more in models.md

Author: xavierr

docs/src/manuals/user_guide/models.md

@@ -1,7 +1,9 @@
 # PXD model
 
-In the following, all the symbols that are not introduced directly in the text are collected in the table at the end of
-the page
+In the following, all the symbols that are not introduced directly in the text are collected in the table at the
+[end](@ref "Symbol list") of the page
+
+## Electrolyte
 
 The mass and charge conservation in the electrolyte are given by
 ```math
@@ -19,6 +21,8 @@ where the fluxes are given by
 ```
 The volumetric reaction rate is given as ``R_\text{elyte} = -\sum_\text{elde} \gamma_\text{elde} R_\text{elde}`` where ``\gamma_{\text{elde}}`` is the volumetric surface area and the expression for ``R_\text{elde}`` is given below. Note that the reaction rates depends on the spatial variable ``x``. For the chemical potential, we use ``\mu = 2RT\log(c_\text{elyte})``. The effective quantities are computed from the intrinsic properties and the volume fraction using a Bruggemann coefficient, denoted ``b``, which yields ``\kappa_{\text{elyte},\text{eff}} = \varepsilon_\text{elyte}^{b}\kappa_{\text{elyte}}`` and ``D_{\text{elyte},\text{eff}} = \varepsilon_\text{elyte}^{b}D_{\text{elyte}}``. For the electrolyte, we have a spatially dependent Bruggeman coefficient.
 
+## Electrode
+
 In the electrode, the charge conservation equation is given by
 ```math
   -\nabla\cdot (\kappa_{\text{elde}, \text{eff}} \nabla \phi_\text{elde}) = F\gamma_\text{elde} R_{\text{elde}}.
@@ -32,7 +36,9 @@ with boundary condition
 - 4\pi r_p^2 D_\text{elde} \frac{\partial c_\text{elde}}{\partial r}(t, x, r_p) = \frac{\gamma_\text{elde} R_\text{elde}}{\varepsilon_\text{elde}}\frac{4\pi r_p^3}{3}.
 ```
 
-Reaction kinetics. The reaction rate ``R_\text{elde}`` at each electrode is given
+## Reaction kinetics
+
+The reaction rate ``R_\text{elde}`` at each electrode is given
 ```math
 R_\text{elde} = j_{\text{elde}}(c_\text{elde}, c_\text{elyte}, T)(e^{\alpha F\frac{\eta_\text{elde}}{RT}} - e^{-(1 - \alpha) F\frac{\eta_\text{elde}}{RT}} ) .
 ```
@@ -47,6 +53,8 @@ and the temperature.  The exchange current density is given by
   j_\text{elde} = k_{\text{elde},0} e^{-\frac{E_a}{R}(1/T - 1/T_{\text{ref}})}\left(c_\text{elyte}(c_{\text{elde},\max} - c_\text{elde})c_\text{elde}\right)^{\frac12}.
 ```
 
+## Symbol list
+
 | Symbol                                      | Definition                                      |
 |---------------------------------------------|-------------------------------------------------|
 | ``c_\text{elyte}``, ``c_\text{elde}``       | Lithium concentration in electrolyte, electrode |