Abstract. Because homogeneous ice nucleation is important for atmospheric science, special assays have been developed to monitor ultra-pure nanoscale water droplets for nucleation as the temperature is gradually lowered to deeply supercooled conditions. To analyze the experimental data and predict droplet freezing, we develop model that accounts for the cooling rate and the distribution of droplet sizes. We use the model to analyze two sets of experimental homogeneous nucleation data with carefully controlled cooling rates and droplet sizes. Rate expressions based on classical nucleation theory describes both experiments well and with rate parameters in approximate agreement with theoretical predictions based on the thermodynamics of water. We further demonstrate that a failure to account for dispersion in droplet volumes reduces the apparent barriers for ice nucleation. We provide an open source code to estimate nucleation parameters from drop-freezing assays, and another code to account for dispersion of droplet volumes and predict the outcome of drop-freezing experiments. We also present a sensitivity analysis to find the effect of temperature uncertainty on the measured nucleation spectrum. Our framework may be directly useful in accounting for droplet polydispersity and cooling rates for ice nucleation in clouds. Although our analysis pertains to homogeneous nucleation, we note that similar strategies may be applied to heterogeneous ice nucleation on minerals and organic particles with variable surface areas and nucleation sites.

中文翻译：

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液滴冷冻实验中的冰成核：液滴体积分散和冷却速率的影响

摘要。由于均匀冰成核对于大气科学很重要，因此开发了特殊的测定方法来监测随着温度逐渐降低至深度过冷条件的超纯纳米级水滴的成核。为了分析实验数据并预测液滴冻结，我们开发了考虑冷却速率和液滴尺寸分布的模型。我们使用该模型来分析两组实验均质成核数据，并仔细控制冷却速率和液滴尺寸。基于经典成核理论的速率表达式很好地描述了这两个实验，并且速率参数与基于水热力学的理论预测大致一致。我们进一步证明，未能考虑液滴体积的分散会减少冰成核的明显障碍。我们提供了一个开源代码来估计液滴冷冻实验的成核参数，以及另一个代码来解释液滴体积的分散并预测液滴冷冻实验的结果。我们还提出了敏感性分析，以找出温度不确定性对测量的成核光谱的影响。我们的框架可能直接用于解释云中冰核形成的液滴多分散性和冷却速率。尽管我们的分析涉及均质成核，但我们注意到类似的策略可以应用于具有可变表面积和成核位点的矿物和有机颗粒上的异质冰成核。