Fast Dynamics of Water Droplets Freezing from the Outside In

Abstract

A drop of water that freezes from the outside-in presents an intriguing problem: the expansion of water upon freezing is incompatible with the self-confinement by a rigid ice shell. Using high-speed imaging we show that this conundrum is resolved through an intermittent fracturing of the brittle ice shell and cavitation in the enclosed liquid, culminating in an explosion of the partially frozen droplet. We propose a basic model to elucidate the interplay between a steady build-up of stresses and their fast release. The model reveals that for millimetric droplets the fragment velocities upon explosion are independent of the droplet size and only depend on material properties (such as the tensile stress of the ice and the bulk modulus of water). For small (sub-millimetric) droplets, on the other hand, surface tension starts to play a role. In this regime we predict that water droplets with radii below 50 µm are unlikely to explode at all. We expect our findings to be relevant in the modeling of freezing cloud and rain droplets.

Cascade Freezing of Supercooled Water Droplet Collectives

“…It has been shown that the shattering of ice spicules, which form during the second stage of freezing, can result in the ejection of rapidly propagating ice particles of a size of about 100 µm, which can cause neighboring droplets to freeze. 22 We carefully analyzed all experiments from Figure 2 where the two droplets froze with F 0.1s t …”

“…This is a very important aspect of the entire icing phenomenon, since droplets do not appear in isolation. Previously, it was demonstrated that freezing can propagate on surfaces by growing frost-halos, 17 ice-bridging, [18][19][20][21] shattering of exploding droplets, 22 and ice shrapnels. 23 Here we report and investigate an unexplored mechanism of cascade freezing amongst supercooled droplets.…”

Initiation of secondary ice production in clouds

“…Another hypothesized mechanism is the shattering of droplets with a diameter of 50 to 100 µm upon freezing (Mason and Maybank, 1960;Cannon et al, 1974;Korolev et al, 2004;Fridlind et al, 2007;Rangno, 2008;Leisner et al, 2014;Lawson et al, 2015;Wildeman et al, 2017). At sufficiently cold temperatures, latent heat release leads to the formation of a liquid core-ice shell structure that eventually shatters upon internal pressure buildup.…”

The effect of secondary ice production parameterization on the simulation of a cold frontal rainband

“…Recent droplet levitation experiments of Leisner et al (2014) and high speed video from Wildeman et al (2017) are elucidating the exact physics behind the shattering of droplets as they freeze. For now, we parameterize this process with the product of a fragment number, a temperature-dependent shattering probability, and the existing droplet freezing tendency:…”

“…This increased pressure eventually leads to spicule ejection or cracking and explosion of the ice shell (Leisner et al, 2014;Wildeman et al, 2017). In ice-ice collisional breakup, the impact of two ice hydrometeors leads to shattering, particularly of dendrites or fragile protuberances (Vardiman, 1978;Takahashi et al, 1995;Yano and Phillips, 2011).…”