A coalescence redispersion model for drop-size distributions in an agitated vessel

A population balance model has been developed accounting for coalescence and redispersion of drops in an agitated liquid—liquid dispersion. It is assumed that drop coalescence is followed by immediate redispersion into two drops whose sizes are distributed according to a uniform distribution in the ratio of the daughter drop-volume to the parent drop-volume. If it is assumed that the coalescence frequency is independent of drop-size, the resulting non-linear integral equation admits an exponential solution for the equilibrium drop-volume distribution in a batch vessel. On comparing experimental data obtained from several sources with the prediction of this model, it is found that for flat-blade turbine agitated systems, the agreement is very good; in fact, the sign test ranks the model as better fitting than empirical expressions for drop-sizes proposed by other workers. For circulation stirring systems, e.g. those having Waldhof agitator, the model predictions are substantially improved by assuming that the coalescence frequency is proportional to the diameters of the interacting drops.