A Simple Model of Particle Coalescence and Breakup

R. C. Srivastava Department of Geophysical Sciences, The University of Chicago, Chicago, IL 60637

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Abstract

A simple model of the evolution of particle size distributions by coalescence and spontaneous and binary disintegrations is formulated. Spontaneous disintegration involves single particles, while coalescence and binary disintegrations involve pairs of particles. Analytical solutions for the mean mass of the distribution and the equilibrium size distribution are obtained for the case of constant collection kernel and disintegration parameters. At equilibrium, the forms of the size distributions are identical under the action of coalescence and either or both disintegration processes; the particle concentration is proportional to the total mass concentration (M) and the mean mass of the distribution is independent of M when only coalescence and binary disintegrations are operative. At small values of M, the effects of spontaneous disintegrations dominate over those of binary disintegrations while the reverse is the case at large values of M. Some of the findings of the present simple model are in qualitative agreement with the results of numerical calculations of the evolution of raindrop size spectra with realistic formulations of drop coalescence and breakup.

Abstract

A simple model of the evolution of particle size distributions by coalescence and spontaneous and binary disintegrations is formulated. Spontaneous disintegration involves single particles, while coalescence and binary disintegrations involve pairs of particles. Analytical solutions for the mean mass of the distribution and the equilibrium size distribution are obtained for the case of constant collection kernel and disintegration parameters. At equilibrium, the forms of the size distributions are identical under the action of coalescence and either or both disintegration processes; the particle concentration is proportional to the total mass concentration (M) and the mean mass of the distribution is independent of M when only coalescence and binary disintegrations are operative. At small values of M, the effects of spontaneous disintegrations dominate over those of binary disintegrations while the reverse is the case at large values of M. Some of the findings of the present simple model are in qualitative agreement with the results of numerical calculations of the evolution of raindrop size spectra with realistic formulations of drop coalescence and breakup.

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