## 3 Results and Discussion  
### Rheological Assessment of the Bioinks  
The n_index was calculated according to the Power Law Model (Ostwald-de Waele) by fitting the curves \(\eta\)(\(\dot{\gamma}\)) (Figure 3) to the following equation [19]:  
\[\eta=m(\dot{\gamma})^{n-1} \tag{4}\]  
where \(\eta\) = viscosity, \(n\) = power-law index, \(m\)= power-law consistency coefficient, and \(\dot{\gamma}\) = shear rate. Thus, Figure 3 displays the apparent viscosity (Pa\(\cdot\)s) as a function of shear rate (s\({}^{-1}\)). According to the results, all samples display shear thinning behavior (n \(<\) 1) at printing temperature (24 \({}^{\circ}\)C) (Table 6), which qualifies them as 3D extrusion printing inks in terms of the second of the necessary qualities [29; 30]. The maximum shear rate that the hydrogel blends experience during extrusion was determined after each hydrogel blend's Power Law index was obtained. For the optimal levels of extrusion piston speed and nozzle diameter that were defined through Taguchi DoE, the maximum shear rate was calculated based on Equations (5) and (6):  
\[\dot{\gamma}=\left[\frac{V_{extr}\times R^{2}}{\left(\frac{\eta}{3n+1}\right) \times R^{\left(\frac{3n+1}{n}\right)}}\right]\times R^{\frac{1}{n}} \tag{5}\]  
\[V_{extr}=V_{p}\times\left(\frac{D_{\text{s}}}{D_{n}}\right)^{2} \tag{6}\]  
where \(V_{extr}\) is the material extrusion speed, R is the nozzle radius (mm), D\({}_{\text{s}}\) is the syringe diameter, D\({}_{\text{n}}\) is the nozzle diameter, and V\({}_{\text{p}}\) is the piston movement speed [19]. The results for the n_index and the maximum shear rate are displayed in Table 7.  
Figure 3: Linear region (1–200 s\({}^{-1}\)) of viscosity measurements (0.1–1000 s\({}^{-1}\)) of the blends listed in Table 6. All measurements were carried out at 24 \({}^{\circ}\)C.  
By performing the maximum shear rate that was calculated for each blend (Table 7) in a triple-step rotational measurement, the viscosity recovery rates of each sample were studied (Figure 4a). As shown in Figure 4b, most of the blends exhibit poor recovery ability after the application of a high shear rate. Moreover, rotational measurements were carried out to enable a comparative analysis of the recovery behavior among the various inks. This involved subjecting all samples to a uniform high shear rate of 100 s\({}^{-1}\), selected as the average value (Figure 4c). By employing the average shear rate value, the rotational measurements conducted ensure a consistent evaluation of the recovery behavior across the eleven different samples. According to the results presented in Figure 4c, pure alginate hydrogels exhibit high recovery rates. Among the alginate-gelatin blends, the blend with the highest alginate ratio (10%) displays promising recovery behavior, as within 30 s regains 30% of its initial viscosity. These findings are in line with the results of [PERSON] et al., showing that with the increase in the alginate ratio, there is a decrease observed in the recovery time. However, \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Alg\_Gel** & & & & & & & & & & & & \\
**Composition** & 0.0\_2.0 & 0.0\_4.0 & 0.0\_6.0 & 2.0\_4.0 & 4.0\_4.0 & 6.0\_4.0 & 8.0\_4.0 & 10.0\_4.0 & 6.0\_0.0 & 8.0\_0.0 & 10.0\_0.0 \\ \hline n & 0.26 & 0.29 & 0.23 & 0.13 & 0.24 & 0.21 & 0.31 & 0.17 & 0.52 & 0.47 & 0.33 \\ m (Pa\({}^{\text{sn}-1}\)) & 74.07 & 508.20 & 630.30 & 470.30 & 801.20 & 1753.30 & 2856.00 & 1117.00 & 48.80 & 122.10 & 493.3 \\ max \(\dot{\gamma}\) (s\({}^{-1}\)) & 91.40 & 86.00 & 98.10 & 142.70 & 95.60 & 103.60 & 83.10 & 118.50 & 65.70 & 68.40 & 80.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results for power-law index, power-law consistency coefficient, and maximum shear rate for each of the developed inks.