## 3 Results and Discussion
This fact indicated an increase in Newtonian character and therefore, a decrease in the structural complexity of the sample. These effects of ultrasounds were previously observed by [PERSON] et al. (2022) [54]. They investigated the flow behavior of chia seed mucilage solutions extracted by a combined thermal-ultrasound process and they observed that an increase in ultrasound time provoked a decrease in viscosity and an increase in n. A similar conclusion to that obtained with the flow index can be drawn from the values of the critical shear rate. This parameter, which is inversely related to the terminal relaxation time, tended to increase significantly with the ultrasonic homogenization time, which means that the terminal relaxation time decreased, increasing the liquid character of the sample. The long ultrasound time provoked a drastic reduction in viscosity, probably related to a reduction in the molecular weight of the fiber polymer [54; 55; 56]. Notably, this result could be explained by the level of chain entanglement: a lower molecular weight leads to a lower density of entanglement, enabling chain mobility and decreasing the time needed to restore the entangled network after deformation [53]. The flow results are in agreement with those  
Figure 3: Steady shear flow curves for aqueous dispersions of flaxseed fiber as a function of different treatments of ultrasounds. The continuous lines correspond to the Carreau model fit. The tests were carried out at T = 20 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c} \hline
**Sample** & **n\({}_{0}\) (Pa-s) \(\pm\) SD\({}_{\mathbf{n}\emptyset}\)** & \(\dot{\gamma_{c}}\)**(s\({}^{-1}\))\(\pm\)SD\(\dot{\gamma_{c}}\)** & **n \(\pm\) SD\({}_{\mathbf{n}}\)** & **R\({}^{2}\)** \\ \hline U-2 min-40\% & 3200 \(\pm\) \textless{}0.1 & 2.4 \(\times\) 10\({}^{-3}\)\(\pm\) 77.4 \(\times\) 10\({}^{-4}\) & 0.17 \(\pm\) \textless{}0.01 & 0.990 \\ \hline U-2 min-60\% & 2500 \(\pm\) \textless{}0.1 & 3.5 \(\times\) 10\({}^{-3}\)\(\pm\) 1.2 \(\times\) 10\({}^{-4}\) & 0.15 \(\pm\) \textless{}0.01 & 0.996 \\ \hline U-2 min-80\% & 2450 \(\pm\) \textless{}0.1 & 2.3 \(\times\) 10\({}^{-3}\)\(\pm\) 5.6 \(\times\) 10\({}^{-4}\) & 0.18 \(\pm\) 0.02 & 0.955 \\ \hline U-2 min-100\% & 2700 \(\pm\) \textless{}0.1 & 2.7 \(\times\) 10\({}^{-3}\)\(\pm\) 4.9 \(\times\) 10\({}^{-4}\) & 0.16 \(\pm\) 0.01 & 0.962 \\ \hline L-0 min & 3690 \(\pm\) 69.4 & 3.5 \(\times\) 10\({}^{-3}\)\(\pm\) 2.4 \(\times\) 10\({}^{-4}\) & 0.13 \(\pm\) \textless{}0.01 & 0.990 \\ \hline LU-10 min-100\% & 122 \(\pm\) 2.8 & 9.2 \(\times\) 10\({}^{-3}\)\(\pm\) 6.3 \(\times\) 10\({}^{-4}\) & 0.30 \(\pm\) \textless{}0.01 & 0.990 \\ \hline LU-20 min-100\% & 118 \(\pm\) 1.3 & 3.5 \(\times\) 10\({}^{-7}\)\(\pm\) \textless{}1 \(\times\) 10\({}^{-4}\) & 0.60 \(\pm\) 0.01 & 0.990 \\ \hline \end{tabular}
\end{table} 
Table 3: Fitting parameters of experimental data for the Carreau model. SD is the standard deviation. obtained in the SAOS tests. Different behaviors were found in fibers such as citrus or lemon peel fibers, both considered mainly insoluble fibers. In lemon peel fiber subjected to different homogenization pressures, [PERSON] et al. (2018) [57] observed that increases in pressure enhance particle hydration and facilitate a restructuring of the particle network, leading to an increase in G\({}^{\prime}\), which reaches a plateau at the highest pressure tested. In the same way, in citrus peel fiber, [PERSON] et al. (2020) [43] also found a stronger three-dimensional network when higher levels of energy or power of mixing were used for the preparation of citrus fiber in aqueous suspension.