## 3 Results and Discussion  
### Effect of Flow Rate and Intel Concentration  
In this section, only the surface step reaction is considered, i.e., the mass transfer is neglected, in order to describe the photocatalytic reaction in the gas-solid phase.  
Table 1 presents the semi-empirical formulas necessary to find the external mass transfer coefficient for tangential flow reactors.  
Table 2 illustrates the Reynolds number, diffusivity, and mass transfer coefficients for two components at various volumetric flow rates. The values of the coefficients \(k_{f}\) resulting from these correlations are used to determine an equivalent diffusion. The numerical solution of the following equation can be used to evaluate the parameters \(k\) and \(K\):  
\[C_{in}-C_{out}=\frac{L\cdot k_{m}\cdot a_{v}}{2\cdot u}\cdot[C_{in}+\frac{1}{K }+\frac{k}{k_{m}\cdot a_{v}}-\sqrt{(-C_{in}+\frac{1}{K}+\frac{k}{k_{m}\cdot a _{v}})^{2}+\frac{4C_{in}}{K}}\ ] \tag{11}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Reactors** & **Formulas** & **Conditions** \\ \hline \multirow{2}{*}{Tangential flow reactor} & \(Sh=1.029\cdot R^{0.55}\times Sc^{0.33}\cdot(\frac{L}{d_{eq}})^{-0.472}\) & Si \(Re\ \leq 2500\) \\  & \(Sh=0.095\cdot R^{0.85}\cdot Sc^{0.33}\cdot(\frac{L}{d_{eq}})^{-0.472}\) & Si \(Re\ \geq 2500\) \\ \hline \hline \end{tabular} \(L\): length; \(d_{eq}\): equivalent diameter of the reactor.  
\end{table}
Table 1: The semi-empirical formulas for the estimation of \(k\)f.  
Figure 2: **(a)** The schematic of the reactor setup and (b) a cross section of the concentric cylindrical Pyrex glass tube reactor.  
The degradation rates of the two VOCs were identical. Whatever the flow rates, the DR was improved with an increasing concentration. However, CB degraded faster than CN under similar experimental conditions, in terms of the concentration and flow rate. Indeed, for a concentration of 1.328 mM\(\cdot\)m\({}^{-3}\), the DR of CB varied from 0.70 to 2.84 \(\mu\)M\(\cdot\)m\({}^{2}\cdot\)s\({}^{-1}\) when the flow rate increased from 1 to 9 m\({}^{3}\cdot\)h\({}^{-1}\), while the DR of CN varied from 0.60 to 2.20 \(\mu\)M\(\cdot\)m\({}^{2}\cdot\)s\({}^{-1}\) for the same flow rate interval. This difference in the DR may be related to the hydrophobicity and stability of the molecules (two aromatic rings) of CN on the surface of TiO\({}_{2}\). This result is in agreement with a study [33] dealing with six aromatic compounds: benzene, toluene, ethylbenzene, and m-, o-, and p-xylenes. In their investigation, the authors showed that these compounds do not have the same photocatalytic reactivity. Benzene was the most challenging compound to degrade due to its extreme stability and the equivalence of its six carbons.  
The simulation results shown in Figure 3a,b based on the L-H model are summarized in Table 3.  
From Table 3, it is interesting to note that the kinetic constants (k) of the L-H model for CN are very different compared to those for CB. However, the two pollutants' adsorption constants (K) were similar. This trend can be explained by the hydrophobicity and stability of the pollutants.  
The degradation rates improved with an increasing flow rate and concentration. Indeed, as the flow rate and concentration increased, the species' movement to the catalyst's interface was enhanced. This analysis is in accordance with the work of [PERSON] and his group [34], who stated that the degradation rate improves with an increasing flow rate and VOC concentration. These results also agree with litterature [27; 28; 29]. [PERSON] and his co-workers [35] argued that the increase in the degradation rate is related to the availability of the active species, i.e., if the formation of the first radical species is facilitated; in this case, the degradation of the adsorbed pollutants starts faster, and the residence time could be shorter.