## 3 Results and Discussion
Evidently, at 170 min, the amplitude of gel 1 was considerably reduced because of collision and adhesion with gel 3, which caused a counteraction of their movements. The gels eventually broke up, and gel 1 started moving again; however, all the gels stopped moving at 250 min. Figure 14 shows the gel movements of case B. Although the amplitude of the vertical motion was small compared with case A, the gels exhibited similar movements for a period of 10 min followed by a gradual decrease in amplitude. At the start of the experiment for case B, some gels became stuck to the heat transfer surfaces (gels 1 and 4 were on top, and gel 3 was on the bottom). Gels 1 and 2 became affixed to other gels (whose trajectories are not shown) at 100 and 120 min, respectively, and could no longer be tracked. At 140 min, gel 4 became stuck to six other gels to form a cluster of seven. Gel 3 was the only gel that individually moved until the end of the experiment. Figure 12: The periodic movement of gels (Case A) in the PAANa solution from 28–40.67 min after the start in increments of 40 sec. The trajectories of the particles in circles are shown in Figure 13 with the corresponding colors. Figure 15 showed the results for case C. At the start, gel 1 was positioned at \(\sim\)5 mm from the bottom of the cavity in a state of shrinkage. It then started to move downward until it reached a position at 2 mm above the base of the cavity. At this level, the gel was affected by the lower temperature of the cooling source, and it started to swell; a quantity of surrounding fluid entered the gel's structure, and its diameter slowly increased. The gel's density became lower than that of the surrounding PAANa solution, and it started to gradually move upward until it reached a position at 3.5 mm above the base of the cavity. In this position, the gel started to shrink again because of the higher temperature of the surrounding fluid. A specific amount of aqueous polymer solution was squeezed out of the gel's structure, and its density became higher than that of the solution. Consequently, the gel moved downward again until it reached a position 3 mm above the base of the cavity. Over time, only very small fluctuations in position were observed, and the gel became stagnant at 2.8 mm above the base of the cavity. In this case, the up-down movement was only seen during approximately the first 20 min. Similar patterns of small initial amplitudes and short continuations of up-down movements were observed for case D, as shown in Figure 16. There is a difference in the oscillation modes of the gels in cases B and C, which could not be clarified in this study. However, the up-down movement continued until the gels and their surrounding fluids reached a state of equilibrium, at which point  
Figure 14: Case B in the PAANa solution. Figure 13: Vertical movements of case A gels in the PAANa solution. aqueous solution. Furthermore, because buoyancy force exceeded gravitational force, the particles tended to float. The gels with larger diameters tended to have longer vertical periodic movements and required more time to reach their equilibrium state compared with gels with smaller diameter. Conceptualization, M.H. ; methodology, M.H. ; validation, R.R.S. and M.H. ; investigation, R.R.S., K.N., and Y.N. ; writing, R.R.S., K.N., and M.H. ; supervision, M.H. and Y.T. All authors have read and agreed to the published version of the manuscript. This research was funded by JSPS KAKENHI, grant number JP17K06191, and the Indonesia Endowment Fund for Education (LPDP) in providing funding via a BUDI-LN Scholarship Scheme. The authors declare no conflict of interest.