## 3 Results and Discussion
### Bacterial Inactivation
#### 3.3.2 Inactivation of Bacteria in a Flow Reactor
Figure 10 shows a contour map illustrating the dependence of the inactivation efficiency on the initial number of bacteria and the contact time with 10 mM H\({}_{2}\)O\({}_{2}\). The map shows three areas of catalyst performance: the effective area, marked in dark blue, the transition area, marked in light blue, and the ineffective area, marked in orange. The  
Figure 8: Bacterial inactivation kinetics at different initial bacterial concentrations (expressed in CFU/L) in the presence of 10 mM hydrogen peroxide: (**a**) absolute survival (N) vs. contact time; (**b**) normalized survival (N/N\({}_{0}\)) as a function of time for low initial bacterial concentrations; (**c**) normalized survival (N/N\({}_{0}\)) as a function of time for high initial bacterial concentrations. effective area with a pronounced bactericidal effect corresponds to an initial bacterial load below 13,800 CFU/L and a contact time of over 7 min. The survival rate is below 25%, which is confirmed by the graphs in Figure 8c. The low concentrations of 1200-6900 CFU/L require only 2-4 min to achieve almost complete inactivation (Figures 8b and 10). Partial inactivation of bacteria is observed in the transition area (Figure 10). The typical initial bacterial load here is 13,800-25,000 CFU/L. To achieve a survival level below 30%, longer exposure (up to 10 min) is necessary. This indicates a time-dependent effect of H\({}_{2}\)O\({}_{2}\) at a medium microbial load. The ineffective area is observed at an initial bacterial load above 41,000 CFU/L (Figure 10). At such a high concentration of bacteria, H\({}_{2}\)O\({}_{2}\) is not able to completely inactivate them. A high survival rate (>30%) is observed even after a long contact time (28 min). The contour map in Figure 10 clearly shows the strong dependence of H\({}_{2}\)O\({}_{2}\) effectiveness on the initial concentration of bacteria and the contact time. Optimal conditions for disinfection are as follows: a low concentration of bacteria and a contact time longer than 5 min. At high initial bacterial loads (25,000-54,000 CFU/L), the disinfection effect of H\({}_{2}\)O\({}_{2}\) is rather limited. To enhance the disinfection effect, a higher concentration of H\({}_{2}\)O\({}_{2}\) or a more effective catalyst can be used. The modeling of bacterial survival under the influence of H\({}_{2}\)O\({}_{2}\) was performed taking into account two variables: contact time and initial bacterial concentration. The applied  
Figure 10: Contour map of bacterial survival depending on the initial number of bacteria and contact time. The thick black line indicates 50% survival. Figure 9: Schematic representation of bacterial survival and biofilm formation in a catalytic reactor with different initial bacterial loads. model is a second-order exponential decay integrated with a logarithmic dependence on the initial bacterial concentration:  
\[\text{N(t, N${}_{0}$)}=\text{a}\cdot\text{e}^{-\text{bt}}+\text{c}+\text{d}\cdot \text{ln(N${}_{0}$)} \tag{5}\]  
where N(t, N${}_{0}\)) is the predicted number of live bacteria (CFU/L) at contact time t (min) and an initial number of bacteria N${}_{0}\) (CFU/L); a, b, c, and d are model parameters determined by fitting the model equation to the experimental values. In the application of the numerical values of the model parameters, the equation is as follows:  
\[\text{N(t, N${}_{0}$)}=-\text{ 2.6 $\times$ 10^{7}$}\cdot\text{e}^{0.0000113 $+$ 2.6 $\times$ 10^{7}$}+\text{ 9833}\cdot\text{ln(N${}_{0}$)} \tag{6}\]  
This model describes a nonlinear decrease in bacterial survival over time with an increasing initial bacterial concentration (Figure 11a). The exponential component 2.6 \(\times\) 10^7-e0.0000113$+$ reflects the time-dependent dynamics of bacterial inactivation, especially in the early phase.