diff --git a/pages/science/index.rst b/pages/science/index.rst
index 678029f7f..977e79311 100644
--- a/pages/science/index.rst
+++ b/pages/science/index.rst
@@ -21,12 +21,11 @@
Chemical Kinetic Theory
-These sections describe some of the theory underpinning the various ways that Cantera models phases
+These sections describe some of the fundamental scientific theory underpinning the ways that Cantera models phases
of matter. This involves calculations for thermodynamic and transport properties and chemical
reaction rates. The above information gives some insight into the basic constitutive models
-available in Cantera: capabilities for calculating the basic properties of
-phases of matter, which can be extended to model a wide range of science and
-technology applications.
+available in Cantera: capabilities for calculating the basic thermodynamic, chemical kinetic, and transport properties of phases of matter, which can be
+extended to model a wide range of science and technology applications.
.. container:: container
:tagname: section
@@ -37,56 +36,55 @@ technology applications.
.. container::
:tagname: a
- :attributes: href=phases.html
- title=Phases
+ :attributes: href=thermodynamics.html
+ title=Thermodynamics
.. container:: card-header section-card
:tagname: div
- Phases
+ Thermodynamics
.. container:: card-body
.. container:: card-text
- The theory behind some of Cantera's phase models.
+ The theory behind how Cantera calculates species and phase thermodynamic properties.
.. container:: card
.. container::
:tagname: a
- :attributes: href=science-species.html
- title=Species
+ :attributes: href=kinetics.html
+ title=Kinetics
.. container:: card-header section-card
:tagname: div
- Species
+ Kinetics and Reaction Rates
.. container:: card-body
.. container:: card-text
- The models Cantera uses to calculate species properties (thermodynamic and
- transport).
+ The models and equations that Cantera uses to calculate chemical reaction rates.
.. container:: card
.. container::
:tagname: a
- :attributes: href=reactions.html
- title=Reactions
+ :attributes: href=transport.html
+ title=Transport
.. container:: card-header section-card
:tagname: div
- Reactions
+ Transport
.. container:: card-body
.. container:: card-text
- The models that Cantera uses to calculate chemical reaction rates.
+ The models that Cantera uses to calculate transport properties and rates.
.. raw:: html
diff --git a/pages/science/reactions.rst b/pages/science/kinetics.rst
similarity index 99%
rename from pages/science/reactions.rst
rename to pages/science/kinetics.rst
index a28717854..e79c22bb3 100644
--- a/pages/science/reactions.rst
+++ b/pages/science/kinetics.rst
@@ -1,4 +1,4 @@
-.. slug: reactions
+.. slug: kinetics
.. has_math: true
.. title: Modeling Chemical Reactions
diff --git a/pages/science/phases.rst b/pages/science/phase-thermo.rst
similarity index 78%
rename from pages/science/phases.rst
rename to pages/science/phase-thermo.rst
index d2f929948..69cc5ad35 100644
--- a/pages/science/phases.rst
+++ b/pages/science/phase-thermo.rst
@@ -1,4 +1,4 @@
-.. slug: phases
+.. slug: phase-thermo
.. has_math: true
.. title: Modeling Phases
@@ -6,7 +6,7 @@
.. raw:: html
- Modeling Phases in Cantera
+ Modeling Phase Thermodynamics in Cantera
.. class:: lead
@@ -29,15 +29,6 @@ Ideal gas mixtures can be defined in the CTI format using the
:cti:class:`ideal_gas` entry, or in the YAML format by specifying
:ref:`ideal-gas ` in the ``thermo`` field.
-.. _sec-transport-models:
-
-Transport Models
-^^^^^^^^^^^^^^^^
-
-Two transport models are available for use with ideal gas mixtures. The first is a multicomponent
-transport model that is based on the model described by Dixon-Lewis [#dl68]_ (see also Kee et al.
-[#Kee2017]_). The second is a model that uses the mixture-averaged rule.
-
Stoichiometric Solid
--------------------
@@ -82,10 +73,3 @@ field.
.. [#Kee1989] R. J. Kee, F. M. Rupley, and J. A. Miller. Chemkin-II: A Fortran
chemical kinetics package for the analysis of gasphase chemical
kinetics. Technical Report SAND89-8009, Sandia National Laboratories, 1989.
-
-.. [#dl68] G. Dixon-Lewis. Flame structure and flame reaction kinetics,
- II: Transport phenomena in multicomponent systems. *Proc. Roy. Soc. A*,
- 307:111--135, 1968.
