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This commit is contained in:
Harry Moffat 2008-11-13 23:21:41 +00:00
parent 2e1f53fa07
commit 66a9b679e1
1 changed files with 32 additions and 27 deletions
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59
Cantera/src/thermo/HMWSoln.h
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@ -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
* <binarySaltParameters cation="Na+" anion="OH-">
<binarySaltParameters cation="Na+" anion="OH-">
<beta0> q0, q1, q2, q3, q4 </beta0>
<\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 </TT> 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<SUP>-1</SUP>.
*
* Note, this treatment may be modified in the future, as events dictate.
*
@ -1110,6 +1114,7 @@ namespace Cantera {
* importPhase(*xm, &dhphase);
* @endcode
*
*
* <HR>
* <H2> XML Example </H2>
* <HR>
@ -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.