From 824dc7f6dedaafcf793944f6a9ede3f1634982b1 Mon Sep 17 00:00:00 2001 From: Harry Moffat Date: Wed, 20 Jun 2007 21:42:24 +0000 Subject: [PATCH] Doxygen update - worked on the header. --- Cantera/src/thermo/HMWSoln.h | 65 +++++++++++++++++++++++------------- 1 file changed, 41 insertions(+), 24 deletions(-) diff --git a/Cantera/src/thermo/HMWSoln.h b/Cantera/src/thermo/HMWSoln.h index 78394e2ce..1c49592a5 100644 --- a/Cantera/src/thermo/HMWSoln.h +++ b/Cantera/src/thermo/HMWSoln.h @@ -380,8 +380,8 @@ namespace Cantera { * The value of \f$ B_{ca}\f$ is given by the following function * * \f[ - * B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha_1 \sqrt{I}) - * + \beta^{(2)}_{ca} g(\alpha_2 \sqrt{I}) + * B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I}) + * + \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) * \f] * * where @@ -399,19 +399,20 @@ namespace Cantera { * coefficients that may have pressure and/or temperature dependencies. * The \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ formulations are * slightly more complicated. \f$ b \f$ is a univeral - * constant defined to be equal to \f$ 1.2 kg^{1/2} gmol^{-1/2} \f$. The exponential - * coefficient \f$ \alpha_1 \f$ is usually fixed at \f$ \alpha_1 = 2.0 kg^{1/2} gmol^{-1/2}\f$ + * constant defined to be equal to \f$ 1.2\ kg^{1/2}\ gmol^{-1/2} \f$. The exponential + * coefficient \f$ \alpha^{(1)}_{ca} \f$ is usually + * fixed at \f$ \alpha^{(1)}_{ca} = 2.0\ kg^{1/2} gmol^{-1/2}\f$ * except for 2-2 electrolytes, while other parameters were fit to experimental - * data. For 2-2 electrolytes, \f$ \alpha_1 = 1.4 kg^{1/2} gmol^{-1/2}\f$ - * is used in combination with either \f$ \alpha_2 = 12 kg^{1/2} gmol^{-1/2}\f$ - * or \f$ \alpha_2 = k A_\psi \f$, where k is a constant. For electrolytes other - * than 2-2 electrolytes the \f$ \beta^{(2)}_{ca} g(\alpha_2 \sqrt{I}) \f$ term + * data. For 2-2 electrolytes, \f$ \alpha^{(1)}_{ca} = 1.4\ kg^{1/2}\ gmol^{-1/2}\f$ + * is used in combination with either \f$ \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}\f$ + * or \f$ \alpha^{(2)}_{ca} = k A_\psi \f$, where k is a constant. For electrolytes other + * than 2-2 electrolytes the \f$ \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \f$ term * is not used in the fitting procedure; it is only used for divalent metal * solfates and other high-valence electrolytes which exhibit significant * association at low ionic strengths. * - * The \f$ \beta^{(0)}_{ca} \f$, \f$ \beta^{(1)}_{ca} \f$, \f$ \beta^{(2)}_{ca} \f$, - * and \f$ C_{ca}\f$ binary coefficients are referred to as ion-interaction or + * The \f$ \beta^{(0)}_{ca} \f$, \f$ \beta^{(1)}_{ca}\f$, \f$ \beta^{(2)}_{ca} \f$, + * and \f$ C_{ca} \f$ binary coefficients are referred to as ion-interaction or * Pitzer parameters. These Pitzer parameters may vary with temperature and pressure * but they do not depend on the ionic strength. Their values and temperature * derivatives of their values have been tabulated for a range of electrolytes @@ -487,8 +488,8 @@ namespace Cantera { * The function \f$ B'_{MX} \f$ is defined as: * * \f[ - * B'_{MX} = \left( \frac{\beta^1_{MX} h(\alpha^1_{MX} \sqrt{I})}{I} \right) - * \left( \frac{\beta^2_{MX} h(\alpha^2_{MX} \sqrt{I})}{I} \right) + * B'_{MX} = \left( \frac{\beta^{(1)}_{MX} h(\alpha^{(1)}_{MX} \sqrt{I})}{I} \right) + * \left( \frac{\beta^{(2)}_{MX} h(\alpha^{(2)}_{MX} \sqrt{I})}{I} \right) * \f] * * where \f$ h(x) \f$ is defined as @@ -541,8 +542,8 @@ namespace Cantera { * It can be shown that the expression * * \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})} + * B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{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 @@ -622,11 +623,10 @@ namespace Cantera { * - Uses the full temperature dependence for the * \f$\beta^{(0)}_{MX} \f$ (5 coeffs), * the \f$\beta^{(1)}_{MX} \f$ (3 coeffs), - * and \f$ C^{\phi}_{MX} \f$ (5) coefficients described above. - * There are + * and \f$ C^{\phi}_{MX} \f$ (5 coeffs) parameters described above. * - PITZER_TEMP_LINEAR - string name "LINEAR" * - Uses just the temperature dependence for the - * \f$\beta^{(0)}_{MX} \f$, the \f$\beta^{(1)}_{MX} \f$, + * \f$\beta^{(0)}_{MX} \f$, the \f$\beta^{(1)}_{MX} \f$, * and \f$ C^{\phi}_{MX} \f$ coefficients described above. * There are 2 coefficients for each term. * @@ -661,7 +661,16 @@ namespace Cantera { q0, q1, q2, q3, q4 * @endcode * - *

Example of the specification of Parameters for the Activity + *

Mixing Parameters

+ * + * + *

Ternary Pitzer Parameters

+ * + * + *

Treatment of Neutral Species

+ * + * + *

Example of the Specification of Parameters for the Activity * Coefficients

* * An example is given below. @@ -744,14 +753,14 @@ namespace Cantera { * where * * \f[ - * B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} + * B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} * \f] * Therefore: - * \f[ - * 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} - * \f] + * \f[ + * 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} + * \f] * * Units = sqrt(kg/gmol) * @@ -797,6 +806,14 @@ namespace Cantera { * @endcode * * + *

Temperature and Pressure Dependence of the Activity Coefficients

+ * + * Temperature dependence of the activity coefficients leads to nonzero terms + * for the excess enthalpy of solution. + * + * The pressure dependence of the activity coefficients leads to non-zero terms + * for the excess Volume of the solution. + * *
*

%Application within %Kinetics Managers

*