-
-.. [#Kee2017] R. J. Kee, M. E. Coltrin, P. Glarborg, and H. Zhu. *Chemically Reacting Flow:
- Theory and Practice*. 2nd Ed. John Wiley and Sons, 2017.
diff --git a/pages/science/species.rst b/pages/science/species-thermo.rst
similarity index 78%
rename from pages/science/species.rst
rename to pages/science/species-thermo.rst
index e3d91dc09..f674a3ed9 100644
--- a/pages/science/species.rst
+++ b/pages/science/species-thermo.rst
@@ -1,4 +1,4 @@
-.. slug: science-species
+.. slug: species-thermo
.. has_math: true
.. title: Elements and Species
@@ -6,7 +6,7 @@
.. raw:: html
- Elements and Species
+ Elements and Species Thermodynamics
.. class:: lead
@@ -73,31 +73,20 @@ defined to be composed solely of electrons.
Thermodynamic Properties
------------------------
-The phase models discussed in the `Phases section `__
+The phase models discussed in the `Phases section `__
implement specific models for the thermodynamic properties appropriate for the
type of phase or interface they represent. Although each one may use different
expressions to compute the properties, they all require thermodynamic property
information for the individual species. For the phase types implemented at
present, the properties needed are:
-1. the molar heat capacity at constant pressure :math:`\hat{c}^0_p(T)` for a
- range of temperatures and a reference pressure :math:`P_0`;
-2. the molar enthalpy :math:`\hat{h}(T_0, P_0)` at :math:`P_0` and a reference
- temperature :math:`T_0`;
-3. the absolute molar entropy :math:`\hat{s}(T_0, P_0)` at :math:`(T_0, P_0)`.
+1. the molar heat capacity at constant pressure :math:`\hat{c}^\circ_p(T)` for a
+ range of temperatures and a reference pressure :math:`p^\circ`;
+2. the molar enthalpy :math:`\hat{h}(T^\circ, p^\circ)` at :math:`p^\circ` and a reference
+ temperature :math:`T^\circ`;
+3. the absolute molar entropy :math:`\hat{s}(T^\circ, p^\circ)` at :math:`(T^\circ, p^\circ)`.
-See: :ref:`the Thermodynamic Models section `
-
-Species Transport Coefficients
-------------------------------
-
-Transport property models in general require coefficients that express the
-effect of each species on the transport properties of the phase. Currently,
-ideal-gas transport property models are implemented.
-
-Transport properties can be defined in the CTI format using the
-:cti:class:`gas_transport` entry, or in the YAML format using the
-:ref:`transport ` field of a ``species`` entry.
+The superscript :math:`^\circ` here represents the *reference state*--a specified state (i.e. set of conditions :math:`T^\circ` and :math:`p^\circ` and fixed chemical composition) at which thermodynamic properties are known.
.. _sec-thermo-models:
@@ -119,20 +108,20 @@ The NASA 7-Coefficient Polynomial Parameterization
--------------------------------------------------
The NASA 7-coefficient polynomial parameterization is used to compute the
-species reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`,
-:math:`\hat{h}^0(T)`, and :math:`\hat{s}^0(T)`.
+species reference-state thermodynamic properties :math:`\hat{c}^\circ_p(T)`,
+:math:`\hat{h}^\circ(T)`, and :math:`\hat{s}^\circ(T)`.
