## 3 Results
### Apparent Viscosity  
Table 4 shows the results of viscosity measurements (\(\eta\)) of quercetin formulations, at the following shear rates: 30 s\({}^{-1}\), 60 s\({}^{-1}\), 100s\({}^{-1}\). The viscosity value determined for the tested formulations at all applied shear rates increased in the following sequence: F-CA \(<\) F-CB \(<\) F-AA \(<\) F-AB \(<\) F-MA \(<\) F-MB. It was observed that the MC-based formulations showed significantly higher viscosity than the other formulations. With regard to the viscosity at a shear rate of 30s\({}^{-1}\), for preparations with a lower API content, the viscosity of F-MA was higher by 47.65% (\(p\leq 0.01\)) and 13.16% (\(p\leq 0.01\)) vs. F-CA and F-AA, respectively, while for preparations with higher API content, the viscosity of F-MB was higher by 58.06% (\(p\leq 0.01\)) and 32.97% (\(p\leq 0.01\)) vs. F-CB and F-AB, respectively. In addition, it was shown that increasing the quercetin concentration in MC-based hydrogel formulations increased their viscosity significantly (\(p\leq 0.05\)). The viscosity curves obtained for the tested formulations are shown in Figure 3.  
It has been shown that viscosity is dependent on shear rate and shear stress and decreases as their values increase (Figure 3). Under the influence of the applied shear stress, the internal structure of the tested samples is destroyed, and the system starts to flow. Shear thinning was observed in all samples, particularly at low shear rates. The system shows pseudoplastic flow. Under the influence of increasing shear stress, the polymer particles arrange themselves in the direction of flow, which lowers the viscosity of the system. This strong shear thinning with a simultaneous decrease in viscosity throughout the experimental area confirms the good spreadability shown earlier in the test for the prepared formulations. \begin{table}
\begin{tabular}{c c c c} \hline
**Formulation Code** & \(\eta\) **(30 s\({}^{-1}\))** & \(\eta\) **(60 s\({}^{-1}\))** & \(\eta\) **(100 s\({}^{-1}\))** \\ \hline
**F-AA** & 11.68 \(\pm\) 0.51 & 8.09 \(\pm\) 0.23 & 8.06 \(\pm\) 0.23 \\ \hline
**F-CA** & 7.04 \(\pm\) 0.42 & 4.66 \(\pm\) 0.21 & 3.86 \(\pm\) 0.25 \\ \hline
**F-MA** & 13.45 \(\pm\) 0.34  \\ \hline
**F-CB** & 7.49 \(\pm\) 0.41 & 5.35 \(\pm\) 0.23 & 4.35 \(\pm\) 0.22 \\ \hline
**F-MB** & 17.86 \(\pm\) 0.65  \\ \hline \end{tabular}
\end{table} 
Table 4: Apparent viscosity of prepared hydrogels depending on the shear rate (\(\eta\)). Figure 4 shows rheograms illustrating flow under increasing and then decreasing shear stress. As can be seen in the figures, at the time of plotting the descending curve, the structure of the system is not yet completely reconstructed, so the curves do not coincide in the rheograms; hysteresis loops are then formed, indicating systems exhibiting thixotropy. The calculated areas of the hysteresis loop for the prepared formulations were arranged in ascending order: 4588.51 (F-CB), 5799.10 (F-CA), 7814.95 (F-AA), 9314.87 (F-AB), 11650.96 (F-MB), 14114.72 (F-MA). Yield strength is an important parameter used to characterize semi-solid formulations. It usually affects the spreadability and retention of formulations. A high value of yield stress indicates a reduction in spreadability and an increase in the ability to retain the formulation at the application site. In a study by [PERSON] _et al._, the yield stress for the formulation and control cream of N,N-diethyl-3-methylbenzamideamide (DEET) was 26.39 and 6.474 Pa, respectively, resulting in better spreadability of the cream than the hydrogel formulation [65]. A significant yield stress was required to break the microgel network present in the hydrogel, which contributed to the higher yield stress observed for the hydrogel compared to the cream. These findings were found to be consistent with the authors' results, where the MC  
Figure 3: Viscosity curves for hydrogel: (**A**) F-AA, F-CA, F-MA; (**B**) F-AB, F-CB, F-MB.