Exploring an approximation for the homogeneous freezing temperature of water droplets

Abstract

Abstract. In this work, based on the well-known formulae of classical nucleation theory (CNT), the temperature TNc = 1 at which the mean number of critical embryos inside a droplet is unity is derived from the Boltzmann distribution function and explored as an approximation for homogeneous freezing temperature of water droplets. Without including the information of the applied cooling rate γcooling and the number of observed droplets Ntotal_droplets in the calculation, the approximation TNc = 1 is able to reproduce the dependence of homogeneous freezing temperature on drop size V and water activity aw of aqueous drops observed in a wide range of experimental studies for droplet diameter > 10 µm and aw > 0.85, suggesting the effect of γcooling and Ntotal_droplets may be secondary compared to the effect of V and aw on homogeneous freezing temperatures in these size and water activity ranges under realistic atmospheric conditions. We use the TNc = 1 approximation to argue that the distribution of homogeneous freezing temperatures observed in the experiments may be partly explained by the spread in the size distribution of droplets used in the particular experiment. It thus appears that the simplicity of this approximation makes it potentially useful for predicting homogeneous freezing temperatures of water droplets in the atmosphere.