diff --git a/Cantera/src/thermo/HMWSoln.h b/Cantera/src/thermo/HMWSoln.h index b03a0e158..d2b2b9ae5 100644 --- a/Cantera/src/thermo/HMWSoln.h +++ b/Cantera/src/thermo/HMWSoln.h @@ -467,7 +467,6 @@ namespace Cantera { * \f] * where the function \f$ F \f$ is given by * - * * \f[ * F = - A_{\phi} \left[ \frac{\sqrt{I}}{1 + b \sqrt{I}} * + \frac{2}{b} \ln{\left(1 + b\sqrt{I}\right)} \right] @@ -483,7 +482,7 @@ namespace Cantera { * A_{\phi} = \frac{A_{Debye}}{3} * \f] * - * In the above formulas, \f$ \Phi'_{c{c'}} \f$ and \f$ \Phi'_{a{a'}} \f$ are the + * In the above formulas, \f$ \Phi'_{c{c'}} \f$ and \f$ \Phi'_{a{a'}} \f$ are the * ionic strength derivatives of \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$, * respectively. * @@ -553,18 +552,19 @@ namespace Cantera { * * \f[ * B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{ca} \sqrt{I})} - * + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I})} + * + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I} )} * \f] * - * is consistent with the expression \f$ B_{ca}\f$ in the \f$ G^{ex}\f$ expression - * after carrying out the derivative wrt \f$ m_M\f$. + * is consistent with the expression \f$ B_{ca} \f$ in the \f$ G^{ex} \f$ expression + * after carrying out the derivative wrt \f$ m_M \f$. * - * Also taking into account that \f$ \Phi_{c{c'}} \f$ and - * \f$ \Phi_{a{a'}} \f$ has an ionic strength dependence + * Also taking into account that \f$ {\Phi}_{c{c'}} \f$ and + * \f$ {\Phi}_{a{a'}} \f$ has an ionic strength dependence. * * \f[ - * \Phi^{\phi}_{c{c'}} = \Phi_{c{c'}} + I \frac{d\Phi_{c{c'}}}{dI} + * \Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI} * \f] + * * \f[ * \Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI} * \f] @@ -612,7 +612,7 @@ namespace Cantera { * where * * \f[ - * C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX} + * C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX} * \f] * * In later papers, Pitzer has added additional temperature dependencies @@ -669,24 +669,24 @@ namespace Cantera { * dependence given above is * * @code - * + q0, q1, q2, q3, q4 <\binarySaltParameters> - * @endcode + @endcode * * The parameters for \f$ \beta^{(0)}\f$ fit the following equation: * * \f[ - * \beta^{(0)} = q_0^{\beta0} + q_1^{\beta0} \left( T - T_r \right) - * + q_2^{\beta0} \left( T^2 - T_r^2 \right) - * + q_3^{\beta0} \left( \frac{1}{T} - \frac{1}{T_r} \right) - * + q_4^{\beta0} \ln \left( \frac{T}{T_r} \right) + * \beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right) + * + q_2^{{\beta}0} \left( T^2 - T_r^2 \right) + * + q_3^{{\beta}0} \left( \frac{1}{T} - \frac{1}{T_r} \right) + * + q_4^{{\beta}0} \ln \left( \frac{T}{T_r} \right) * \f] * * This same COMPLEX1 temperature * dependence given above is used for the following parameters: * \f$\beta^{(0)}_{MX} \f$, \f$\beta^{(1)}_{MX} \f$, - * \f$\beta^{(2)}_{MX} \f$, \f$\Theta_{cc'} \f$, \f$\Theta_{aa'}, + * \f$\beta^{(2)}_{MX} \f$, \f$ \Theta_{cc'} \f$, \f$\Theta_{aa'} \f$, * \f$ \Psi_{c{c'}a}\f$ and \f$ \Psi_{ca{a'}} \f$. * * @@ -706,10 +706,13 @@ namespace Cantera { * charges. \f$ \Phi_{ij} \f$, where \f$ ij \f$ is either \f$ a{a'} \f$ * or \f$ c{c'} \f$ is given by * - * \f[ - * \Phi_{i{j}} = \Theta_{ij} + \,^E\Theta_{ij}(I) + * + * + * \f[ + * {\Phi}_{ij} = \Theta_{ij} + \,^E \Theta_{ij}(I) * \f] * + * * \f$ \Theta_{ij} \f$ is the small virial coefficient expansion term. * Dependent in general on temperature and pressure, it's ionic * strength dependence is ignored in Pitzer's approach. @@ -719,7 +722,7 @@ namespace Cantera { * the dielectric constant and density of the solvent. * This seems to be a relatively well-documented part of the theory. * They theory below comes from Pitzer summation (Pitzer) in the - * appendix. It's also mentioned in bethke's book (Bethke), and + * appendix. It's also mentioned in Bethke's book (Bethke), and * the equations are summarized in Harvie & Weare (1980). * Within the code, \f$ \,^E\Theta_{ij}(I) \f$ is evaluated according * to the algorithm described in Appendix B [Pitzer] as @@ -734,8 +737,8 @@ namespace Cantera { * * \f[ * J(x) = \frac{1}{x} \int_0^{\infty}{\left( 1 + q + - * \frac{1}{2} q^2 - e^q \right) y^2 dy} - * \f] + * \frac{1}{2} q^2 - e^q \right) y^2 dy} + * \f] * * and \f$ q = - (\frac{x}{y}) e^{-y} \f$. \f$ J(x) \f$ is evaluated by * numerical integration. @@ -1031,6 +1034,7 @@ namespace Cantera { * following equation for its rate of progress variable, \f$ R^1 \f$, which has * units of kmol m-3 s-1. * + * * \f[ * R^1 = k^1 C_j^a C_k^a = k^1 (C_o a_j) (C_o a_k) * \f] @@ -1054,19 +1058,19 @@ namespace Cantera { * \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} ) * \f] * - * \f$ K^{o,1} \f$ is the dimensionless form of the equilibrium constant. + * \f$ K^{o,1} \f$ is the dimensionless form of the equilibrium constant. * * \f[ - * R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l) + * R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l) * \f] * * where * - * \f[ + * \f[ * k^{-1} = k^1 K^{o,1} C_o * \f] * - * \f$k^{-1} \f$ has units of s-1. + * \f$ k^{-1} \f$ has units of s-1. * * Note, this treatment may be modified in the future, as events dictate. * @@ -1110,6 +1114,7 @@ namespace Cantera { * importPhase(*xm, &dhphase); * @endcode * + * *
*

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@@ -2937,7 +2942,7 @@ namespace Cantera { */ mutable vector_fp IMS_lnActCoeffMolal_; - // IMS Cutoff type + //! IMS Cutoff type int IMS_typeCutoff_; //! value of the solute mole fraction that centers the cutoff polynomials @@ -3202,7 +3207,7 @@ namespace Cantera { //! Precalculate the IMS Cutoff parameters for typeCutoff = 2 - void HMWSoln::calcIMSCutoffParams_(); + void calcIMSCutoffParams_(); //! Utility function to assign an integer value from a string //! for the ElectrolyteSpeciesType field.