Cascades and Corrugations: Self-similar mechanisms of droplet aerobreakup in extreme regimes

Droplet formation is relevant in many applications spanning natural and artificial settings. Comprehending droplet aerobreakup or air-assisted secondary atomization is challenging, especially in high-speed flows. In the present study, we look into shockwave-induced breakups and associated intermediate processes happening at smaller spatiotemporal scales. This entails multi-scale interface deformations with intricate wave dynamics that conform to a non-linear cascade. The local undulation breakup or sub-secondary atomization processes are reminiscent of a scaled-down droplet breakup, indicating a self-similar cascade that terminates in corrugated ligaments producing the final daughter droplets. The droplet size distribution shows transient behaviour, with normalized statistics collapsing onto a universal curve across different times and Weber numbers (We=900-4000). This universality stems from ligament-mediated droplet generation, where ligament corrugations determine the distribution parameters, modelled by a Gamma distribution. Under catastrophic conditions, corrugations saturate to the threshold regardless of We. The intricate interplay of self-similar hierarchical deformation cascade and chaotic randomness evokes parallels with turbulent cascades, suggesting that droplet aerobreakup in extreme conditions may share fundamental mechanisms with (multiphase) turbulence. This premise offers potential for new insights and unified frameworks.