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- worked on the header.
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Harry Moffat 2007-06-20 21:42:24 +00:00
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65
Cantera/src/thermo/HMWSoln.h
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@ -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$, where <I>k</I> is a constant. For electrolytes other
* than 2-2 electrolytes the \f$ \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 {
<beta0> q0, q1, q2, q3, q4 </beta0>
* @endcode
*
* <H3> Example of the specification of Parameters for the Activity
* <H3> Mixing Parameters </H3>
*
*
* <H3> Ternary Pitzer Parameters </H3>
*
*
* <H3> Treatment of Neutral Species </H3>
*
*
* <H3> Example of the Specification of Parameters for the Activity
* Coefficients </H3>
*
* 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
*
*
* <H3> Temperature and Pressure Dependence of the Activity Coefficients </H3>
*
* 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.
*
* <HR>
* <H2> %Application within %Kinetics Managers </H2>
* <HR>