Collisions between Small Precipitation Drops. Part II: Formulas for Coalescence, Temporary Coalescence, and Satellites

Abstract

Collisions between small precipitation drops in free fall were analyzed for sizes applicable to self-collection, the process that controls the spreading of precipitation drops to larger sizes. Results from 45 laboratory experiments were generalized using dimensionless parameters to scale the coalescence efficiency, for the temporary coalescence probability, and the satellite occurrence frequency. The coalescence efficiency for uncharged drops (?0) was found to be highly correlated (? = 0.99) with a simple combination of factors that scale the tendency for colliding drops to bounce apart as a function of the Weber number (We) and size ratio (p). Charge-induced coalescence was scaled by the electric field between the drops, assuming charged conducting spheres. The coalescence efficiency was obtained as a function of the normalized charge using a semiempirical formula (? = 0.95) for the amount of charge required to eliminate bounce and temporary coalescence. The occurrence of temporary coalescence is predicted by p We > 4 with a lower limit of p We > 1 for charge-induced coalescence. The fraction of collisions resulting in temporary coalescences increased with (1 ? ?0)p We, whereas the fraction of collisions producing satellites increased with (1 ? ?0) We2. Both fractions were highly correlated with their respective scaling parameters (? = 0.99). Satellite drop radii were found to increase linearly with the geometric mean radius of the parent drops. Mass transfer in collisions involving temporary coalescence and satellite generation was estimated for use in modeling studies. Contour diagrams are provided for coalescence efficiency, temporary coalescence probability, and satellite occurrence frequency over a wide range of drop sizes for comparison with formulas based on previous laboratory results in the accretion and breakup regimes. Recommendations are given for applying present formulas to self-collection, as well as extending our findings to accretion and breakup.