## 3 Results and Discussion
### Mayonnaise Characterization
#### 3.2.3. Rheological Characterization  
Regarding the rheological behavior, the low-fat mayonnaies fit well with the power law model (r\({}^{2}\) = 0.998-0.999 and RMSE = 0.284-1.442). All samples showed a power law index in a range of 0.28-0.33 (Table 2), indicating a shear-thinning fluid (pseudoplastic fluid) behavior (power law index \(<\) 1). The results herein agree with previous reports of low-fat mayonnaies where this parameter was 0.28-0.52 [25; 48].  
On the other hand, the consistency index (\(K\)) represents the viscosity of the sample; the highest \(K\) values were found in samples with 30% oil (66-35 Pa\(\cdot\)s\({}^{\rm n}\)), while the minimum values (20-35 Pa\(\cdot\)s\({}^{\rm n}\)) were determined in the mayonnaies elaborated containing 15% oil (Table 2). [PERSON] et al. [38] prepared low-fat mayonnaies (30% oil) using _Chorella_, _Spiulina_, and _Dunaliella_ microalgae, demonstrating higher \(K\) (74-94.5 Pa\(\cdot\)s\({}^{\rm n}\)) than those found in this work, probably because these products also contained 4% starch, which increased the viscosity of the product. However, the \(K\) values of our samples agree with previous reports of low-fat mayonnaies (\(K\) = 31-49 Pa\(\cdot\)s\({}^{\rm n}\)) elaborated with different gums such as xanthan gum, guar gum, and corn-dextran [25; 48]. Like the behavior observed herein, [PERSON] et al. [8] also determined that the consistency index of low-fat mayonnaise can reduce from 90-51 and 87-23 Pa\(\cdot\)s\({}^{\rm n}\) when the oil content is reduced from 54 to 38%. This could be explained by the role of oil particle-particle interactions in developing the viscosity of mayonnaise [49]. Hence, if the oil content is low, the number of oil particle-particle interactions will be reduced, and the system's viscosity will be lower.  
It was found that the use of vegetable proteins, the WHC, and the OHC showed a negative correlation (CI = \(-\)0.936, \(-\)0.732, and \(-\)0.571, respectively) with the \(\Delta K\) (loss of consistency index), indicating that proteins helped to mitigate the loss of viscosity. For instance, the reduction of oil content (from 30 to 15%) in samples with SPI (D, E, and F) and SPC (D', E,' and F') results in minor losses of consistency index (\(\Delta K\) = 3-15 Pa\(\cdot\)s\({}^{\rm n}\)) in comparison to samples containing only sodium alginate (\(\Delta K\) = 31-45 Pa\(\cdot\)s\({}^{\rm n}\)). This was probably because the techno-functional properties of proteins might increase the number and strength of inter and intramolecular interactions [50; 51].  
The viscosity showed to be positively affected by the oil content (\(p<\) 0.05); as can be seen in Figure 4, the viscosity of the systems showed to reduce at higher shear stress; moreover, the viscosity at zero shear rate tends to reduce with reduced oil concentrations. The highest viscosities at zero shear rate were obtained in samples A (175 Pa\(\cdot\)s) and D' (125 Pa\(\cdot\)s), while the lowest values were found in the D (\(\sim\)100 Pa\(\cdot\)s). In summary, the samples A, D' and E' were demonstrated to have similar rheological characteristics (consistency index, viscosity, and power law index) to the commercial product.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mayonnaie Sample** & \(K\) **(Pa\(\cdot\)s\({}^{\rm n}\))** & \(\Delta K\) & \(n\) & **RMSE** & **r\({}^{2}\)** \\ \hline Commercial & 43.284 & ND & 0.297 & 0.583 & 0.999 \\ A & 66.262 & 0.000 & 0.281 & 1.442 & 0.998 \\ B & 35.008 & 31.223 & 0.260 & 1.397 & 0.999 \\ C & 20.922 & 45.291 & 0.335 & 0.915 & 0.999 \\ D & 35.284 & 0.000 & 0.281 & 0.883 & 0.999 \\ E & 31.524 & 3.524 & 0.299 & 1.062 & 0.998