## 3 Results and Discussions
### Model Fit and Adequacy for the Stability of ACM Stabilized O/W-Type Nanoemulsion
Effects of Mixture Components on Stability as a Function of Sauter Mean Diameter of ACM Stabilized O/W-Type Nanoemulsion  
Figure 1 shows the Piepel trace and response surface plot for the effect of 3 components (A: ACM, B: oil, and C: water) on D\({}_{(3,2)}\). The observation of dominance of ACM concentration in the stability (D\({}_{(3,2)}\)) as evidenced by higher RC values in the interactions of oil and water with ACM was confirmed in the Piepel trace plots as the stability (low D\({}_{(3,2)}\)) was greatly influenced by ACM (Figure 1a). A curvature was observed in the Piepel trace plots for all independent variables ACM, oil, and water (Figure 1a). It was observed that as the concentration of ACM increased, the stability increased as D\({}_{(3,2)}\) values became lower also, a sharp curvature was observed as the concentration of ACM increased. This means that stability (low D\({}_{(3,2)}\)) can be achieved at a certain concentration of mixture constituents and subsequent increases in the concentration of ACM would continually lower D\({}_{(3,2)}\) and increase stability as shown in Figure 1a. For the influence of water, the curvature was more pronounced forming a parabola shape curvature. This means that higher concentrations of water did not negatively impact the stability because the D\({}_{(3,2)}\) was low. This occurrence was confirmed with the high RC interaction value of ACM and water and is in line with the theory that water-solubility enhances HLB values and ensures the stability of O/W-type nanoemulsions. The curvature for oil was slight, hence, as the concentration of oil increased, the stability decreased as evidenced by high D\({}_{(3,2)}\) values. An extremely sensitive response by ACM (mucilage) shown by a sharp curvature effect on stability as a function of D\({}_{(3,2)}\) was the most dominant effect among the three mixture constituents consistent with [25]. The observation of dominance of ACM concentration in \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F Value** & \
\begin{tabular}{l} _p-Value_ \\ **Prob \textgreater{} F** \\ \end{tabular} &
\begin{tabular}{l} **Significance** \\ **Level** \\ \end{tabular} \\ \hline Model & 1178.55 & 5 & 235.71 & 1805.99 & \textless{}0.0001 & Significant \\ \(\text{lL}\) & 909.19 & 2 & 454.6 & 3483.07 & \textless{}0.0001 & \\ AB & 32.44 & 1 & 32.44 & 248.53 & \textless{}0.0001 & \\ AC & 11.06 & 1 & 11.06 & 84.76 & \textless{}0.0001 & \\ BC & 26.97 & 1 & 26.97 & 206.65 & \textless{}0.0001 & \\ Residual & 0.91 & 7 & 0.13 & & & \\ Lack of fit & 0.34 & 2 & 0.17 & 1.49 & 0.3104 & Not significant \\ Pure error & 0.57 & 5 & 0.11 & & & \\ Cor total & 1179.46 & 12 & & & & \\ R-squared & 0.9992 & & & & & \\ Adjusted & 0.9987 & & & & & \\ R-squared & 0.9977 & & & & & \\ Adequate & & & & & & \\ precision & 104.158 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance for the effect of the three variables of Sauter mean diameter D\({}_{(3,2)}\). the stability (D\({}_{(3,2)}\)) as evidenced by higher RC values in the interactions of oil and water with ACM was confirmed in the response surface plots as the stability (D\({}_{(3,2)}\)) was greatly influenced by ACM (Figure 1b). The actual stability-D\({}_{(3,2)}\) value obtained on the response surface plots (Figure 1b) was 6.6 nm which compares favorably with the value obtained as the average D\({}_{(3,2)}\) (6.7 \(\pm\) 0.1 nm). The significance of a low D\({}_{(3,2)}\) is that the particles of the ACM stabilized O/W-type nanoemulsions are more tightly packed which makes them less susceptible to kinetic instability mechanisms. Hence, with the low D\({}_{(3,2)}\), the nanoemulsion takes a longer time to coalesce hence they remain stable. Although the D\({}_{(3,2)}\) is low, as a result of the adhesion of ACM at the oil and water interface, the creaming of the emulsion is avoided hence the nanoemulsion maintains stability.