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8 changes: 5 additions & 3 deletions _docs_v7/Thermochemical-Nonequilibrium.md
Original file line number Diff line number Diff line change
Expand Up @@ -46,13 +46,15 @@ $$
0 & \text{for monatomic species and electrons,}
\end{cases}
$$
\
where $$\xi$$ is an integer specifying the number of axes of rotation,
$$
e^{vib}_s =\begin{cases}
\frac{R}{M_s} \frac{\theta^{vib}_s}{exp\left( \theta^{vib}_s / T^{ve}\right) - 1} & \text{for polyatomic species,}\\
0 & \text{for monatomic species and electrons,}
\end{cases}
$$
\
where $$\theta^{vib}_s$$ is the characteristic vibrational temperature of the species, and


Expand All @@ -73,7 +75,7 @@ where $$\theta^{el}_s$$ is the characteristic electronic temperature of the spec
| --- | --- |
| `NEMO_EULER`, `NEMO_NAVIER_STOKES` | 7.0.0 |

The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $r$, and can be expressed as
The source terms in the species conservation equations are the volumetric mass production rates which are governed by the forward and backward reaction rates, $$R^f$$ and $$R^b$$, for a given reaction $$r$$, and can be expressed as
$$
\dot{w}_s = M_s \sum_r (\beta_{s,r} - \alpha_{s,r})(R_{r}^{f} - R_{r}^{b}).
$$
Expand All @@ -98,7 +100,7 @@ $$
T_r = (T)^{a_r}(T^{ve})^{b_r}.
$$

The value of he equilibrium constant $K_{eq}$ is expressed as
The value of he equilibrium constant $$K_{eq}$$ is expressed as

$$
K_{eq} = \exp( A_0 \left(\frac{T^c}{10,000}\right) + A_1 + A_2 \log \left( \frac{10,000}{T^c} \right) + A_3 \left( \frac{10,000}{T^c} \right) + A_4 \left( \frac{10,000}{T^c} \right)^2 ),
Expand Down Expand Up @@ -146,7 +148,7 @@ where $$\sigma_s$$ is the effective collision~cross-section.
| `NEMO_NAVIER_STOKES` | 7.0.0 |


Mass, momentum, and energy transport in fluids are all governed by molecular collisions, and expressions for these transport properties can be derived from the kinetic theory. The mass diffusion fluxes, $\mathbf{J}_s$, are computed using Fick's Law of Diffusion:
Mass, momentum, and energy transport in fluids are all governed by molecular collisions, and expressions for these transport properties can be derived from the kinetic theory. The mass diffusion fluxes, $$\mathbf{J}_s$$, are computed using Fick's Law of Diffusion:
$$
\mathbf{J}_s = - \rho D_s \nabla(Y_s) + Y_s \sum_k \rho D_k \nabla(Y_k)
$$
Expand Down