Modelling droplet breakage in continuous emulsification using static mixers in the framework of entire spectrum of turbulent energy

Abstract

Droplets breakage during continuous emulsification in static mixers is investigated in this work. It is clearly shown that for viscous continuous phases, droplet breakage occurs mostly in the dissipation range of isotropic turbulence. To consider this, a modified breakage kernel of Coulaloglou and Tavlarides based on the full turbulence spectrum of Pope is employed within a population balance model to describe the time evolution of the droplet size distribution during the emulsification process. This full-spectrum-based model is tested against a wide range of experimental data and showed to be predictive and accurate. The full-spectrum-based model requires the knowledge of the mean turbulent kinetic energy and the mean energy dissipation rate that are obtained from computational fluid dynamic simulations (CFD). To allow a rapid implementation of the model without time-consuming CFD simulations, a model reduction is proposed based on mean energy dissipation rate estimation through pressure drop measurements only. The new model gives comparable predictive capabilities as that based on CFD simulations with improved computational efficiency.