**Table 7 here**
Higher levels of potency increase the emulsification of the reactants facilitating the hydrolysis reaction (Özbek and Ülgen, 2000; Wang et al., 2015), however, the enzymatic deactivation effect may also occur due to the thermal effect generate through the ultrasonic treatment, given that the reaction temperature increases during cavitation, besides of the shear and pressure forces that cause damage to the structure of the enzyme (Froment et al., 1998; Vercet et al., 2001). The effect of temperature in the enzymes activities is well know, in one example, Avelar et al. (Avelar et al., 2013) reported on the influence of temperature in enzymatic hydrolysis of canola oil employing oil-free castor seeds as a lipase source; the activity decreased with temperature increase after 50°C. Cavalcanti et al.(Cavalcanti et al., 2007), shown similar deactivation of oil-free castor seeds after 40°C. The effect of deactivation by the ultrasound power was notable after 5 minutes of reaction, and small or no further activity was detected after this time when the reaction was continued in a shaker; also it can be noted that the equilibrium yield for the oil-free seeds was lower, suggesting that the enzymes may have suffered a more significant deactivation in this reaction system.
Despite the fact that the lipase concentration is higher on oil-free seeds, another aspect that allows the use of significantly less amount of the catalyst mass, is the smaller granulometry of the oil-free seeds, which provides a higher superficial area favoring the aqueous-organic interfacial reaction (Pourzolfaghar et al., 2016). Besides, a more substantial amount of buffer solution was needed for both particle forms when the reaction was performed in ultrasound since the emulsion of the system is better, and the aqueous-organic interface increased.
Comparing the yield of reaction at an equivalent time, both systems exhibit similar behavior under optimal ultrasound conditions. The oil-free seeds, however, reached equilibrium at a lower yield compared with in natura seeds, which is resulted from the less stability and higher deactivation of oil-free seeds, since in previous experiments, it was demonstrated that after 30 days at 4°C the oil-free seeds had 9% of deactivation while no deactivation detected for the in natura seeds (Tavares et al., 2018a). The deactivation can be accelerated by the ultrasound power used in the reaction. However, notably, the reaction could be intensified with the use of ultrasound since the time of 4 hours for a yield of 86% (Tavares et al., 2018a) was decreased to 5 minutes of reaction with the in natura seeds. Other intensification process methods can be performed with microwaves. Nguyen et al. (Nguyen et al., 2020) reported a green approach to produce FFA from soybean oil involving autocatalytic hydrolysis employing microwave irradiation. For this process, however, a surfactant had to be added to the mixture to reach a satisfactory emulsion; furthermore, the reaction achieves equilibrium at 96.6% of conversion into FFA after four h at 195 °C. Therefore, the use of ultrasound for oil hydrolysis catalyzed by vegetal lipases features a considerable enhancement in intensification of an eco-friendly process.
The reports in the literature employing castor bean seeds as a source of lipase for triglyceride hydrolysis reactions use the seeds in the oil-free form. Coelho et al. (Coelho et al., 2013) used lipase from oil-free castor seeds (0.075–0.090 mm) to produce FFA by hydrolysis of vegetable oils (corn and sunflower). The maximum percentage of hydrolysis of corn oil (84.0%) and sunflower (76.4%) was reached in 60% w/w oil, 0.1 M acetate, pH 4.5, 33°C, and 5% m/m seed particles after 70 and 80 min of reaction. Performing the enzymatic hydrolysis of canola oil, Avelar et al., (Avelar et al., 2013), achieved complete hydrolysis of the oil at 37.5°C, buffer/oil ratio 22.1% after 2 hours, using castor seeds without oil (2.0% of mass ratio and particles smaller than 1 mm). Santos et al. (Santos et al., 2013) evaluate oil-free castor bean seeds (0.075–0.090 mm) and reported the complete hydrolysis of the soybean after 80 minutes at 44.1% w/w oil/buffer (100 mM sodium acetate pH 4.5), 37°C, 2.0% w/w lipase, and sodium acetate. The results obtained in the present study, 86% yield after 5 minutes, using in natura seeds, without process costs for seed preparation, show impressive enhancement in the processes that are so far described in the literature.
The oil average extracted in the oil-free catalyst preparation was 47.4 ± 1.3%, resulting in 21% of the initial seed mass after sifting. From the optimum conditions, it was taken that for 10 g of Crambe oil, 6.1 g of in natura seeds were used, while 1.8 g of oil-free was necessary, representing 8.6 g of seed. The higher performance of the in natura seeds can be explained by the presence of components in the lipase that contribute to its activity. Ory (1969) reported the existence of three elements in castor bean lipase, a solid fraction, called apoenzyme, a lipid cofactor, and an activator protein, and concluded that for maximal lipase activity, all the components are necessary. The use of in natura seeds, thus, reflects in more enzymatic activity and can be considered more advantageous for the oil hydrolysis. On the other hand, the use of oil-free seeds can benefit from the residues of the castor oil industry.

4. Conclusion

To improve the yield of the hydrolysis of Crambe oil using seeds of castor beans as the catalyst, the use of ultrasound in the reaction was evaluated using two forms of seeds, in natura and oil-free. The CCRD factorial design was employed to assess each form of the seed particles, and optimum conditions were found, reaching approximately 86% yield after 5 minutes of ultrasound reaction for in natura seed particles and 73% for the oil-free seeds. Mathematical modeling, based on a Ping Pong Bi Bi kinetic mechanism, was applied for the experimental kinetic data representation. From unrelated experiments, the FFA concentration values were predicted using the estimated kinetic constants, demonstrating the suitability of the model for process optimization and understanding of the mechanisms in the ultrasound-assisted enzymatic hydrolysis of oils employing vegetal lipases. The potential of the process of ultrasonic enzymatic hydrolysis of oil using castor bean seeds as a source of lipases is highlighted since high conversions were achieved in an impressive short time. The best yield was obtained with the use of in natura seeds, which do not undergo any preparation process resulting in a much lower cost than compared to the use of animal or microbial lipase enzymes that are usually commercialized.