Drop breakage in liquid-liquid stirred dispersions : modelling of single drop breakage

A new experimental approach has been developed for the identification of reasonable break-up mechanisms in stirred dispersions and of a physically based model for the daughter drop size distribution. In the experiments, breakage of a single organic droplet and the subsequent fragments formation are analyzed by image processing techniques. The experimental data are then fitted by means of a daughter drop size distribution function written in terms of a probability density function (pdt). The mathematical approach that matches the theoretical requirements and that provides the best fit of the experimental data is the pdf proposed by Diemer and Olson [2002. A moment methodology for coagulation and breakage problems: part 3-generalized daughter distribution functions. Chemical Engineering Science 57(19), 4187-4198]. This is a purely statistical model that does not contain any dependence on physical parameters, such as turbulence intensity and mother drop size. Based on the experimental results, an extension of the Diemer and Olson model is proposed, in which dependence on the Weber number as well as on the mother drop diameter can be inserted. Other models appeared in the literature [Coulaloglou and Tavlarides, 1977. Description of interaction processes in agitated liquid-liquid dispersions. Chemical Engineering Science 32(11), 1289-1297; Konno et al., 1983. Scale effect on breakup process in liquid-liquid agitated tanks. Journal of Chemical Engineering of Japan 16(4), 312-319; Martinez-Bazan et al., 1999. On the breakup of an air bubble injected into a fully developed turbulent flow: part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics 401, 183-207] are also discussed and compared with experimental data. Out of them, the only model that approaches experimental data in a satisfactory way is the model by Martinez-Bazan et al. [1999. On the breakup of an air bubble injected into a fully developed turbulent flow: part 2. Size PDF of the resulting daughter bubbles. Journal of Fluid Mechanics 401, 183-207]. Eventually, the presence of the maximum break-up probability for symmetric breakage, in contrast with some theoretical models published in the literature, is explained and justified by means of energy considerations.