Theoretical model of the Bergeron–Findeisen mechanism of ice crystal growth in clouds

A numerical study of growth rate of ice particles in an array of water droplets (Bergeron–Findeisen mechanism) has used the method of electrostatic image charges to determine the vapour field in which a particle grows. Analysis of growth rate in various conditions of relevance to clouds has shown that it is proportional to liquid water content and to ice particle size, while it is inversely proportional to cloud droplet size. The results show that growth rate is enhanced by several percent relative to the usual treatment in which vapour is assumed to diffuse from infinity towards a growing ice particle. The study was performed for ice particles between 25 and 150 μm radii, water droplet sizes between 6 and 20 μm diameter and a wide range of liquid water contents. A study was also made to determine the effect of reducing the vapour source at infinity so that the droplets alone provided the vapour for particle growth. A parameterisation of ice particle growth rate is given as a function of liquid water content and ice particle and droplet sizes. These studies are of importance to considerations in thunderstorm electrification processes, where the mechanism of charge transfer between ice particles and graupel could take place.