Application of the master equation to coalescence and dispersion phenomena

Abstract In the present work the master equation is applied to the phenomena of coalescence and dispersion. Specifically, expressions are derived to model binary coalescence and breakage with a particular emphasis on the results which are unique to the stochastic treatment, namely the covariances and correlation functions. A probabilistic analysis is also introduced in an attempt to rationally derive the daughter size distribution from knowledge about breakage probabilities of individual droplets or particles. This analysis is valid for binary or higher order breakage and any combination thereof. One possible assignment of the probability for binary breakage is proposed; it is based on the excess surface energy of a dispersed phase droplet. Finally, the general contributions of stochastic models are discussed.