Computational Investigation of the Effect of non-Axisymmetric Initial Rayleigh Modes on Secondary Fragmentation of Droplets

Through our previous work, we explored the rich variety in the secondary fragmentation morphologies observed in initially spherical droplets under impulsive acceleration. A critical Weber number for fragmentation was observed and the corresponding fragmentation morphology strongly depended on the rheology of the droplet fluid, through properties such as Density ratio, Drop (Oh_d) and Ambient Ohnesorge numbers. However, a non-spherical initial shape raises the total energy of the system and can hinder or support the fragmentation process depending on the initial phase of the oscillation. In this work, 3D Volume-of-Fluid simulations are used to study the role of third and fourth Rayleigh fundamental frequencies and their degenerate (non-axisymmetric) modes on the near threshold fragmentation process. It is observed that depending on the droplet Ohnesorge number, an initial mode can have substantial effects on its fragmentation threshold.This change in threshold is sometimes also accompanied with the appearance of multimodal features such as surface plumes at the upstream pole of the droplet for low Oh_{d ­}systems, which directly effects the morphology and drop size distribution of the secondary fragmentation process. The 3D simulations also serve to highlight the role of oscillation amplitude in the appearance of three dimensional surface features in initially axisymmetric oscillation modes.