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Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows

Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the flow. Number of closures for both breakup and coalescence can be identified in the literature and most of them need an estimation of model parameters that can differ even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identification allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup and co- alescence models over multiple cases and we propose a correlation based on non-dimensional numbers that is applicable to number of different flows over wide range of Reynolds numbers.