_d2lnMolalityActCoeff_dT2 ( ) const
private

Calculate the temperature 2nd derivative of the activity coefficient.

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

We assume that the activity coefficients are current in this routine

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

Definition at line 1720 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::getPartialMolarCp().

void s_update_dlnMolalityActCoeff_dP ( ) const
private

Calculate the pressure derivative of the activity coefficient.

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

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

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

Definition at line 1842 of file DebyeHuckel.cpp.

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

Referenced by DebyeHuckel::getPartialMolarVolumes().

Member Data Documentation

int m_formDH
protected

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

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

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

Definition at line 1351 of file DebyeHuckel.h.

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

int m_formGC
protected

Format for the generalized concentration:

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

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

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

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

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

Definition at line 1382 of file DebyeHuckel.h.

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

vector_int m_electrolyteSpeciesType
protected

Vector containing the electrolyte species type.

The possible types are:

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

Definition at line 1395 of file DebyeHuckel.h.

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

vector_fp m_Aionic
protected
double m_IionicMolality
mutableprotected
double m_maxIionicStrength
protected

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

Definition at line 1410 of file DebyeHuckel.h.

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

bool m_useHelgesonFixedForm

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

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

Definition at line 1421 of file DebyeHuckel.h.

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

double m_IionicMolalityStoich
mutableprotected

Stoichiometric ionic strength on the molality scale.

Definition at line 1425 of file DebyeHuckel.h.

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

int m_form_A_Debye

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

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

  A_DEBYE_CONST  0
  A_DEBYE_WATER  1

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

Definition at line 1445 of file DebyeHuckel.h.

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

double m_A_Debye
mutableprotected

Current value of the Debye Constant, A_Debye.

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

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

Units = sqrt(kg/gmol)

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

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

Definition at line 1469 of file DebyeHuckel.h.

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

double m_B_Debye
protected

Current value of the constant that appears in the denominator.

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

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

Units = sqrt(kg/gmol) / m

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

Definition at line 1488 of file DebyeHuckel.h.

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

vector_fp m_B_Dot
protected

Array of B_Dot values.

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

Definition at line 1496 of file DebyeHuckel.h.

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

vector_fp m_npActCoeff
protected

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

Definition at line 1503 of file DebyeHuckel.h.

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

PDSS_Water* m_waterSS
protected

Pointer to the Water standard state object.

derived from the equation of state for water.

Definition at line 1510 of file DebyeHuckel.h.

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

double m_densWaterSS
protected

Storage for the density of water's standard state.

Density depends on temperature and pressure.

Definition at line 1516 of file DebyeHuckel.h.

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

WaterProps* m_waterProps
protected
vector_fp m_pp
mutableprotected

Temporary array used in equilibrium calculations.

Definition at line 1522 of file DebyeHuckel.h.

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

vector_fp m_tmpV
mutableprotected
vector_fp m_speciesCharge_Stoich
protected

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

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

Definition at line 1539 of file DebyeHuckel.h.

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

Array2D m_Beta_ij
protected

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

Definition at line 1547 of file DebyeHuckel.h.

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

vector_fp m_lnActCoeffMolal
mutableprotected
vector_fp m_dlnActCoeffMolaldT
mutableprotected
vector_fp m_d2lnActCoeffMolaldT2
mutableprotected
vector_fp m_dlnActCoeffMolaldP
mutableprotected

Derivative of log act coeff wrt P.

Definition at line 1563 of file DebyeHuckel.h.

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


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