Size distribution of daughter bubbles or drops resulting from binary breakup due to random initial deformation conditions

Abstract

The prediction of the interfacial area and hence the size distribution of bubbles or droplets in dispersed multiphase systems is of key importance as these are fundamentals parameters used in the design of apparatus used in separation and purification technologies. This paper presents a simplified model for the evolution of the fluid particle shape (bubble or droplet) breaking in turbulent flow. The model assumes that the particle is initially deformed into a dumbbell shape. The time evolution of the particle shape is modelled by a set of Rayleigh-Plesset equations and the internal flow through the neck is included, assuming the inertial and viscous forces of the inner phase. The effect of the external flow is simulated by the initial deformation of the particle, the initial deformation rates and the Weber number, which characterises the ratio of the kinetic energy of the flow around the particle to the surface energy of the particle. The final daughter size distribution is obtained by applying random initial conditions, reflecting the random nature of turbulence. The results obtained from the model suggest that the size distribution of the daughter particles is strongly influenced by the ability of the inner phase to move between parts of the particle. In the case of bubbles, the gas moves easily resulting in a ∪-shaped bubble size distribution. Conversely, in the case of liquid droplets, the motion of the inner liquid is resisted by its higher inertia, resulting in a ∩-shaped droplet size distribution. Despite the simplified description of particle shape and deformation rates, the present model allows to physically capture and explain the differences in particle size distribution resulting from the binary breakup of bubbles and droplets in turbulent flows.