## 3 Results and Discussion
### Effect of Electrode Length on NO Oxidation
** & **Rate Coefficients (cm\({}^{3}\)/s or cm\({}^{6}\)/s)** & **References** \\ \hline \(e+N_{2}(X)\to e+N_{2}(X,v)\) & R1 & \(f(E/N)\) & [24] \\ \(e+N_{2}(X)\to e+N_{2}\big{(}A^{3}\sum_{u}^{+}\big{)}\) & R2 & \(f(E/N)\) & [25] \\ \(e+N_{2}(X)\to e+N+N\) & R3 & \(f(E/N)\) & [25] \\ \(e+O_{2}\to e+O+O\) & R4 & \(f(E/N)\) & [26] \\ \(e+O_{2}\to e+O+O(^{1}D)\) & R5 & \(f(E/N)\) & [26] \\ \(O+O_{2}+N_{2}\to O_{3}+N_{2}\) & R6 & \(k=6.2\times 10^{-34}\times\big{(}\frac{300}{1}\big{)}^{2}\) & [27] \\ \(O+O_{2}+O_{2}\to O_{3}+O_{2}\) & R7 & \(k=6.9\times 10^{-34}\times\big{(}\frac{300}{1}\big{)}^{1.25}\) & [27] \\ \(O_{3}+NO\to NO_{2}+O_{2}\) & R8 & \(k=1.4\times 10^{-12}\times\exp\big{(}-\frac{1310}{1}\big{)}\) & [28] \\ \(O+NO+M\to NO_{2}+M\) & R9 & \(k=1.03\times 10^{-30}\big{(}\frac{T}{968}\big{)}^{-2.87}\exp\big{(}\frac{780}{1} \big{)}\) & [28] \\ \(N_{2}(X,v\geq 13)+O\to NO+N\) & R10 & \(k=1\times 10^{-13}\) & [29] \\ \(N+O_{2}\to NO+O\) & R11 & \(k=1.1\times 10^{-14}\times T\times\exp\big{(}-\frac{3150}{1}\big{)}\) & [29] \\ \(N_{2}\big{(}A^{3}\sum_{u}^{+}\big{)}+O_{2}\to N_{2}+O+O\)Because the dissociation energy of N\({}_{2}\) (9.8 eV) is higher than that of O\({}_{2}\) (5.1 eV), the formation of O radicals is easier than that of N radicals in the process of plasma discharge [30]. O and O\({}_{3}\) are generated firstly in the DBD reactor, which promote the oxidation of NO to NO\({}_{2}\) via R4-R9 [26; 27; 28]. Therefore, the concentration of NO decreases, the concentration of NO\({}_{2}\) increases and the oxidation degree of NO\({}_{X}\) increases gradually with the increase of SED at the initial discharge stage. With the increase of SED, the E/N further increases, which promotes the dissociation of N\({}_{2}\) to generate N radicals via R3, especially when the E/N accesses 200 Td [16]. Under oxygen-enriched condition, the N radicals will react with O, O\({}_{2}\) and O\({}_{3}\) to generate NO via R11, R14 and R15 [29], which causes the increase of NO. To analyze the effect of E/N on the generation of radicals and excitation species in NTP process, BOLSIG+ were used to calculate the electron energy distribution function (EEDF) and mean electron energy under different E/N conditions. The electron Boltzmann equation (BE) in an ionized gas is [31]:  
\[\frac{\partial f}{\partial t}+v\cdot\
abla f-\frac{e}{m}E\cdot\
abla_{V}f=C[f] \tag{4}\]  
where \(f\) is the electron distribution in six-dimensional phase space, \(v\) are the velocity coordinates, \(e\) is the elementary charge, \(m\) is the electron mass, \(E\) is the electric field, \(\
abla_{V}\) is the velocity-gradient operator and \(C\) represents the rate of change in \(f\) due to collisions. The mean electron energy was given by:  
\[\overline{e}=\int_{0}^{\infty}\varepsilon^{3/2}f_{0}d\varepsilon \tag{5}\]  
where \(\overline{e}\) is the mean electron energy, \(f_{0}\) is isotropic part of EEDF. The rate coefficient related to electron collisions is defined as:  
\[k_{k}=\sqrt{\frac{2e}{m}}\int_{0}^{\infty}\varepsilon\sigma_{k}f_{0}d\varepsilon \tag{6}\]  
where \(\sigma_{k}\) is the cross section of collision process \(k\). The electron-molecule collision cross sections are derived from LXCat [24; 25; 26]. The efficiency for a particular electron collision process can be calculated by [32]:  
\[G\ value=100k/(v_{d}E/N) \tag{7}\]  
Figure 8: (**a**) The effect of SED on discharge voltage; and (**b**) the effect of SED on \(E/N\) in gas gap of DBD reactor (electrode length is 50 mm and \(V_{pp}\) means peak-to-peak voltage). where \(k\) is the rate coefficient of a particular electron collision process and \(v_{d}\) is the drift velocity of electron. The G value represents the number of reactions per 100 eV of input energy. The rate coefficient \(k\) represents the number of reactions in a unit volume per unit time. The quantity \(v_{d}E/N\) represents the amount of energy expended by the electrons in a unit volume per unit time.