# Evaluation of UV-Curable Solid Rocket Propellants' Properties for Advanced 3D Printing Technologies
## 4 Results  
### Pseudoplasticity Test  
Figure 7 illustrates the results, depicted with the blue lines, obtained by varying the applied shear stress on the propellant while maintaining constant temperatures of \(60\pm 1.5\)\({}^{\circ}\)C and \(80\pm 1.5\)\({}^{\circ}\)C.  
The graph is represented as a function of the shear rate (\(\dot{\gamma}\)), obtained by multiplying the spindle rotation speed (\(\omega_{s}\)) by the large cylinder gap geometric factor reported by [PERSON] [25]. The pseudoplastic behavior followed the Ostwald-de Waele model. This law associates the shear stress (\(\tau\)) with the shear rate (\(\dot{\gamma}\)) through the following relationship:  
\[\tau=K\dot{\gamma}^{n} \tag{4}\]  
The curves were interpolated using the equation  
\[\eta=\frac{\tau}{\dot{\gamma}}=K\dot{\gamma}^{n-1} \tag{5}\]  
where \(K\) is the consistency index in [Pa\(\cdots\)\({}^{n}\)], and n is the flow index. The consistency index is a specific constant of the analyzed fluid, while the flow index describes how the viscosity changes in response to shear stress. When \(n=1\), the fluid behaves like a Newtonian  
Figure 6: Specimens freshly extracted from toluene (**left**) and dried for three days, completely free of toluene (**right**). fluid (\(K=\eta\)). If \(n<1\), the fluid exhibits pseudoplastic behavior, and if \(n>1\), it shows dilatant behavior [25]. The R\({}^{2}\) values for the fits at 60 \({}^{\circ}\)C and 80 \({}^{\circ}\)C were \(R^{2}=0.977\) and \(R^{2}=0.987\), respectively. As the temperature increased, the pseudoplastic properties of the propellant decreased, resulting in a less pronounced reduction in viscosity with increasing shear stress. This phenomenon is illustrated by the red line in Figure 7, which represents the ratio between the two blue lines. The \(n_{1}\) parameter was consistently greater than one, indicating that it is always advantageous to increase the temperature. However, as will be discussed in the following paragraph, the pot-life imposes a limit on the slurry temperature. Therefore, a trade-off between these two rheological characteristics is needed to optimize the print quality. This aspect is extremely important when determining the printing speed and, consequently, the shear stress to which the propellant is subjected. The advantage of a temperature increase is demonstrated in other studies in the literature [11]. The analysis was constrained by the small number of selectable rotor speeds. Nevertheless, the speeds used during the measurements fell within the appropriate range for qualitatively describing the pseudoplastic behavior of photocurable propellants [25]. The viscosity results are summarized in Table 1. The standard deviation (SD%) of the viscosity was affected by temperature fluctuations, which were present despite the use of a PID controller. These fluctuations contributed to the variability of the measurements. It can be concluded that the mean value of the samples provides an adequate approximation of the propellant viscosity at temperatures close to 60 \({}^{\circ}\)C and 80 \({}^{\circ}\)C, respectively. The calculated flow index n was 0.32 at 60 \({}^{\circ}\)C and 0.46 at 80 \({}^{\circ}\)C. These values differ from those reported in the literature [9; 10; 11], which presents values between 0.5 and 0.7, suggesting less pronounced shear-thinning behavior. This discrepancy can be attributed to the significant sensitivity of the propellant's rheological behavior to the size and proportion of oxidant powders, as well as the presence of thiols in this specific instance. The selected particle sizes of ammonium sulfate played a crucial role in this effect. Specifically, a diameter ratio below 0.155 allowed the fine particles to move more freely among the larger particles, thereby reducing the propellant's viscosity. Consequently, an enhancement in the pseudoplastic properties was observed, indicated by a decreasing value of the n index [8].