## 2 Materials and Methods
### Method for Generating Mono-dispersed Thermosensitive Gels  
In this study, NIPA gels were generated by the cross-linked polymerization of the monomer (NIPA) and N,N'-methylenebisacrylamide (BIS) as cross-linker (see Figure 1), with the aid of other three chemicals and water measured in a unit mass. The method for synthesizing the gels was similar to that described by [PERSON] et al. [18; 19]. The chemicals included 150 mg of NIPA (Wako Chemicals, Tokyo, Japan), 5 mg of BIS (Nacalai Tesque Inc., Kyoto, Japan), 25 mg of DDBAB (Wako Chemicals) as an initiator, 10 \(\upmu\)L of N,N,N',N'-tetramethylethylenediamine (TEMED) (Wako Chemicals) as an accelerator, 6 mg of APS (Nacalai Tesque Inc.) as an initiator, and 1.6 g of deionized water. NIPA, BIS, DDBAB, and TEMED were dissolved in half of the deionized water (0.8 g) and loaded into the first 3-mL syringe (inner diameter = 10.1 mm). Similarly, APS was dissolved in the remaining half of the deionized water (0.8 g) and loaded into the second 3-mL syringe. Two different viscosities of silicone oil (50 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s and 300 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s, Shin-Etsu Chemical, Tokyo, Japan) were used as continuous-phase fluids. Figure 2 shows the setup of the research apparatus. Based on the figures, the steps to synthesize the gels are described as follows: a 3 mL syringe containing NIPA components and another 3 mL syringe containing APS components were precisely mounted in the linear actuator module. The tips of both syringes were closely connected to the 2 mm square duct using the silicone tube, and the speed of both piston syringes was set to 0.002 mm/s. A video-recording camera was positioned close to the surface of the square duct to capture footage of the flowing gel droplets for subsequent analysis of their diameters. After inspecting all the connections, the linear actuator was activated. The actuator started pushing both piston syringes to deliver the NIPA and APS solutions at the same volumetric flow rate. Consequently, both solutions were deposited in front of the needle nozzle prior to mixing and before forming a gel solution (considered as dispersed flow). A constant dispersed flow rate (\(Q_{d}\)) of 3.2 \(\times\) 10\({}^{-10}\) m\({}^{3}\)/s was maintained throughout the study. The gel solution was then ejected from the nozzle's tip (outside diameter = 300 \(\upmu\)m) while the other co-flow of silicone oil (continuous-phase flow) was simultaneously ejected in the same direction by another pump (mzr-2521, HNP Mikrosysteme, Schwerin, Germany). The co-flows inside the square duct were primarily responsible for forming the gel droplets. Finally, all the gels were collected in a silicone oil reservoir on a cold plate, which was maintained at a constant temperature of \(-\)30 \({}^{\circ}\)C. In particular, the silicone tube within the reservoir was sufficiently long to increase the residence time of the gel droplets for the freezing process, which prevented droplet coalescence. The resulting gels were then stored in a freezer for 1 day to complete the polymerization process, and the diameter of the gel droplets flowing within the square duct was measured via image analysis. Based on the output of the diameter readings, the average diameter of the gels was calculated.