3.2.5. Effect of Ultrasonic Power on the Mean Droplet Size of LEO-NEs

To study the effects of ultrasonic power on the mean droplet size of LEO-NEs, the preparation process was carried out with different ultrasonic powers ranging from 100 to 900 W. As shown in Figure 1e, the value of droplet size decreased with the increase in ultrasonic power from 100 to 700 W. However, the particle size increased instead when the ultrasonic power was increased from 700 to 900 W. Excessive ultrasonic power may induce a rise in the number of bubbles in solvents during cavitation, lowering the efficiency of the ultrasound energy delivered into the medium [24]. As a result, the ultrasonic power of 700 W was chosen for further experiments.

#### *3.3. Response Surface Optimization of LEO-NEs*

The preparation process was further optimized using BBD experiments to obtain the best experimental parameters. The BBD of the response surface was used to optimize the formulation and preparation of LEO-NEs. The following regression equation model was obtained by regression analysis:


As shown in Table 4, the generation of a model with no significant lack of fit implied it suitability. The *R2* > 90% indicated that the model could accurately reflect the change in the response value when the fitness was high. The coefficient of variance (CV), which is the ratio of the estimated standard error to the mean of the observed responses, is related to the model reproducibility. Our model had a CV of 9.97% (<10%), which is usually considered to be sufficiently reproducible. The ratio of adequate precision reflects the ratio of response to the deviation, and its value was 11.840 (>4), indicating an adequate signal.

An analysis of variance of the regression coefficient revealed that C was extremely significantly different (*p* < 0.01), while A significantly differed in its linear effect (*p* < 0.05), remaining factors indicated a non-significant difference. The main effect relationship of each factor could be ranked as ultrasonic time > HLB value > ultrasonic power > surfactant content. Among interaction effects, B2 had extremely significant differences (*p* < 0.01), while BC and C<sup>2</sup> significantly differed (*p* < 0.05). The remaining effects were not significant (*p* > 0.1). The experimental values of mean droplet size of nanoemulsions are presented in Table 5.


**Table 4.** ANOVA of RSM outcome <sup>α</sup>.

<sup>α</sup> *R2* = 0.97; adj. *R<sup>2</sup>* = 0.85; C.V. (%) = 9.97; adequate precision = 11.84.

**Table 5.** Experimental values of mean droplet size of nanoemulsions obtained from BBD experimental design.


Finally, the response surface was plotted using Design-expert 13. The effect of the two-factor interaction on the size of the mean droplet is intuitively shown in Figure 2. The response surface slope was steeper in Figure 2d, indicating that the interplay of surfactant content and ultrasound time had a bigger impact on LEO-NE particle size. The gradient of the response surface was moderate, as shown in Figure 2c, showing that the interaction of HLB value and ultrasonic power had less of an effect on the droplet size.

#### *3.4. Physicochemical Properties and Stability of LEO-NEs*

The above regression model was used to generate the optimum process parameters and validation results. When the HLB value (A) was 13, surfactant content (B) was 0.157 g/mL, ultrasonic time (C) was 23.50 min, and ultrasonic power (D) was 761.65 W, the predicted minimum mean droplet size was 66.82 nm. The actual mean particle diameter was 64.60 nm, and the PDI was 0.255. The

particle size distribution of NEO-NEs is shown in Figure 3a. Then, the morphological changes and the changes in particle size of NEs during the storage period were observed, and the difference in antioxidant activity between emulsion and essential oil was compared.

**Figure 2.** Response surface plot showing the significant (*p* < 0.05) interaction effect for mean droplet size as a function of (**a**) HLB value of STmix and STmix content, (**b**) HLB value of STmix and ultrasonic time, (**c**) HLB value of STmix and ultrasonic power, (**d**) STmix content and ultrasonic time, (**e**) STmix content and ultrasonic power, and (**f**) ultrasonic time and ultrasonic power.
