## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Flow Rate of \(50\times 10^{-6}\) m\({}^{2}\)/s** & **Gel Diameter** & **Flow Rate of \(300\times 10^{-6}\) m\({}^{2}\)/s** & **Gel Diameter** \\ (\(\times\)\(10^{-9}\) m\({}^{3}\)/s)** & **(mm)** & **(\(\times\)\(10^{-9}\) m\({}^{3}\)/s)** & **(mm)** \\ \hline
5.94 & 1.29 & 3.96 & 1.04 \\
7.92 & 1.19 & 7.92 & 0.77 \\
11.9 & 1.04 & 11.9 & 0.65 \\
15.8 & 0.95 & 13.9 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average gel-droplet diameter for the two types of continuous-phase flows. Figure 5: Relationship between (**a**) the continuous-phase flow rate and the gel-droplets’ average diameter and (**b**) the shear stress and the average diameter with respect to silicone oil viscosity. is that a higher-viscosity continuous-phase flow (\(300\times 10^{-6}\) m\({}^{2}\)/s) can generate smaller gel droplets than a lower viscosity flow (\(50\times 10^{-6}\) m\({}^{2}\)/s) or, more generally, the smaller the kinematic viscosity of the continuous-phase flow rate, the bigger the droplet diameter that can be generated. Moreover, this result was supported by the results of other researchers [24; 43; 42; 44]. To illustrate this using one of the nine cases as an example, \(7.92\times 10^{-9}\) m\({}^{3}\)/s of the \(50\times 10^{-6}\) m\({}^{2}\)/s silicone oil generated a gel droplet of 1.19 mm in diameter. However, for the \(300\times 10^{-6}\) m\({}^{2}\)/s silicone oil with an identical flow rate, the diameter of the gel droplet was only 0.77 mm, i.e., the gel droplet decreased in volume by 72%. This significant decrease in the droplet's volume was clearly affected by an increasing flow rate and the kinematic viscosity of the continuous-phase flow. The increase in the continuous-phase flow rate correlated with an increase in drag induced by the flow, which supported droplet detachment from the tip of the nozzle. Hence, a smaller size of droplet was generated as the droplet-formation time was decreased. Furthermore, an increase in viscosity of the continuous-phase flow contributed to an increase in drag. According to [PERSON] et al., a greater drag force correlated with the diameter of the detached droplet [34]. Therefore, this study determined that droplet size was mostly affected by flow rate and the kinematic viscosity of the continuous-phase fluid (silicone oil). To examine the effect of these two factors on the droplet size, we estimated the shear stress on the interface as \(\mu u_{c}\)/\(\beta\) where the average velocity \(u_{c}\) was continuous phased flow rate \(Q_{c}\) divided by the duct cross section (4 mm\({}^{2}\)), neglecting the needle cross section which was less than 2 % of the duct's one. The reference length \(\delta\) was taken as half the duct width. The dynamic viscosity \(\mu\) was calculated using the densities of 958 and 966 kg/m\({}^{3}\) for \(50\times 10^{-6}\) and \(300\times 10^{-6}\) m\({}^{2}\)/s silicone oils, respectively. The results are shown in Figure 5b. The two curves show a unified trend through the whole range of the shear stress, although there exists a discontinuity between them. It is presumably due to the difficulty to accurately evaluate the shear rate since the flow pattern was not simple around the droplet evolving near the nozzle tip in a narrow duct which width was comparable to the droplet size. Figure 6 shows images of the selected gels submerged in water at temperatures of 10, 25, and 40 \({}^{\circ}\)C for cases A and C and shows their physical appearance after polymerization. Three gel samples were selected and placed on an acrylic plate for observation. A similar shrinkage trend was exhibited by a cylindrical NIPA gel reported by [PERSON] et al. [13]. The size of the gel rod significantly decreased when the temperature of the solution was increased from 10 to 40 \({}^{\circ}\)C. At 40 \({}^{\circ}\)C, the NIPA gel shrank and demonstrated a negative thermal expansion characteristic.