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

摘要

Population balance framework is a useful tool that can be used to describe size distributionof droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures formathematical formulation of the population balance equation (PBE) and are crucial for accu-rate predictions of the mean droplet size in the ow. Number of closures for both breakup andcoalescence can be identi ed in the literature and most of them need an estimation of modelparameters that can di er even by several orders of magnitude on a case to case basis. In thispaper we review the fundamental assumptions and derivation of breakup and coalescence ker-nels. Subsequently, we rigorously apply two-stage optimization over several independent sets ofexperiments in order to identify model parameters. Two-stage identi cation allows us to estab-lish new parametric dependencies valid for experiments that vary over large ranges of importantnon-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-dimensionalnumbers that is applicable to number of di erent ows over wide range of Reynolds numbers.