Nonthermal ice nucleation observed at distorted contact lines of supercooled water drops

Ice nucleation is the crucial step for ice formation in atmospheric clouds and therefore underlies climatologically relevant precipitation and radiative properties. Progress has been made in understanding the roles of temperature, supersaturation, and material properties, but an explanation for the efficient ice nucleation occurring when a particle contacts a supercooled water drop has been elusive for over half a century. Here, we explore ice nucleation initiated at constant temperature and observe that mechanical agitation induces freezing of supercooled water drops at distorted contact lines. Results show that symmetric motion of supercooled water on a vertically oscillating substrate does not freeze, no matter how we agitate it. However, when the moving contact line is distorted with the help of trace amounts of oil or inhomogeneous pinning on the substrate, freezing can occur at temperatures much higher than in a static droplet, equivalent to $\sim {10}^{10}$ increase in nucleation rate. Several possible mechanisms are proposed to explain the observations. One plausible explanation among them, decreased pressure due to interface curvature, is explored theoretically and compared with the observational results quasiquantitatively. Indeed, the observed freezing-temperature increase scales with contact line speed in a manner consistent with the pressure hypothesis. Whatever the mechanism, the experiments demonstrate a strong preference for ice nucleation at three-phase contact lines compared to the two-phase interface, and they also show that movement and distortion of the contact line are necessary contributions to stimulating the nucleation process.

Figure 1

Response of a $30\mu \text{l}$ (a) pure water and (b) water with a trace amount (10 mg/ml) of pump oil on a silica glass substrate for different amplitudes at 30 Hz and $-17.0\pm 0.5{}^{\circ }\text{C}$. Amplitude is represented by the maximum velocity ($v$ in unit of $cm/s$) of the substrate for each case, with $v=\omega A$. Equal-time increments from individual experiments are separated by vertical red dash lines. The thick blue line is the relative spreading distance measured from a side view. The thin blue line is the estimated uncertainty. The relative spreading distance is defined as $[D\left(t\right)-D_0]/D_0$, where $D\left(t\right)$ is the diameter captured from the side view using 1000 Hz frame rate with $27.8\mu \mathrm{m}$ resolution, and $D_0$ is the diameter of droplet before vibration. Gray lines in (b) are the response of pure water for comparison. The red bars represent the fraction of drops that experience freezing (freezing probability) for each case.

Figure 2

Individual video frames, taken with the high-speed camera (5000 fps), showing pure water (left) and water with a trace (10 mg/ml) of pump oil (right) at different stages of oscillation on a silica glass substrate with 30 Hz and $v_{\text{max}}=56.0\mathrm{cm}/\mathrm{s}$ (see Supplemental Material Movie S1 for pure water [30] and Supplemental Material Movie S2 for water with a trace of oil [30]). (A1) and (B1) represent the state before oscillation. For water, (A2), (A4), and (A6) are examples of maximum spreading area, while (A3) and (A5) are examples of minimum spreading area. For the water with a trace of oil, (B2) is an example of maximum spreading area and (B3) is an example of minimum spreading area before freezing. (B4), (B5), and (B6) show how ice nucleates at the edge and how it propagates inward. Yellow arrows point out the multiple ice nucleation sites.

Figure 3

Example of macroscopic pinning behavior during oscillation of (a) the water droplet with a trace of oil, on a silica glass substrate (see Supplemental Material Movie S3 [30]) and (b) pure water on a PDMS substrate (see Supplemental Material Movie S4 [30]). Yellow arrows indicate the locally curved contact line.

Figure 4

(a) Response of a $30\mu \text{l}$ pure water droplet on a PDMS substrate for different amplitudes at 30 Hz. Format and line styles are as in Fig. 1. The contact line starts to move when $v_{\text{max}}\ge 42.2\mathrm{cm}/\mathrm{s}$, substantially larger than that observed for the silica glass substrate. (b) Fraction of droplets that freeze for different amplitudes with 30 Hz at three temperatures. The green, yellow, and red bars represent the freezing fraction for each case at $-11.0\pm 0.5{}^{\circ }\text{C}$, $-14.0\pm 0.5{}^{\circ }\text{C}$, and $-17.0\pm 0.5{}^{\circ }\text{C}$, respectively. The natural freezing temperature for a static water drop on PDMS is $-24.2\pm 0.4{}^{\circ }\text{C}$. The inset shows the $\mathrm{\Delta }T$ vs. $\mathrm{\Delta }p$ scaling discussed in the text, with $\mathrm{\Delta }{p}_c/\mathrm{\Delta }{p}_b\sim {(v_c/v_b)}^2\sim {(62.2/56.0)}^2=1.23$ compared to $\mathrm{\Delta }{T}_c/\mathrm{\Delta }{T}_b=(24.2-11.0)/(24.2-14.0)=1.29$, $\mathrm{\Delta }{p}_b/\mathrm{\Delta }{p}_a\sim 1.30$ compared to $\mathrm{\Delta }{T}_b/\mathrm{\Delta }{T}_a=1.42$, and $\mathrm{\Delta }{p}_c/\mathrm{\Delta }{p}_a\sim 1.60$ compared to $\mathrm{\Delta }{T}_c/\mathrm{\Delta }{T}_a=1.83$ (a, b, and c are labeled in the red, yellow, and green bars, respectively, with near 0.5 freezing probability). Note that $\mathrm{\Delta }{T}_1/\mathrm{\Delta }{T}_2$ is closer to ${(v_1/v_2)}^2$, as opposed to $v_1/v_2$ or ${(v_1/v_2)}^3$. Uncertainties shown represent the observed temperature variability.