## 3 Results and Discussion
### Response Surface Methodology Results and Analysis  
(1) Orthogonal Experimental Design and Results  
The orthogonal experimental design was conducted based on the single-factor experiment results, taking the gas-liquid ratio (A), generator running time (B), and inlet water temperature (C) as independent variables, and the CO\({}_{2}\) content (R) in the MNB water as the response value. The results are listed in Table S1.  
(2) Response Surface Model Fitting and Analysis  
This research compared the fitting results of the first-order model and second-order model. Table S2 lists the ANOVA results of these two types of models. We can observe that the second-order model fits the experimental data better than the first-order model. In addition, a regression model  
The \(R^{2}\) value was 0.9973, which is close to 1, indicating that the stage two model had an excellent fitting effect. The signal-to-noise ratio of 65.718 was much greater than 4. For the same reason, the reliability and accuracy of the model were high. A comparison between the model's predicted values and the actual values is shown in Figure 5.  
The results showed that the values predicted by the model were very close to the actual measured values and contained only minor errors, which further confirmed that the model had a high degree of fit and was the ideal model.  
(3) Response Surface and Contour Diagram Analysis  
The three-dimensional response surface diagram and the corresponding contour diagram were established to better understand the impact of the influencing factor variables and their interactions with each other. The results are shown in Figures 6-8.  
\begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value** \\ \hline Std. Dev. & 0.090 \\ Mean & 6.31 \\ C.V.\% & 1.42 \\ PRESS & 0.80 \\ \(R^{2}\) & 0.9973 \\ Adj \(R^{2}\) & 0.9938 \\ Pred \(R^{2}\) & 0.9608 \\ Adeq Precision & 65.718 \\ \hline \end{tabular}
\end{table}
Table 4: Statistical analysis results for the regression model errors.  
Figure 5: Comparison diagram of the predicted values and the actual values.  
Figure 6: The interaction between the gas–liquid ratio and the generator running time: (**a**) response surface and (**b**) contour lines.  
Figure 7: The interaction between the gas–liquid ratio and the inlet water temperature: (**a**) response surface and (**b**) contour lines.  
The interaction between the gas-liquid ratio and the generator cycle running time had a more apparent impact on the CO\({}_{2}\) content in the MNB water than the other two factors. The gas-liquid ratio had the most significant influence on the CO\({}_{2}\) content. The interaction between the gas-liquid ratio and the water temperature had a weaker impact on the CO\({}_{2}\) content. Figure 7 shows that the effect of the water temperature was smaller than that of the gas-liquid ratio, which was consistent with the previous single-factor experimental results. Figure 8 illustrates the effect of the interaction between the water temperature and the generator cycle running time. Compared with the interaction between the water temperature and the gas-liquid  
ranges of 70-80 nm and 700-900 nm. The size of the bubbles tended to decrease with an increase in the generator circulation time, which was consistent with the conclusion of [PERSON] et al. [21]. According to the understanding of the generation mechanism for MNPs, it can be concluded that the size of the generated MNPs was determined by a range of factors, including the physicochemical qualities of the gas, the pressure at which the MNPs were formed, and the duration of the reaction.  
The particle size distribution and concentration information of the CO2 MNPs under the optimized conditions are listed in Table S4 and shown in Figure S1. The average particle size of the bubbles was 134.9 nm, and the bubble diameters corresponding to cumulative distributions of 10%, 50%, and 90% were 33.8 nm, 105.6 nm, and 255.5 nm, respectively. The concentration was 6.8 \(\times\) 10\({}^{6}\) pieces/mL.