# Fast dynamics of water droplets freezing from the outside-in

## TL;DR

This study investigates the rapid explosion of water droplets freezing from outside-in, revealing how ice shell fracturing and cavitation lead to droplet breakup, with implications for atmospheric phenomena.

## Contribution

The paper introduces a model explaining the dynamics of water droplet explosions during freezing, highlighting size-dependent behaviors and the role of material properties.

## Key findings

- Droplet explosion velocities are independent of size for millimetric droplets.
- Small droplets below 50 micrometers are unlikely to explode due to surface tension effects.
- The model links stress buildup and release to the explosive breakup process.

## 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 micrometer are unlikely to explode at all. We expect our findings to be relevant in the modeling of freezing cloud and rain droplets.