## 1 Introduction
They used cylindrical-shaped thermosensitive gels that were flat on both sides. One of the gels showed a vertical motion frequency of one cycle per 10 min for a duration of 230 min within a PAA solution. Other gels became easily attached to each other; they frequently adhered to the walls of the rectangular cavity, which promptly stopped their vertical movements because of the large contact areas on their flat sides. However, observations of NIPA gel behavior within an upper heating rectangular cavity have not received considerable attention, and literature on this topic is quite limited. [PERSON] et al. revealed that for NIPA gel particles that are smaller than 200 nm, as their cross-linking density decreases, the volume change of the NIPA particles becomes more discontinuous [14]. This result corresponds with that obtained by [PERSON] and [PERSON] [15]. Furthermore, the behavior of the gels at lower temperatures of about 20 \({}^{\circ}\)C demonstrates that those gels with a lower cross-linking density tend to have higher swelling rates than those with higher cross-linking densities. In fact, the temperature at which the gels start to swell is higher for those gels with higher cross-linking densities [14]. Moreover, the swelling behavior of NIPA gels is enhanced by increasing the gels' porous structures [16, 17, 18, 19]. The addition of an initiator, such as dodecyl dimethyl benzyl ammonium bromide (DDBAB) and ammonium persulfate (APS), produced a hydrophobic initiator, dodecyl dimethyl benzyl ammonium persulfate, which provides a heterogeneous initiation mechanism and triggers the development of macro-porous structures [18] and an increased temperature response in the gel, as reported by [PERSON] et al. [18,19]. Recently, NIPA gels of various shapes and sizes have been produced. To minimize size variations, monodispersed spherical-shaped gels are generally made in laboratory scales using microfluidic devices [20, 21, 22, 23, 24, 25]. The droplet diameter is controlled by adjusting the droplet-breakup mechanism, which is affected by the capillary number of the continuous-phaseflow [26; 27; 28]. Previously, studies have reported that increases in flow-rate ratios and capillary numbers correspond to a significant decrease in droplet diameter [29; 30]. The flow rate of the continuous phase plays a significant role in controlling droplet size. A reduced flow rate in the continuous phase affects the neck length, current contact angle, and mean drop-growth velocity, which in turn affects droplet formation [31]. Other studies highlight the significant effect of interfacial tension on droplet size [32; 33]. Furthermore, density differences between the continuous-phase flow and the dispersed flow affect the formation of the droplet's diameter as has been explained by [PERSON] et al. [34]. Based on research by [PERSON] et al., by implementing two different diameters of a capillary tube for a constant velocity of the dispersed-phase flow, the droplet-size formation in both tubes decreased as the continuous-phase flow velocity increased. In their study, the diameter difference between the capillaries was quite small; therefore, decreases in droplet size were primarily affected by the drag force triggered by the continuous-phase flow [35]. Similar to the results reported by [PERSON] et al. [32] and [PERSON] et al. [33], according to those reported by [PERSON] et al., drop-size formation correlates with the interfacial tension in the two phases, in addition to capillary tip diameter and viscosity. Thus, during droplet formation, the detachment of a droplet from its capillary occurs when stream-wise forces exceed the force induced by interfacial tension [36]. Moreover, droplet size is affected by the junction geometry of the microfluidic devices, the flow rates of the continuous phase, and the physical characteristics of the fluid i.e., its interfacial tension and viscosity [37].