-The NASA parameterization represents :math:`\hat{c}^0_p(T)` with a fourth-order
+The NASA parameterization represents :math:`\hat{c}^\circ_p(T)` with a fourth-order
polynomial:
.. math::
- \frac{c_p^0(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4
+ \frac{\hat{c}_p^\circ(T)}{\overline{R}} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4
- \frac{h^0 (T)}{R T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 +
+ \frac{\hat{h}^\circ (T)}{\overline{R} T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 +
\frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T}
- \frac{s^0(T)}{R} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 +
+ \frac{\hat{s}^\circ(T)}{\overline{R}} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 +
\frac{a_4}{4} T^4 + a_6
Note that this is the "old" NASA polynomial form, used in the original NASA
@@ -160,14 +149,14 @@ the following equations:
.. math::
- \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T
+ \frac{\hat{c}_p^\circ(T)}{\overline{R}} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T
+ a_4 T^2 + a_5 T^3 + a_6 T^4
- \frac{H^0(T)}{R T} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2
+ \frac{\hat{h}^\circ(T)}{\overline{R} T} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2
+ \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 +
\frac{a_6}{5} T^4 + \frac{a_7}{T}
- \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T
+ \frac{\hat{s}^\circ(T)}{\overline{R}} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T
+ a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8
A common source for species data in the NASA9 format is the
@@ -184,12 +173,12 @@ The Shomate parameterization is:
.. math::
- \hat{c}_p^0(T) = A + Bt + Ct^2 + Dt^3 + \frac{E}{t^2}
+ \hat{c}_p^\circ(T) = A + Bt + Ct^2 + Dt^3 + \frac{E}{t^2}
- \hat{h}^0(T) = At + \frac{Bt^2}{2} + \frac{Ct^3}{3} + \frac{Dt^4}{4} -
+ \hat{h}^\circ(T) = At + \frac{Bt^2}{2} + \frac{Ct^3}{3} + \frac{Dt^4}{4} -
\frac{E}{t} + F
- \hat{s}^0(T) = A \ln t + B t + \frac{Ct^2}{2} + \frac{Dt^3}{3} -
+ \hat{s}^\circ(T) = A \ln t + B t + \frac{Ct^2}{2} + \frac{Dt^3}{3} -
\frac{E}{2t^2} + G
where :math:`t = T / 1000 K`. It requires 7 coefficients :math:`A`, :math:`B`, :math:`C`, :math:`D`,
@@ -213,14 +202,14 @@ thermodynamic properties:
.. math::
- \hat{c}_p^0(T) = \hat{c}_p^0(T_0)
+ \hat{c}_p^\circ(T) = \hat{c}_p^\circ(T^\circ)
- \hat{h}^0(T) = \hat{h}^0(T_0) + \hat{c}_p^0\cdot(T-T_0)
+ \hat{h}^\circ(T) = \hat{h}^\circ\left(T_0\right) + \hat{c}_p^\circ \left(T-T^\circ\right)
- \hat{s}^0(T) = \hat{s}^0(T_0) + \hat{c}_p^0 \ln (T/T_0)
+ \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln{\left(\frac{T}{T^\circ}\right)}
-The parameterization uses four constants: :math:`T_0, \hat{c}_p^0(T_0),
-\hat{h}^0(T_0), \hat{s}^0(T)`. The default value of :math:`T_0` is 298.15 K; the
+The parameterization uses four constants: :math:`T^\circ, \hat{c}_p^\circ(T^\circ),
+\hat{h}^\circ(T^\circ), and \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the
default value for the other parameters is 0.0.
A constant heat capacity parameterization can be defined in the CTI format using
diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst
new file mode 100644
index 000000000..2d76fb2a4
--- /dev/null
+++ b/pages/science/thermodynamics.rst
@@ -0,0 +1,81 @@
+.. slug: thermodynamics
+.. has_math: true
+.. title: Calculating phase and species thermodynamics
+
+.. jumbotron::
+
+ .. raw:: html
+
+ Calculating thermodynamic properties in Cantera
+
+ .. class:: lead
+
+ Here, we describe how Cantera uses species and phase information to calculate thermodynamic properties.
+
+ Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair certain non-ideal species thermodyamic models with an ideal phase model.
+
+ - The user must specify a thermodynamic model for each species and provide inputs that inform how species properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature.
+ - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`p`-:math:`\hat{v}`-:math:`T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables
+
+Example: The Ideal Gas Model
+============================
+For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species reference thermodynamic quantities. These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`. See the `NASA Polynomials Species Thermo entry `__ for more information.
+
+At the phase level, the Ideal Gas Law provides the :math:`P`-:math:`\hat{v}`-:math:`T` relationship. The ideal gas law is an example of an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}`, and temperature, :math:`T`:
+
+.. math::
+ p = \frac{\overline{R}T}{\hat{v}}
+
+where :math:`\overline{R}` is the Universal Gas Constant. The `Maxwell relations `__ are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are:
+
+.. math::
+ \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v}
+
+ \hat{s}_k = \hat{s}^\circ_k(T) - \overline{R}\ln\left(\frac{pX_k}{p^\circ}\right)
+
+where :math:`X_k` is the mole fraction of species :math:`k`, and where :math:`p^\circ` is the reference pressure at which the properties :math:`\hat{h}_k^\circ(T)` and :math:`\hat{s}_k^\circ(T)` are known.
