Modeling of turbulent drop coalescence in the presence of electrostatic forces

Droplet breakage and coalescence in liquid–liquid dispersions: Comparison of different kernels with EQMOM and QMOM

“…In such pure systems significant coalescence can be observed in a very short time, making the system very quick in responding to external stimuli (e.g. change in stirring rate), on the contrary of what happens when surfactants, that makes the system dynamics much slower, are present . The predictions obtained with the MF coalescence and breakage kernels are here compared with those obtained with the first, and still very popular, kernels proposed by Coulaloglou and Tavlarides and referred to in the rest of the manuscript as CT kernels.…”

“…change in stirring rate), on the contrary of what happens when surfactants, that makes the system dynamics much slower, are present. 38,47 The predictions obtained with the MF coalescence and breakage kernels are here compared with those obtained with the first, and still very popular, kernels proposed by Coulaloglou and Tavlarides 1 and referred to in the rest of the manuscript as CT kernels. In fact, although the CT kernels were derived for immobile interfaces they are often used to describe nonstabilized dispersions, such as the ones considered in this work.…”

The Influence of Internal Intermittency, Large Scale Inhomogeneity, and Impeller Type on Drop Size Distribution in Turbulent Liquid-Liquid Dispersions

“…A multifractal model allows the probability of stresses characterized by different multifractal exponents, α, for a given average energy dissipation rate calculated for a given zone to be predicted. Such a model gives excellent results in predicting drop size evolution as was shown in previous papers [30,33,43]. The details of the flow pattern were not used.…”

“…This extra stress is due to the difference between the dynamic interfacial tension of the fresh surface (exposed during drop deformation under the action of pressure fluctuations), σ t→0 , and static interfacial tension, σ [28]. This extra stress is observed when surfactant can be easily removed from the surface [28,33], but is not observed when surface active additive is strongly grafted to the surface [43]. The multifractal exponent characterizing the weakest eddies that can disperse the drop covered with surfactant, which can be removed from the surface during its deformation, is given by [28]:…”

“…Models for droplets smaller than the Kolmogorov scale were also formulated using multifractal formalism [2]. Multifractal breakage and coalescence models allow proper predictions to be made of the changes of the drop size distribution both for short and long agitation times [2,[28][29][30][31][32][33]. The coalescence process can be considered as an interaction triangle consisting of the continuous phase flow and two fluid particles.…”