## 3 Results and Discussion  
### Extraction Yield  
One of the main discriminants justifying usage of alternative extraction methods, like UAE, is oil yield improvement. The goal is to reach maximum possible yield with lowest possible energy and time consumption in order to make the process profitable. Multiple studies proved UAE was an effective method in terms of oil yield improvement [20; 21; 22; 23].  
Results of extraction yield obtained in 30 experimental runs for each oil were used to fit the mathematical models and their equations which reflected changes in response depending on extraction time and ultrasound amplitude. The graphical expressions of three-dimensional surface plots and contour graphs of variable interactions are shown in Figure 1. The suggested mathematical models were verified by the coefficient of determination (R\({}^{2}\)) and in the ANOVA tests (Table 2). Also, adequate Equations (9)-(11) outlining existing relationships between variables and responses were determined. For BB and CH seed oils, the yield quadratic model was significant (\(p<0.05\)), with a non-significant lack of fit value (\(p>0.05\)). The interactions between variables were less essential in case of RB seed oil extraction yield, as the two-factorial model was fit with significance (\(p<0.05\)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Oil** & **Model** & **R\({}^{2}\)** & **CV (\%)** & \begin{tabular}{c} **Model** \\ _p_**-Value** \\ \end{tabular} & \
\begin{tabular}{c} **Model** \\ **F-Value** \\ \end{tabular} &
\begin{tabular}{c} **Lack of Fit** \\ _p_**-Value** \\ \end{tabular} \\ \hline BB & Quadratic & 0.9676 & 3.48 & 0.0044 & 23.97 & 0.4097 \\ CH & Quadratic & 0.9030 & 2.47 & 0.0373 & 7.44 & 0.5320 \\ RB & 2 FI & 0.7258 & 7.42 & 0.0402 & 5.29 & 0.1294 \\ \hline \hline \end{tabular} CV—coefficient of variation.  
\end{table}
Table 2: Model fitting of oil extraction yields.  
Figure 1: Three-diemnsional and contour graphs showing oil yield dependence from extraction time and ultrasound amplitude.  
Cavitation affects transport and extraction rates, which are impacted by acoustic power, frequency, and ultrasonic intensity [6]. Thus, ultrasound amplitude level significantly influenced the oil yield. However, the results differed slightly depending on seeds used in the extraction procedure. Generally, mild extraction conditions, considering ultrasound amplitude, were the most suitable in terms of oil yield. In previous studies, for cranberry seed oil [10] and black and redcurrant seed oils [11], the most favorable were the highest ultrasound amplitude values.  
From surface plots, it can be observed that increasing the time up to around 10 min for BB and CH and to around 15 min for RB seeds leads to the highest oil yield results. The effect of time connects with prolonged sonoporation, erosion, and detexturation of the matrix, which promotes mass transfer from cells to the solvent [6]. However, prolonged time may result in the more local rapid events presence in the ultrasonic field. That may lead to solvent evaporation which may have a negative impact on the yield, as it was described by [PERSON] and [PERSON] [24].  
\[Yield_{BB}=6.18+0.05\cdot X_{1}+0.48\cdot X_{2}+0.003\cdot X_{1}X_{2}-0.001\cdot{ X_{1}}^{2}-0.04\cdot{X_{2}}^{2} \tag{9}\]  
\[Yield_{CH}=3.18+0.04\cdot X_{1}+0.34\cdot X_{2}-0.001\cdot X_{1}X_{2}-0.0003 \cdot{X_{1}}^{2}-0.02\cdot{X_{2}}^{2} \tag{10}\]  
\[Yield_{RB}=2.28+0.06\cdot X_{1}+0.38\cdot X_{2}-0.005\cdot X_{1}X_{2} \tag{11}\]