## 3 Results and Discussion
The tests were carried out at 20 \({}^{\circ}\)C, 24 h after preparation. Concerning slope \"b\", the sample that was not subjected to ultrasonic homogenization; L-0 min presented the lowest value, followed by U-2 min-40%. Afterwards, U-2 min-60%, U-2 min-80%, and U-2 min-100% showed similar slopes between them but slightly higher slopes than U-2 min-40%. Next, L-10 min-100% exhibited a higher value, and finally the sample L-20 min-100% showed the highest slope. Regarding the variation of the parameter \"a\" with the treatment employed, a tendency to decrease with an increase in the time or amplitude of ultrasonic homogenization was observed. A relation between the microstructure and the energy applied per mass unity during the preparation of the aqueous dispersion of flaxseed fiber (Table 1) can be established. The increase in amplitude percentage in ultrasonic homogenization was associated with a greater energy applied to the sample, which caused a small breakdown of the interactions between macromolecules, and therefore, a loss of part of the tridimensional network formed. As a consequence, a slight decrease in moduli was observed and a slight increase in dependence on the frequency occurred, according to a sample with shorter relaxation times. Nevertheless, at these energy levels, the ultrasound effects on fiber were reduced. The application of pre-shear with Ultraturrax T50 and a higher ultrasonic homogenization time (10 min) noticeably increased the energy applied which provoked not only a higher level of breakage, and consequently a higher loss of entanglements, but also probably a significant decrease of the molecular weight, hence the change in the shape of the mechanical spectrum. When the time was 20 min, the alteration of the microstructure was considerable to such an extent that the network was completely broken, and the sample behaved as a liquid. From these results, we can deduce that shear during the preparation of aqueous dispersions of flaxseed fiber can negatively influence their microstructure and therefore, potential applications. In addition, if L-0 min and U-2 min-100% are compared, it is possible to conclude that the Ultraturrax T50 rotor-stator device was less effective than ultrasonic homogenization, since applying similar energy per mass unity results in a slightly stronger microstructure. Regarding flow behavior (Figure 3), all the samples presented a shear thinning behavior, characterized by a decrease in viscosity as the shear rate increases and a tendency to reach a Newtonian viscosity at very low shear rates. The application of shear induces an alignment of the initially disordered polymer chains along the flow direction, thereby reducing entanglements and intermolecular interactions, which results in a lower viscosity of the solution. Other fibers also exhibit pseudoplastic behavior, such as aloe vera mucilage, which is considered a type of soluble fiber [53], microfluidized wheat bran suspensions [36], or citrus fiber [43]. The flow curves demonstrated negligible sensitivity to variations in ultrasound amplitude, but showed marked sensitivity to the duration of ultrasonic exposure. The application time of ultrasonic homogenization created a negative impact, causing a decrease in viscosity values and a change in the flow index toward a more Newtonian behavior. The experimental results have been quite well adjusted to the Carreau model (Equation (2)) as can be deduced from the regression coefficient R\({}^{2}\) (>0.99). The fitting parameters of the experimental results of the model can be found in Table 3.  
As mentioned above, the amplitude variable did not influence the fitting parameters. Instead, a trend to decrease zero shear rate viscosity was observed with the homogenization time, this fact being significant after submitting the control sample to ultrasonic homogenization (compare L-0 min and LU-10 min-100%). In contrast, the flow index, which was less than one in all samples supporting the shear thinning behavior previously mentioned, increased.