## 3 Results  
### Rheological and Physical Characterization of Solutions  
The rheological behavior of different solutions changes according to the nucilage-alginate concentration, as shown in Figure 1. Here, it is essential to highlight that greater shear thinning is detected [33; 34] when the nucilage concentration is higher than the alginate concentration, as shown in the graph of Figure 1A, with a steeper slope when the viscosity of the solution decreases with increasing shear velocity. The highest viscosity was for chia seed nucilage, as reported by [PERSON] et al. [35; 36], when comparing against barley root and maize root nucilage, but at a single concentration. This pseudoplastic characteristic can be attributed to the expansion of polysaccharide chains when they begin to hydrate, as reported by [PERSON] et al. [37], who suggest electrostatic intermolecular repulsion in peach gum exudates induces the formation of more viscous solutions; this also occurs with chia nucilage as observed in Figure 1A. Flow curves also demonstrate that this property is shear stress dependent. In this regard, the behavior of the dynamic flow (shear stress vs. shear velocity) of the solutions at different concentrations of nucilage and alginate is depicted in Figure 1B. Here, it is observed that at low shear rates (0.001 s\({}^{-1}\)), the shear stress increases with the nucilage concentration (Figure 1B) and then decreases slightly as shear rates improve, observing a linear trend when the alginate concentration increases (Figure 1B). These results were fitted to the Herschel-Bulkley model: \(\sigma=\sigma_{0}+\mathrm{K}\mathrm{y}^{n}\) to relate the variations in rheological behavior under constant shear, where \(n\) is the flow behavior index, and two types of phenomena, shear thinning (\(n<1\)) or shear thickening (\(n>1\)) [29], typical behaviors of pseudoplastic macromolecular systems, occur for both polymers [38; 39; 40]. These results may also be related to the nucilage composition, since some studies report that although the nucilage has a similar uronic acid content to low-methoxy pectin, the interactions that occur are different. Mucilage is mainly governed by weak electrostatic interactions between entangled polymer chains [11; 13], which is why shear thinning could be explained by how the nucilage hydrates, which can form small aggregates in a similar way to that reported by [PERSON] et al. [41] for Arabic gum. Changes in intrinsic viscosity could also be used to track the macromolecular interactions and capacity of entrapment or release during the encapsulation process, given the hydration capacity of the chia seed nucilage and the high content of hydroxyl (\(-\)OH) groups that are the major source of bioadhesion or adsorption [42]. Regarding the above, [PERSON] et al. [43] emphasize that the mesquite gum solution presenting low viscosity brings about very rapid diffusion and anchoring of gum molecules into the oil-water interface when microencapsulating lemon essential oil. On the other hand, some research shows that natural polysaccharide fibers have a high affinity for polar dyes due to hydrogen bonding and dipole interactions [44; 45]. Therefore, chia seed nucilage, by  
Figure 1: Rheological properties: (**A**) shear rate vs. viscosity and (**B**) stress vs. shear rate at different concentrations of nucilage–alginate. generating higher viscosities, could have a greater retention capacity of molecules such as rhodamine B. Table 2 shows the results of flow curve data fitting using a Herschel-Bulkley rheology model. The best fit was evaluated through the coefficient of determination R2 and the lowest value of the minimum mean square error (RMSE), showing that all the solutions follow a thinning behavior due to index values of (\(n\)) less than 1, which explains the non-Newtonian pseudoplastic behavior. The results showed that the addition of alginate increased the flow behavior index, indicating a decrease in pseudo-elasticity.