Abstract: Liquid-liquid dispersion is often performed in stirred tanks, which are valued for their ease of operation, high droplet generation rate and effective droplet dispersion. Many relevant simulations use the Eulerian-Eulerian method, combining population balance equations with statistical models to forecast droplet breakage. Conversely, the Eulerian-Lagrangian (E-L) method provides precise tracking of individual droplets, which is crucial for simulating dispersion processes. However, E-L simulation faces challenges in integrating droplet breakage effectively. To address this issue, our research introduces a probabilistic approach for droplet breakages. It assumes that a longer time increases the likelihood of breakup; a droplet breaks if the calculated probability exceeds a random value from 0 to 1. Consequently, the simulated breakage frequency becomes independent of the Lagrangian time step. The Sauter mean diameter and droplet size distribution can be accurately predicted by this probabilistic approach. By closely monitoring droplet motion, we reveal the complexity of droplet trajectories and the detailed patterns of circulation in stirred tanks. These insights contribute to a deeper understanding of liquidliquid dispersion dynamics.

Key words: Eulerian-Lagrangian method, Liquid-liquid dispersion, Droplet breakage, Stirred vessel, Turbulent flow, Computational fluid dynamics

摘要： Liquid-liquid dispersion is often performed in stirred tanks, which are valued for their ease of operation, high droplet generation rate and effective droplet dispersion. Many relevant simulations use the Eulerian-Eulerian method, combining population balance equations with statistical models to forecast droplet breakage. Conversely, the Eulerian-Lagrangian (E-L) method provides precise tracking of individual droplets, which is crucial for simulating dispersion processes. However, E-L simulation faces challenges in integrating droplet breakage effectively. To address this issue, our research introduces a probabilistic approach for droplet breakages. It assumes that a longer time increases the likelihood of breakup; a droplet breaks if the calculated probability exceeds a random value from 0 to 1. Consequently, the simulated breakage frequency becomes independent of the Lagrangian time step. The Sauter mean diameter and droplet size distribution can be accurately predicted by this probabilistic approach. By closely monitoring droplet motion, we reveal the complexity of droplet trajectories and the detailed patterns of circulation in stirred tanks. These insights contribute to a deeper understanding of liquidliquid dispersion dynamics.

关键词: Eulerian-Lagrangian method, Liquid-liquid dispersion, Droplet breakage, Stirred vessel, Turbulent flow, Computational fluid dynamics