+
+Please click either of the cards below for details on the species and phase models available in Cantera:
+
+.. container:: container
+ :tagname: section
+
+ .. container:: card-deck
+
+ .. container:: card
+
+ .. container::
+ :tagname: a
+ :attributes: href=species-thermo.html
+ title=Species
+
+ .. container:: card-header section-card
+ :tagname: div
+
+ Species
+
+ .. container:: card-body
+
+ .. container:: card-text
+
+ The models and equations that Cantera uses to calculate species thermodynamic properties, such as the NASA 7-parameter polynomial form.
+
+ .. container:: card
+
+ .. container::
+ :tagname: a
+ :attributes: href=phase-thermo.html
+ title=Phases
+
+ .. container:: card-header section-card
+ :tagname: div
+
+ Phases
+
+ .. container:: card-body
+
+ .. container:: card-text
+
+ The theory behind some of Cantera's phase models, such as the Ideal Gas Law.
+
+
\ No newline at end of file
diff --git a/pages/science/transport.rst b/pages/science/transport.rst
new file mode 100644
index 000000000..3571e7fdb
--- /dev/null
+++ b/pages/science/transport.rst
@@ -0,0 +1,49 @@
+.. slug: transport
+.. has_math: true
+.. title: Calculating phase and species transport properties and rates
+
+.. jumbotron::
+
+ .. raw:: html
+
+ Calculating transport properties and rates in Cantera
+
+ .. class:: lead
+
+ Here, we describe how Cantera uses species and phase information to calculate transport properties and rates.
+
+ Similar to Cantera's approach to `thermodynamic properties `__, transport property calculations in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another.
+
+ - The user must specify a transport model for each species and provide inputs that inform how species properties are calculated. For example, the user provides inputs that allow Cantera to calculate species collision integrals based on species-specific Lennard-Jones parameters.
+ - The user also selects a phase model. This model describes how the species interact with one another to determine phase-averaged properties (such viscosity or thermal conductivity) and species specific properties (such as diffusion coefficients), for a given thermodynamic state.
+
+Species Transport Coefficients
+------------------------------
+
+Transport property models in general require coefficients that express the
+effect of each species on the transport properties of the phase. Currently,
+ideal-gas transport property models are implemented.
+
+Transport properties can be defined in the CTI format using the
+:cti:class:`gas_transport` entry, or in the YAML format using the
+:ref:`transport ` field of a ``species`` entry.
+
+.. _sec-phase-transport-models:
+
+Phase Transport Models
+----------------------
+
+Two transport models are available for use with ideal gas mixtures. The first is a multicomponent
+transport model that is based on the model described by Dixon-Lewis [#dl68]_ (see also Kee et al.
+[#Kee2017]_). The second is a model that uses the mixture-averaged rule.
+
+
+
+.. rubric:: References
+
+.. [#dl68] G. Dixon-Lewis. Flame structure and flame reaction kinetics,
+ II: Transport phenomena in multicomponent systems. *Proc. Roy. Soc. A*,
+ 307:111--135, 1968.
+
+.. [#Kee2017] R. J. Kee, M. E. Coltrin, P. Glarborg, and H. Zhu. *Chemically Reacting Flow:
+ Theory and Practice*. 2nd Ed. John Wiley and Sons, 2017.
\ No newline at end of file
diff --git a/pages/tutorials/cti/phases.rst b/pages/tutorials/cti/phases.rst
index f922ea648..79814797e 100644
--- a/pages/tutorials/cti/phases.rst
+++ b/pages/tutorials/cti/phases.rst
@@ -215,7 +215,7 @@ The Transport Model
A *transport model* is a set of equations used to compute transport
properties. For :cti:class:`ideal_gas` phases, multiple transport models are
available; the one desired can be selected by assigning a string to this
-field. See :ref:`Transport Models ` for more details.
+field. See :ref:`Transport Models ` for more details.
The Initial State
^^^^^^^^^^^^^^^^^
diff --git a/pages/tutorials/yaml/phases.rst b/pages/tutorials/yaml/phases.rst
index 8a545d1aa..045d89f67 100644
--- a/pages/tutorials/yaml/phases.rst
+++ b/pages/tutorials/yaml/phases.rst
@@ -5,7 +5,7 @@
.. raw:: html
- Phases and their Interfaces
+ Phases and their Interfaces in YAML
.. class:: lead
diff --git a/pages/tutorials/yaml/species.rst b/pages/tutorials/yaml/species.rst
index 0abed7313..23c57f7ad 100644
--- a/pages/tutorials/yaml/species.rst
+++ b/pages/tutorials/yaml/species.rst
@@ -6,7 +6,7 @@
.. raw:: html
- Elements and Species
+ Elements and Species in YAML
.. class:: lead