Frozen patterns of impacted droplets: From conical tips to toroidal shapes

We report frozen ice patterns for the water droplets impacting on a cold substrate through high-speed images. These patterns can be manipulated by several physical parameters (the droplet size, falling height, and substrate temperature), and the scaling analysis has a remarkable agreement with the phase diagram. The observed double-concentric toroidal shape is attributed to the correlation between the impacting dynamics and freezing process, as confirmed by the spatiotemporal evolution of the droplet temperature, the identified timescale associated with the morphology and solidification $(t_{\mathrm{inn}}\simeq {\tau }_{\mathrm{sol}})$, and the ice front-advection model. These results for frozen patterns provide insight into the complex interplay of the rapid impacting hydrodynamics, the transient heat transfer, and the intricate solidification process.

Figure 1

Four frozen patterns are visualized by the high-speed images for the spreading dynamics and the subsequent solidification process during the droplet impacted on a cold substrate at $T_s=-15{}^{\circ }\mathrm{C}$. (a) Ice with a conical tip, (b) a spherical cap on the pancake, (c) a single toroidal shape, and (d) a double-concentric toroidal shape for $H_0$ = 10, 35, 70, and 80 cm, respectively. $t=0$ ms is defined as droplets landing on or starting to impact on the substrate, as shown by the first-column images.

Figure 2

Formation of toroidal shapes at $T_s=-15{}^{\circ }\mathrm{C}$. (a) The full dynamics of $D_{\mathrm{out}}$, indicating ${\tau }_{\mathrm{SCL}}$ during which the bottom-pancake ice is formed. (b) The scaling law of $D_{\max }\sim {\mathrm{We}}^{1/4}$. [(c), (d)] Dynamics of $D_{\mathrm{out}}$ and $D_{\mathrm{inn}}$ for STS and DTS. Sketch mechanism for STS due to the doughnut shape at $t_{\mathrm{out}}$, and for DTS based on the ice front-advection model.

Figure 3

Spatiotemporal evolution of surface temperature for four patterns demonstrates the correlation between the morphology and temperature distribution. The experimental parameters are the same as those in Fig. 1, and [(a)–(d)] for $H_0=10$, 35, 70, and 80 cm, respectively.

Figure 4

Phase diagram of frozen patterns dependent on ${\tilde{H}}_0$ and ${\tilde{D}}_0$ ($T_s=-20{}^{\circ }\mathrm{C}$), and their transition described excellently by the scaling law of ${\tilde{D}}_0\sim {\tilde{H}}_0^{\alpha }(\alpha =-1/5,-3/2,-2)$.

Figure 5

Mechanism of DTS due to the coupling of the droplet impacting hydrodynamics and solidification ($T_s=-15{}^{\circ }\mathrm{C}$). (a) A typical synchronized high-speed image (top) and thermal image (bottom) at $t=88$ ms, revealing the correlation between the morphology and temperature distribution ($H_0=80$ cm). (b) Spatiotemporal evolution of the observed temperature along a horizontal line $R_{\mathrm{position}}$ in panel (a), the white line for the zero isotherm. (c) The identified $t_{\mathrm{inn}}\simeq {\tau }_{\mathrm{sol}}$, and error bars for three experiments. (d) The calculated ${\tau }_{\mathrm{cross}}$ from Eq. (8) around 10 ms corresponding to $T_{sl}$ from the heat transfer model.