## 3 Results and Discussion
### Foaming Property  
The FC and FS of aqueous solutions of WRP are shown in Figure 4 and Table 2. The FC of the WRP solution was in the range of 81.5 \(\pm\) 0.7% to 87.25 \(\pm\) 0.7%. Statistical analysis  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **MAE** & \multicolumn{4}{c}{**MAUPE**} \\  & **0 W** & **150 W–10 min** & **150 W–20 min** & **300 W–10 min** & **300 W-20 min** \\ \hline
**Surface tension** & 45.75 \(\pm\) 0.21 b  & 45.5 \(\pm\) 0.14 b  & 44.6 \(\pm\) 0.28 a  & 44.4 \(\pm\) 0.28 a  & 44.2 \(\pm\) 0.20 a  \\
**WHC** & 12.43 \(\pm\) 0.19 b  & 11.95 \(\pm\) 0.32 ab  & 11.94 \(\pm\) 0.5 ab  & 11.97 \(\pm\) 0.27 ab  & 11.72 \(\pm\) 0.30 a  \\
**FC** & 81.5 \(\pm\) 0.7 a  & 83.9 \(\pm\) 0.5 ab  & 86.3 \(\pm\) 0.8 bc  & 86.5 \(\pm\) 0.8 bc  & 87.25 \(\pm\) 0.7 c  \\
**FS** & 30.0 \(\pm\) 0.8 a  & 30.5 \(\pm\) 0.7 ab  & 31.2 \(\pm\) 1.2 b  & 31.8 \(\pm\) 0.7 b  & 31.5 \(\pm\) 0.9 b  \\ \hline \end{tabular}
\end{table}
Table 2: Water holding capacity, foam properties and surface tension of 1% (\(w/v\)) pectin solutions at 25 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **MAE** & \multicolumn{4}{c}{**MAUPE**} \\  & & **150 W–10 min** & **150 W–20 min** & **300 W–10 min** & **300 W–20 min** \\ \hline a & 82.56 & 85.12 & 86.43 & 86.5 & 86.98 \\ k & 37.04 & 37.24 & 39.52 & 37.91 & 39.47 \\ t\({}_{1/2}\) & 2.78 & 3.69 & 2.49 & 3.73 & 2.64 \\ R\({}^{2}\) & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 \\ RMSE & 1.135 & 0.68 & 0.86 & 0.52 & 1.06 \\ \hline \end{tabular}
\end{table}
Table 3: Kinetics parameters for the foaming characteristics of WRP.  
revealed that the power and duration of the extraction pretreatment could significantly affect the FC. The pectin obtained using MAUPE (ultrasonic power 300 W) showed a significant difference in the FC and FS from the MAE sample. These results for the FC of WRP solutions agreed with the surface tension measurement and protein data. The FS of the samples was in the range of 30.5 \(\pm\) 0.7% to 31.8 \(\pm\) 0.7%.  
In the foam formation process, the foaming agent adsorbs at the air-water interface [11]. Then, the foam was stabilized by inter-molecular interactions of the foaming agent to create a cohesive viscoelastic film [42]. The branching of the RG-I domains in some pectin molecules can provide a steric stabilization of some dispersions [43]. The molecular weight reduction probably leads to a faster adsorption of pectin molecules to the interface of dispersion. It is also possible that hydrophobic-hydrophilic groups, such as protein groups, were more accessible by pectin depolymerization [41]. Therefore, according to the molecular weight results (Section 3.7) and increasing of the sample protein content, ultrasonic pretreatment probably affects the FC. [PERSON] et al. also reported an increase in the foaming capacity due to a reduction in particle size of apple pectin after plasma treatment [44].  
The results showed that the FS of pectin from MAUPE at 300 W for 20 min (31.8 \(\pm\) 0.7) was higher than that of pectin from MAE (30.5 \(\pm\) 0.7). No significant difference was observed among the samples obtained from MAUPE. Figure 4 shows that the foam instability rate is very fast in the early stages of storage and slows down with increasing storage time. The results of the kinetic evaluation (Table 3) revealed that the empirical model fit the foam properties properly, by evaluating the highest \(R^{2}\) and the least RMSE values. A decrease in the kinetics rate (\(k\)) indicates a decrease in the foam destruction rate. Therefore, the prolonged pretreatment had the greatest effect on the half-time and  
Figure 4: Foam ratio (%). Samples obtained from MAUPE were shown using pretreatment power and time.  
the foam destruction rate. The half-time of the foam system using MAUPE ranged from 2.4 to 3.93 min. An increase in \(k\) and a decrease in t\(\frac{1}{2}\) showed a decrease in viscosity after pretreatment.