Abstract: The accurate prediction of the droplet size distribution (DSD) in liquid-liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model. When a surfactant is included in liquid-liquid dispersions, the droplet breakup behavior will change as an effect of the reduction of the interfacial tension. Moreover, also the dynamic interfacial tension may be different with respect to the static, due to the fact that the surfactant may be easily desorbed from the droplet surface, generating additional disruptive stresses. In this work, the performance of five breakup kernels from the literature is assessed, to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter, when different surfactants are employed. Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressibleTwoPhaseEulerFoam solver of the open-source computational fluid dynamics (CFD) code OpenFOAM v. 2.2.x. The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants (Tween 20 and PVA 88%) at different concentrations operating under different stirrer rates. Our results show that for the dispersion containing Tween 20 additional stress is generated, the multifractal breakup kernel properly predicts the DSD evolution, whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA. Kernels derived originally for bubbles completely fail.

Key words: Breakup, Stirred tank, Liquid-liquid dispersions, Interfacial tension, CFD-PBM

摘要： The accurate prediction of the droplet size distribution (DSD) in liquid-liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model. When a surfactant is included in liquid-liquid dispersions, the droplet breakup behavior will change as an effect of the reduction of the interfacial tension. Moreover, also the dynamic interfacial tension may be different with respect to the static, due to the fact that the surfactant may be easily desorbed from the droplet surface, generating additional disruptive stresses. In this work, the performance of five breakup kernels from the literature is assessed, to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter, when different surfactants are employed. Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressibleTwoPhaseEulerFoam solver of the open-source computational fluid dynamics (CFD) code OpenFOAM v. 2.2.x. The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants (Tween 20 and PVA 88%) at different concentrations operating under different stirrer rates. Our results show that for the dispersion containing Tween 20 additional stress is generated, the multifractal breakup kernel properly predicts the DSD evolution, whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA. Kernels derived originally for bubbles completely fail.

关键词: Breakup, Stirred tank, Liquid-liquid dispersions, Interfacial tension, CFD-PBM