## 1 Introduction
Furthermore, the effect of flat-tip wettability (metallic nozzle) on droplet-size formation revealed that when a droplet of liquid is applied to the wetted flat tip of the nozzle, further adhesion forces occur on the base of the droplet and affect the attachment range. Hence, the intensity of adhesion tensions in the metal phase, the dispersed phase, and the continuous phase determine the contact area of the phase fluids, which consequently affect the droplet size [38]. [PERSON] et al. reported a flow-focusing method in which the initial strength of polymer concentration affected the droplets' mean particle-size distribution [39]. A high polymeric concentration caused an increase in mean particle-size distribution, which was attributed to the correlation between lower concentrations of polymer solution and lower viscosity of the dispersed phase and vice versa. Therefore, the force required by the droplet to break off from its dispersed-phase flow reduced [39]. Studies have also suggested that a lower concentration of polymeric solution in the continuous-phase flow is preferable for narrower particle dispersion. Similar results were reported by [PERSON] et al. regarding the formation of microspheres using a modified water-in-oil-in-water emulsion solvent-evaporation technique [40]. The effects of orifice length and width on droplet size in a flow-focusing device were investigated by [PERSON] et al. [41]. Their research revealed that by increasing the orifice length, the droplet size exponentially decreased until it became constant at a certain critical length and continued further beyond this length. Furthermore, by increasing the width of the orifice, a non-linear increase in droplet size occurred, and a constant orifice width resulted in the creation of a smaller-sized droplet as the capillary number increased. In their study, the effect of the capillary number on droplet size was similar to the findings reported by [PERSON] et al. [29] and [PERSON] et al. [30]. Regarding the connection between continuous-phase velocity and drop-formation time, the higher the velocity of the continuous-phase flow, the lower the drop-formation time [20]. Other studies highlight the effect of the continuous-phase flow (bond number, capillary number, and viscosity ratio) on droplet-break-off length, droplet-break-off time, and droplet volume [25]. Increasing the continuous-phase flow rate increased the flow's Reynolds number [22; 24]. According to [PERSON] et al., in one case, neither the continuous-phase flow rate nor the diameter of the external tube affected the average drop-size diameter in a jetting regime in which droplet breakage occurred some distance from the tip of the nozzle [27]. The episodic motions continuously occur provided a relevant condition supporting the movements that can be maintained, i.e., the satisfactory concentration of the solution, the appropriate gel diameter, and a preserved temperature difference between the upper and lower walls of the enclosure. The cyclical motion of the gels within the cavity is a function of time and is determined by the sum of the external forces acting on the gels, including gravity, drag, and buoyancy. In particular, these forces are affected by variables such as solution density,gel density, drag coefficient, and gel size. To summarize, based on the abovementioned studies and as a continuation of the previous research reported by [PERSON] et al. [13], the current study's preference is for a typical gel with a smaller contact surface (i.e., a sphere). Gels of various sizes are required to observe their behavior in an upper heating system of a rectangular cavity filled with aqueous solutions. The spherically shaped monodispersed gels were generated using a microfluidic device with a constant micro-sized nozzle (outside diameter = 300 \(\upmu\)m) by varying the viscosity and flow rate of the continuous-phase flow.