## 3 Results and Discussion
### Comparison of Different Extraction Methods  
#### 3.4.1 Extraction Kinetics for Flavonoids  
It can be seen from Figure 6 that the yields of flavonoids are different at different extraction times. As can be shown from experimental data in Figure 6 that the total yield of flavonoids obtained by UAE, HRE and UHRE was significantly dependent on extraction time. The extraction of flavonoids could be finished by three successive steps: (i) a rapid increase in flavonoids yield, which was attributed to the penetration of extraction solvent into the cellular interior and the dissolution of most of the flavonoids into extraction solvent, combined with the destruction of cell walls; (ii) a slower increase in flavonoids yield, which may be due to the exhaustion of flavonoids contained in the plant materials, reducing the release of flavonoids into extraction solution; (iii) the yield of flavonoids did not significantly change, which may be due to distribution of flavonoids in plant materials, and, in the extraction solution, reached equilibrium.  
Compared with UAE and HRE, UHRE was found to reduce the time consumption. The time to reach extraction equilibrium was 25 min for UHRE, 30 min for UAE and 90 min for HRE, respectively. Moreover, when the extraction equilibrium is reached, UHRE had a higher total yield of flavonoids (0.901 mg/g) than UAE (0.719 mg/g) and HRE (0.733 mg/g). The difference in yields of flavonoids was statistically significant (\(p\) < 0.01). Higher extraction efficiency of flavonoids obtained in the UHRE process from Mairei Yew leaves might be attributed to the combined effect of the boiling solvent and  
Figure 6: The dynamic curves of total yield of flavonoids obtained using three different methods on extraction time. Total yield of flavonoids (mg/g) = QU yield + KA yield + GI yield + SC yield.  
ultrasound. The cavitation effect is decreased when the temperature is near the solvent's boiling point, thus causing a reduction in the desorption of target compounds from the plant matrix [24]. Therefore, using boiling 80% methanol as solvent, it is highly probably that the efficiency of ultrasound was dramatically reduced. However, compared with UAE and HRE, the increase in extraction yields of flavonoids obtained by UHRE can probably mainly be related to the shaking effect due to ultrasonic baths.  
The fitting mathematical model is a useful engineering tool for the optimization, simulation, design and control of processes and contributes to better use of energy, time and solvents. The phenomenological, pseudo-second order and power law model listed in Table 1 have modeled the solid-liquid extraction process for natural products from plant materials [42; 44; 46; 47; 44]. The extraction kinetics of flavonoids (mg/g) from Mairei Yew for HRE, UAE and UHRE were investigated according to three models listed in Table 1.  
The kinetic curves fitted by the models for yield of flavonoids obtained by three various methods are demonstrated in Figure 6. Figure 6 showed the kinetic curves fitted by the phenomenological models were in accordance with the experimental data, but the curves fitted by the pseudo-second order and power law model are not in accordance with the experimental data. The results of correlation coefficient (R\({}^{2}\)), standard error (SE) of estimation for the different model are presented in Table 4. Generally, phenomenological models demonstrate a good relationship with experimental data with higher R\({}^{2}\) and lowest SE. Those phenomenological models could be applied to describe the dynamic process of extraction for flavonoids.