*2.3. Rheological Tests*

Microscopic imaging for nanoemulsion systems with proteins presented by Zhu et al. [39] corresponded to our findings. In their studies, optical microscopic imaging was compared with confocal laser scanning microscopy (CLSM). It was suggested that using CLSM allowed for the determination of a core–shell structure in the emulsion systems where proteins were located at the surface of the emulsion droplets. More detailed studies are needed for our nanoemulsion systems. First of all, signals from all the fluorescent structures should be identified and separated (i.e., from HSO, AHE) [12,31]. Then, Figure 4a shows the flow curves of the various samples, which illustrate the samples' rheological properties. The flow curves showed a non-Newtonian behavior, with a decreasing slope (viscosity) up to a certain cut-off, suggesting typical pseudoplastic behavior. However, the viscosity increased after a certain shear rate, which is a typical property of a dilatant fluid. The changes in the dynamic viscosity of the samples with increasing shear rate are shown in Figure 4b. It was apparent that the S08 sample had the highest viscosity, followed by S13 and S02, with S14 being least viscous at various shear rates. All the samples exhibited two types of behavior: first, shear thinning, and then shear thickening, after a particular shear rate cut-off. This became more apparent in Figure 4c when the power law was used to model these curves to evaluate the coefficient that depicted clearly the two zones, with a cut-off close to 130 Hz. As a result, a broken power law model (Equation (1)) was used to describe the flow behavior of the samples.

$$\mathfrak{n} = \mathsf{K}\_1(\dot{\mathfrak{y}})^{\mathfrak{n}\_1 - 1} \text{ for } \dot{\mathfrak{y}} < 130 \\ = \mathsf{K}\_2(\dot{\mathfrak{y}})^{\mathfrak{n}\_2 - 1} \text{ for } \dot{\mathfrak{y}} \ge 130 \tag{1}$$

where <sup>η</sup> is the dynamic viscosity, K<sup>1</sup> and K<sup>2</sup> are the consistency coefficients, . γ is the shear rate and n<sup>1</sup> and n<sup>2</sup> are the flow behavior indices. additional studies on the impact of whey protein on the fluorescent behavior of the components should be investigated. Ren and Giusti [40] showed that anthocyanin-rich

*Molecules* **2021**, *26*, x FOR PEER REVIEW 8 of 20

Table 4 shows the broken power law model parameters. The consistency coefficient K<sup>1</sup> at shear rates less than 130 Hz was found to be highest for S08, while those of other samples were not significantly different. This measure is an indicator of the initial system viscosity [41], suggesting that sample S08 had higher viscosity to begin with, which was sustained even at changing shear rates. extracts decreased the fluorescence intensity of whey protein while increasing λmax. The study concluded that thermally induced whey protein was effective in protecting anthocyanin from color degradation. Using an optical microscope, we focused only on the verification of the homogeneity of the samples as well as possible coalescence (which was not observed in the optimal nanoemulsions). Nevertheless, we strongly recommend using more than one technique for the analysis of the emulsion systems droplets size.

**Figure 3.** Microscopic images of the emulsion droplets (magnification, ×40, ×100, and ×100; 2.5D image): (**A**) S02, (**B**) S08, (**C**) S13, (**D**) S14 (the images were adjusted as the best fit and colored with software). **Figure 3.** Microscopic images of the emulsion droplets (magnification, ×40, ×100, and ×100; 2.5D image): (**A**) S02, (**B**) S08, (**C**) S13, (**D**) S14 (the images were adjusted as the best fit and colored with software).

*2.3. Rheological Tests* 


**Table 4.** Parameters of the broken power model describing the viscosity curves of the samples: consistency coefficient (K<sup>1</sup> and K<sup>2</sup> ), flow index (n<sup>1</sup> and n<sup>2</sup> ).

a–c Values in the same column with the same superscript alphabet letters are not significantly different from each other according to Duncan's grouping of means.

> The higher viscosity of S08 as compared to the other samples could be attributed to the highest HSO (5%) content amongst the four tested samples. Furthermore, S14 was found to possess the lowest viscosity on account of having the lowest HSO content (1%). This showed that a higher oil loading was associated with higher viscosity, which is consistent with observations of other researchers [42–44]. Rha [45] and Jarzebski et al. [12] attributed this phenomenon of increasing viscosity with increasing oil loading to the greater formation of interphase layers, creating a larger barrier between the emulsion components.

> At a shear rate of 130 Hz, all the samples exhibited a transition from shear thinning behavior to shear thickening behavior. Again, samples S08, having the highest oil loading, and sample S14, with the lowest oil and whey loading, demonstrated the highest and the lowest viscosity, respectively. This transition from shear thinning to the shear thickening behavior could be attributed to the phenomenon that at very high shear rates, tremendous turbulence occurs. When such turbulence occurs after a certain shear rate cut-off (which was 130 Hz in our case), any increase in the shear rate will result in increased turbulence, resulting in increased viscous dissipation and higher resistance to flow, which in turn makes the flow appear as shear-thickening. This effect is a typical example of the Taylor vortex flow in shear-thinning fluids [46,47]. The interpretation of Chhabra and Richardson [48] could be used to explain such transitionary behavior of our shear-thinning samples. At rest, the emulsion has sufficient interfacial tension to be stable. At low shear rates, lubrication for particle motion of the continuous phase between the plates is provided by the dispersed oil phase resulting in decreased stress with increasing shear (shear-thinning behavior). However, at high shear rates, the emulsion breaks, and the dispersed phase is completely separated from the continuous phase due to centrifugal forces. Furthermore, continuous and dispersed phases expand or dilate slightly under increasing shear strain, resulting in increased friction and shear stress, causing the dynamic viscosity to increase rapidly with shear rate.
