The validity of the kinetic collection equation revisited

Abstract

The kinetic collection equation (KCE) describes the evolution of the average droplet spectrum due to successive events of collision and coalescence. Fluctuations and non-zero correlations present in the stochastic coalescence process would imply that the size distributions may not be correctly modeled by the KCE. In this study we expand the known analytical studies of the coalescence equation with some numerical tools such as Monte Carlo simulations of the coalescence process. The validity time of the KCE was estimated by calculating the maximum of the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value. A good correspondence between the analytical and the numerical approaches was found for all the kernels. The expected values from analytical solutions of the KCE, were compared with true expected values of the stochastic collection equation (SCE) estimated with Gillespie's Monte Carlo algorithm and analytical solutions of the SCE, after and before the breakdown time. The possible implications for cloud physics are discussed, in particular the possibility of application of these results to kernels modified by turbulence and electrical processes.