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A General Model for Temperature of Heterogeneous Nucleation of Supercooled Water Droplets

W. E. BardsleyEarth Sciences, University of Waikato, Hamilton, New Zealand

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M. M. KhatepDepartment of Geology, University of Otago, Dunedin, New Zealand

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Abstract

Asymptotic extreme-value theory is used as the basis of a stochastic model which predicts aspects of the freezing behavior of supercooled water droplets. The model gives a general theoretical base to an earlier empirical function relating droplet volume to droplet freezing temperature. At the same time, the model indicates that the established empirical relation is only one of three possible functions linking droplet volume and temperature of freezing.

The free functions arise as a consequence of three possible extreme-value distributions of droplet freezing temperatures, and the form of each function predicts the type and parameter values of the distributions concerned. The proposed model is amenable to rigorous experimental verification since both the distribution type and parameter values can be estimated independently from droplet freezing data.

Abstract

Asymptotic extreme-value theory is used as the basis of a stochastic model which predicts aspects of the freezing behavior of supercooled water droplets. The model gives a general theoretical base to an earlier empirical function relating droplet volume to droplet freezing temperature. At the same time, the model indicates that the established empirical relation is only one of three possible functions linking droplet volume and temperature of freezing.

The free functions arise as a consequence of three possible extreme-value distributions of droplet freezing temperatures, and the form of each function predicts the type and parameter values of the distributions concerned. The proposed model is amenable to rigorous experimental verification since both the distribution type and parameter values can be estimated independently from droplet freezing data.

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