We investigate the arrested spreading of room temperature droplets impacting flat ice. The use of an icy substrate eliminates the nucleation energy barrier, such that a freeze front can initiate as soon as the droplet’s temperature cools down to $0°\mathrm{C}$. We employ scaling analysis to rationalize distinct regimes of arrested hydrodynamics. For gently deposited droplets, capillary-inertial spreading is halted at the onset of contact line freezing, yielding a $1/7$ scaling law for the arrested diameter. At low impact velocities ($\mathrm{We}\lesssim 100$), inertial effects result in a $1/2$ scaling law. At higher impact velocities ($\mathrm{We}>100$), inertio-viscous spreading can spill over the frozen base of the droplet until its velocity matches that of a kinetic freeze front caused by local undercooling, resulting in a $1/5$ scaling law.

中文翻译：

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液滴在冰上扩散的动力学受阻

我们调查了影响平冰的室温液滴的停滞扩散。使用冰冷的基底消除了成核能垒，这样一旦液滴的温度冷却到$0°\mathrm{C}$. 我们采用比例分析来合理化不同的停滞流体动力学机制。对于轻轻沉积的液滴，毛细管惯性扩散在接触线冻结开始时停止，产生$1/7$截留直径的比例定律。在低冲击速度下（$\mathrm{我们}\lesssim 100$)，惯性效应导致$1/2$缩放定律。在更高的冲击速度下（$\mathrm{我们}>100$），惯性粘性扩散可以溢出液滴的冻结底部，直到其速度与局部过冷引起的动力学冻结前沿相匹配，导致$1/5$缩放定律。