Extended spreading of saline droplets upon impact on a frosty surface

Understanding the solidification dynamics of impacted water droplets is fundamental and crucial for applications, especially with the presence of frost and salt. Here, we experimentally investigate the spreading and freezing dynamics of saline droplets upon impact on a cold, frosty surface. Our findings demonstrate that the frost and salt can lead to an extended spreading of impacted droplets under specific conditions. In addition to the well-known 1/2 inertial spreading scaling law for droplets impact on a cold substrate, we observe a distinct transition to a 1/10 scaling law dominated by the capillary-viscous relation at low impacting velocities. We formulate the onset criterion for this extended spreading regime and derive a scaling dependence that captures the droplet's arrested diameter over various supercooling temperatures, by incorporating the effect of impact inertia, partial-wetting behavior, and salinity. Based on the analysis, a unified model is proposed for predicting the droplet arrested diameter over a wide range of impact velocity and salinity.

Figure 1

Experimental setup.

Figure 2

Characterization of the frosty substrate. (a-b) Macro- and micro-scale visualization of the frost. (c) Size distribution of frost sites.

Figure 3

Extended spreading dynamics of saline droplet impacting on a frosty substrate. (a) Schematic of droplet impacting, spreading, and arresting. (b)–(d) Snapshots for water and saline droplets impacting on the cold substrate maintained at the same temperature $T_s=-{20}^{\circ }\mathrm{C}$ and the same velocity $U_0=1.0$ m/s; (b) Water droplet impacts on a surface without frost; (c) Water droplet impacts on a surface with frost; (d) Saline droplet ($S_i=15\%$) impacts on a surface with frost; (e) Spreading diameter versus time corresponds to the droplets in (b)–(d).

Figure 4

Effect of $U_0$ and $S_i$ on the spreading dynamics of saline droplets impacting on a frosty substrate. (a) $U_0=0.8$ m/s, $We\approx 30$; (b) $U_0=1.9$ m/s, $We\approx 180$; (c) $U_0=2.9$ m/s, $We\approx 400$. The substrate is maintained at the same temperature $T_s=-15{}^{\circ }\mathrm{C}$.

Figure 5

Normalized arrested diameter $D_{\mathrm{arrest}}/D_0$ as a function of $We$ of saline droplet impacting on a frosty substrate.

Figure 6

Normalized arrest time of saline droplet impacting on a frosty surface.

Figure 7

Phase diagram for spreading dynamics of saline droplet impacting on a frosty substrate. The triangle and the square represent the presence and absence of the extended spreading stage, respectively. The shaded region represents the spreading process without freezing.

Figure 8

Dimensionless arrested diameter $D_{\mathrm{arrest}}/D_0$ as a function of dimensionless supercooling temperature $\mathrm{\Delta }T/\sqrt{\gamma /\kappa \mu }$. The square and the circle represent $We\approx 80$ and $We\approx 30$, respectively.

Figure 9

Comparison of the dimensionless arrested diameter $D_{\mathrm{arrest}}/D_0$ between the experimental measurements and the model predictions.

Figure 10

Sketch of the droplet profile.