title: 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 buildup 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 (submillimetric) 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.
authors.affiliation: Physics of Fluids group, University of Twente, 7500 AE Enschede, The Netherlands.
authors.forename: Sander
authors.initials: S
authors.lastname: Wildeman
authors.affiliation: Physics of Fluids group, University of Twente, 7500 AE Enschede, The Netherlands.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Sterl
authors.affiliation: Physics of Fluids group, University of Twente, 7500 AE Enschede, The Netherlands.|Centre for Combustion Energy and Department of Thermal Engineering, Tsinghua University, 100084 Beijing, China.
authors.forename: Chao
authors.initials: C
authors.lastname: Sun
authors.affiliation: Physics of Fluids group, University of Twente, 7500 AE Enschede, The Netherlands.|Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.
authors.forename: Detlef
authors.initials: D
authors.lastname: Lohse