(general)=
# General Notes

The main conventions and assumptions used in the documentation are listed below.

1. $f_v$ and $\varphi$ denote the volume of particles ($V_{p}$) normalized by the volume of gas ($V_{g}$) and reactor ($V_{r}=V_{g}+V_{p}$), respectively.

```{math}
:label: eq-fv
\begin{aligned}
    f_v &= \frac{V_{p}}{V_{g}}, \\
    \varphi &= \frac{V_{p}}{V_{g} + V_{p}},\\
\end{aligned}
```


2. ${\dot{x}_k}$ denotes the rate production/consumption of $k^{th}$ gaseous species (i.e., gas scrubbing) due to particle inception, surface growth and oxidation. It is positive when the species is released to the gas mixture.

3. 	The word *particle* refers to carbonacoues nanoparticles both spheres and agglomerates.

4. Each agglomerate consists of monodisperse spherical primary particles, which are in point contact. So, Omnisoot does not consider formation of necking (or sintering) in agglomerates by surface growth.

5. The density of carbonaceous particles is assumed constant at the value of $\rho_{p}=1800\;\mathrm{kg/m^3}$, but in reality varies with particle maturity due to changes in internal nanostruture that are often linked to the elemental C/H ratio of soot particles {cite:p}`michelsen2021effects`. Here, the considered value represents an average between density of mature soot with high C/H ratios ($\mathrm{\rho_{p}=2000\;kg/m^3}$) and that of nascent soot with low C/H ratios ($\rho_{p}=\mathrm{1600\;kg/m^3}$) {cite:p}`jensen2007measurement, michelsen2021effects`.

6. The incipient particles are 2 nm in diameter, so the model does not allow particles with a primary particle diameter smaller than 2 nm. The number of carbon atoms in the incipient particle, $n_{c,min}$, is calculated from the mass of a sphere with a diameter of $d_{p,min}=2$~nm assuming pure carbon content, which results in:

```{math}
:label: eqn:nc_min
\begin{equation}
    n_{c,min} =\frac{\pi}{6}\rho_{p}d^3_{p,min}\frac{1}{W_{carbon}}\approx378.
\end{equation}
```

7. The specific heat, internal energy and enthalpy of carbonaceous particles are approximated by those of pure graphite, and are employed to close the energy balance in the system {cite:p}`mcbride1993coefficients`.

8. Particles and gas are in thermal equilibrium during particle formation processes, and there is no temperature gradient within each agglomerate.

9. $\psi$ denotes a *particle tracked variable* that represents a mean property of particles in each section tracked in Omnisoot by solving transport equations for the total concentration of agglomerates, $N_\mathrm{agg}$ and primary particles, $N_\mathrm{pri}$, and the total carbon, $C_\mathrm{tot}$ and hydrogen content, $H_\mathrm{tot}$ of soot. $S_{\psi}$ is the source term of the soot variable, $\psi$, which appears in particle transport equations.

10. The single superscript *i* denotes the section number of a soot variable or a derived property. For example, $d^i_p$ represents the primary particle diameter of section *i*. The double superscript *ij* indicates a property related to two sections; for example, $\beta^{ij}$ denotes the collision frequency between sections *i and *j*. In the case of the monodisperse model, the section number can be omitted because it is equivalent to the sectional model with only one section.

11. The computation of morphological parameters is done similarly in both particle dynamics models, but they are explained separately in Section ****.

12. *Precursors* often refer to the PAHs equal and larger than naphthalene used for inception and PAH adsorption. However, users can set any species available in the reaction mechanism as precursors.