## 3 Results and Discussion
### Incorporation of a Physical Stabilizer and Rheology Modifier  
Figure 6 shows the flow behavior for the optimized emulsions containing 0.1, 0.3 and 0.5 wt.% rhamsan gum. All the samples studied exhibited shear thinning behavior, which was also fitted to a Cross model (R\({}^{2}\) > 0.99):  
\[\eta=\frac{\eta_{0}-\eta_{\infty}}{1+\left(k\gamma\right)^{1-n}} \tag{4}\]  
The fitting parameters are given in Table 2. The flow curve of the emulsion formulated without rhamsan gum, not shown in Figure 6, showed a Newtonian behavior with a constant viscosity of 2.74 mPa\(\cdot\)s. In contrast, all the emulsions formulated with rhamsan gum show a very pseudoplastic behavior. The presence of the food grade biopolymer in the continuous phase induced a marked increase in viscosity and a pronounced decrease  
Figure 5: Backscattering versus container height as a function of time for the emulsion formulated with 2 wt.% of cricket flour and prepared using ultrasound at 75% amplitude. Figure 6: Flow curves for all emulsions formulated with different rhamsan gum concentrations. in the flow index. In addition, a higher flow resistance is shown, with higher k values as the concentration of the rubber increases. The results show that these emulsions behave similarly to other systems containing rhamsan gum as a stabilizer [22]. The frequency dependence of the linear viscoelastic functions (the storage modulus, G\({}^{\prime}\), and the loss modulus, G\({}^{\prime\prime}\)), which illustrates the influence of the biopolymer concentration, of the samples studied is shown in Figure 7. Samples formulated in the absence of rhamsan gum showed no linear viscoelastic range measurable by stress sweeps, so frequency sweeps were not carried out for these systems. Two types of behaviors are observed in the systems formulated with the biopolymer. For the 0.1 wt.% sample, a significant frequency dependence of the viscoelastic properties is observed, with G\({}^{\prime}\) being higher than G\({}^{\prime\prime}\) over almost the whole range. There is therefore a low frequency crossover point where the viscous component dominates. All samples above 0.3 wt.% yield mechanical spectra of gel-like materials, with a higher storage modulus than loss modulus and little frequency dependence for either modulus. These results have previously been found in concentrated emulsions and seem to indicate the presence of three-dimensional networks similar to those of strong gels [23]. However, these emulgels formulated with rhamsan gum cannot be classified as strong gels, as they do not fulfill the criteria proposed by [PERSON] [24] for strong gels. Finally, to check the effect of the addition of rhamsan gum on the physical stability of the emulsions, the results of the Turbiscan stability index (T \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Rhamsan Gum**} & \multicolumn{1}{c}{**\(\eta_{0}\) (Pa-s)**} & \multicolumn{1}{c}{**\(\eta_{\infty}\) (Pa-s)**} & \multicolumn{1}{c}{**k (s)**} \\ \hline
0.1 & 4.3 & \textless{}0.001 & 738.7 \\ \hline
0.3 & 32.4 & \textless{}0.001 & 571.1 \\ \hline
0.5 & 280.8 & \textless{}0.001 & 354.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cross model fitting parameters: \(\eta_{0}\) is the viscosity at very low shear rates, \(\eta_{\infty}\) is the viscosity at very high shear rates and k is the inverse of the critical shear rate. The values were obtained using a nonlinear regression analysis. Figure 7: Mechanical spectra for all emulsions formulated with different rhamsan gum concentrations. are shown in Figure 8. Firstly, this parameter shows that the emulsions prepared with ultrasound (US) are more stable than those prepared only with a rotor-stator system (RS), confirming what has already been discussed in Figures 3 and 5. On the other hand, the addition of rhamsan gum significantly improves the physical stability (lower TSI vales) of the systems, especially in emulsions with concentrations above 0.3 wt.%.