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 bala...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 compressible Two Phase Euler Foam solver of the open-source computational fluid dynamics(CFD)code Open FOAM 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.展开更多
This paper is concerned with the dispersion of particles on the fluid-liquid interface. In a previous study we have shown that when small particles, e.g., flour, pollen, glass beads, etc., contact an air-liquid interf...This paper is concerned with the dispersion of particles on the fluid-liquid interface. In a previous study we have shown that when small particles, e.g., flour, pollen, glass beads, etc., contact an air-liquid interface, they disperse rapidly as if they were in an explosion. The rapid dispersion is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a large velocity. In this paper we show that motion of particles normal to the interface is inertia dominated; they oscillate vertically about their equilibrium position before coming to rest under viscous drag. This vertical motion of a particle causes a radially-outward lateral （secondary） flow on the interface that causes nearby particles to move away. The dispersion on a liquid-liquid interface, which is the primary focus of this study, was relatively weaker than on an air-liquid interface, and occurred over a longer period of time. When falling through an upper liquid the particles have a slower velocity than when falling through air because the liquid has a greater viscosity. Another difference for the liquid-liquid interface is that the separation of particles begins in the upper liquid before the particles reach the interface. The rate of dispersion depended on the size of the particles, the densities of the particle and liquids, the viscosities of the liquids involved, and the contact angle. For small particles, partial pinning and hysteresis of the three-phase contact line on the surface of the particle during adsorption on liquid-liquid interfaces was also important. The frequency of oscillation of particles about their floating equilibrium increased with decreasing particle size on both air-water and liquid-liquid interfaces, and the time to reach equilibrium decreased with decreasing particle size. These results are in agreement with our analysis.展开更多
文摘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 compressible Two Phase Euler Foam solver of the open-source computational fluid dynamics(CFD)code Open FOAM 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.
文摘This paper is concerned with the dispersion of particles on the fluid-liquid interface. In a previous study we have shown that when small particles, e.g., flour, pollen, glass beads, etc., contact an air-liquid interface, they disperse rapidly as if they were in an explosion. The rapid dispersion is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a large velocity. In this paper we show that motion of particles normal to the interface is inertia dominated; they oscillate vertically about their equilibrium position before coming to rest under viscous drag. This vertical motion of a particle causes a radially-outward lateral （secondary） flow on the interface that causes nearby particles to move away. The dispersion on a liquid-liquid interface, which is the primary focus of this study, was relatively weaker than on an air-liquid interface, and occurred over a longer period of time. When falling through an upper liquid the particles have a slower velocity than when falling through air because the liquid has a greater viscosity. Another difference for the liquid-liquid interface is that the separation of particles begins in the upper liquid before the particles reach the interface. The rate of dispersion depended on the size of the particles, the densities of the particle and liquids, the viscosities of the liquids involved, and the contact angle. For small particles, partial pinning and hysteresis of the three-phase contact line on the surface of the particle during adsorption on liquid-liquid interfaces was also important. The frequency of oscillation of particles about their floating equilibrium increased with decreasing particle size on both air-water and liquid-liquid interfaces, and the time to reach equilibrium decreased with decreasing particle size. These results are in agreement with our analysis.
