Wildeman Sander, Sterl Sebastian, Sun Chao, Lohse Detlef
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.
Phys Rev Lett. 2017 Feb 24;118(8):084101. doi: 10.1103/PhysRevLett.118.084101. Epub 2017 Feb 23.
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.
水在冻结时的膨胀与坚硬冰壳的自我限制不相容。通过高速成像，我们表明这个难题是通过脆性冰壳的间歇性破裂和封闭液体中的空化来解决的，最终导致部分冻结的液滴爆炸。我们提出了一个基本模型来阐明应力的稳定积累与其快速释放之间的相互作用。该模型表明，对于毫米级的液滴，爆炸时的碎片速度与液滴大小无关，仅取决于材料特性（如冰的拉伸应力和水的体积模量）。另一方面，对于小（亚毫米级）液滴，表面张力开始起作用。在这种情况下，我们预测半径低于50μm的水滴根本不太可能爆炸。我们预计我们的发现与冻结云滴和雨滴的建模相关。
