## 2 Fluid Model, Plasma Chemistry, and Reactor Configuration
### Fluid Model Formulae
#### 2.1.2 Heavy Species Equation  
Heavy species are supposed to comprise a reacting flow that consists of k = 1, 2, \(\ldots\), Q species, except for the electron. The mass transport equations of these heavy species are summarized in Equation (6). \[\rho\frac{\partial w_{k}}{\partial t}=\
abla\cdot\mathbf{j}_{k}+R_{k}. \tag{6}\]  
Herein, \(\rho\) is the total mass density of heavy species and \(w_{k}\) is the mass fraction of species \(k\). \(\mathbf{j}_{k}\) is the vectoral diffusive and drift flux of species \(k\) and expressed in Equation (7). \[ \begin{array}{l}\mathbf{j}_{k}=\rho w_{k}\mathbf{V}_{k},\\ \mathbf{V}_{k}=D_{k,m}\
abla\ln(w_{k})-z_{k}\mu_{m}\mathbf{E}.\end{array}  \tag{7}\]  
Herein, \(\mathbf{V}_{k}\) is the vectoral velocity of species \(k\), \(z_{k}\) is elementary charge number that species \(k\) carries, \(\mu_{m}\) is the mobility, and \(\mathbf{E}\) is the electrostatic field vector, calculated from the [PERSON]'s equation (see the Section 2.1.4). It is noted that the multi-component mass diffusion is considered and \(D_{k,m}\) is the averaged diffusion coefficient of mixture, expressed in Equation (8). \[D_{k,m}=\frac{1-w_{k}}{\sum\limits_{j\
eq k}^{Q}x_{j}/D_{kj}}. \tag{8}\]  
Herein, \(x_{j}\) is the number fraction of species \(j\) and \(D_{k,j}\) is the Chapman-Enskog binary diffusion coefficient [22; 23]. The source term of Equation (6), \(R_{k}\), is expressed in Equation (9). \[R_{k}=M_{k}\sum\limits_{j=1}^{N}l_{k,j}r_{j}. \tag{9}\]  
Herein, \(M_{k}\) is the molecular weight, \(r_{j}\) is the rate of reaction j that creates or consumes species \(k\), \(N\) is the reaction number, and \(l_{k,j}\) is the particle number of species \(k\) created or consumed for each reaction \(j\). The reaction rate, \(r_{j}\), is expressed in Equation (10). \[r_{j}=k_{j}\prod\limits_{m=1}^{S}c_{m}{}^{v_{jm}}. \tag{10}\]  
Herein, \(k_{j}\) is the rate coefficient, also given in Sections 2.2 and 2.3 for the Ar/SF\({}_{6}\) and Ar/O\({}_{2}\) plasmas, respectively. \(S\) is the number of reactants and \(v_{jm}\) is the stoichiometric coefficient of reaction \(j\) with arbitrary reactant \(m\) and the target reactant species \(k\). \(c_{m}\) is the molar concentration of reactant \(m\). In sum, the heavy species equation of Equation (6) sequentially describes the inertia term, diffusion, drift, and chemical kinetics of heavy species. It is noted the inertia term considered herein is the inertia of mass, like the electron equation of Equation (1) (not the flux inertia) which we believe is one possible origin of self-coagulation happened in electronegative plasmas, i.e., the inertial effect of density quantity (see next the Section 4.3). In addition, only Q-2 equations are used since the mass fractions of feedstock gases of mixture, Ar and SF\({}_{6}\) (or Ar and O\({}_{2}\)), are governed by the mass constraint condition, \(\omega_{\text{Ar},\text{SF}_{6}}=1-\sum\limits_{k}^{Q-2}\omega_{k}\), and the gas ratio between them assigned. The total mass density of heavy species, \(\rho\), is obtained from the ideal gas law in Equation (11). \[\rho=\frac{P}{kT}\frac{M}{N_{A}}. \tag{11}\]  
Herein, \(k\) is the [PERSON]'s constant, \(T\) is gas temperature, equal to 300 K, \(P\) is the fixed gas pressure in a range of 10 mTorr to 90 mTorr as considered, and \(N_{A}\) is the Avogadro's constant. \(M\) is the mole averaged molecular weight, expressed in Equation (12). \[\frac{1}{M}=\sum_{k=1}^{Q}\frac{w_{k}}{M_{k}}. \tag{12}\]  
In general, the mean molecular weight of Equation (12), \(M\), is not a constant, since it is a function of the mass fractions, \(w_{k}\), and molecular weights of various species, \(M_{k}\). The mass fractions that are calculated in Equation (6) are spatially and temporally varied.