## 3 Results  
Figure 1b shows the evaporation of both pure water and an aqueous urea solution at an ambient temperature of 24 \(\pm\) 0.2 \({}^{\circ}\)C and a relative humidity of 42 \(\pm\) 2%. The interplay  
Figure 1: **(a)** Schematic of the experimental setup for contactless thermography measurement of a supersaturating droplet. **(b)** Drying kinetic curves of pure water droplet (red) and urea solution droplet with an initial concentration of 76 g/100 mL (blue). **(c)** A saturation curve exemplifying the behavior of levitated droplets containing urea solution. between the sound pressure acting on the sample surface and its surface tension resulted in a continuous alteration of the vertical-to-lateral dimensions ratio throughout the entire evaporation process. To measure volume changes over time, sequential snapshots of backlight-illuminated droplet images were captured. An edge detection algorithm was employed to extract the droplet's shape profile from these images. Subsequently, a 6 th-order Legendre polynomial fitting was used to obtain volumes of the droplet as a function of time [26]. Assuming a spherical shape of the drop, this procedure enabled the calculation of the temporal evolution of its diameter, represented as \(D(t)\). As depicted in Figure 1a, the drying kinetics of the pure water drop followed the \(D^{2}\) law [26; 30], indicating that the square of the droplet diameter decreased linearly over time according to the following relationship:  
\[\frac{D(t)^{2}}{D_{o}^{2}}=1-\beta\frac{t}{D_{o}^{2}}, \tag{1}\]  
where \(D_{o}\) is the diameter of the droplet at t = 0. The evaporation rate \(\beta\) = 2.88 \(\times\) 10\({}^{-3}\) mm\({}^{2}\)/s was obtained by fitting Equation (1) to the water data. Assuming the evaporation of water is solely during levitation, the evaporation kinetics of the urea solution were considered. This assumption is grounded in the non-volatile nature of urea, which resulted in a minimal initial-to-final mass difference of less than 1%. Thus, the evaporation of the solution led to a progressive rise in solute concentration. As shown in Figure 1b, within the relatively dilute concentration range, its evaporation kinetic was close to that of the water. However, this rate continuously decreased with increasing solute concentration, eventually falling below 20% of the water's rate beyond its solubility limit. Figure 1c illustrates the water activity-corrected supersaturation curve [31; 32] for the urea solution across relevant time scales. When the supersaturation reached approximately S = 2, a rapid solidification occurred within 0.2 s (see Figure 2 (top)). Figure 2: **(top)** The top view of the time-lapse images shows a rapid progression of crystallization within the levitated droplet. The position where crystallization initiates is indicated by the yellow arrow. **(bottom)** Differential temperature curve measured from the droplet surface as a function of time. The instant at which the temperature of the droplet begins to rapidly increase near S = 2 coincides with the initial time point \(\Delta\)t = 0.00 s in the figure above. The time span denoted by the red arrow signifies the supersaturated regimes, while the blue arrow marks the subsequent progression following the onset of crystallization. The surface temperature of the supersaturating solution droplet was monitored by using an IR thermographic camera with an emissivity value of 0.9. The measurement was performed at a constant interval of 0.2 s throughout the entire evaporation and solidification processes. Overall, a progressive increase in droplet temperature was measured with increasing solute concentration, and this trend continued until the culmination of final crystallization. Furthermore, our data showed a concurrent temperature increase with slowing evaporation rates. As shown in Figure 2 (bottom), the temperature increase within the initial 1000 s after levitation was minimal, suggesting the presence of a stable hydration structure in the solution.