Fragmentation Mechanisms of a Droplet in a Turbulent Flow: a Direct Numerical Simulation Approach

Droplet and bubble fragmentation in turbulent multiphase flows is a long-standing challenge in fluid mechanics, with profound implications for processes ranging from fuel atomization in industrial combustors to aerosol generation at the air-sea interface. This work studies the multiscale nature of these processes by systematically isolating the roles of different turbulent scales through spectral filtering of the carrier velocity field. Using high- fidelity Direct Numerical Simulations of a single deformable droplet immersed in homogeneous isotropic turbulence, numerical experiments are performed where the carrier flow field is spec- trally truncated. Specifically, low-pass and high-pass filters are applied to the velocity field at multiple cutoff scales proportional to the initial droplet diameter D. The results reveal a fundamental asymmetry in the scale-dependent breakup dynamics. Iso- lated small-scale turbulent fluctuations (high-pass cases) are shown to be incapable of triggering droplet breakup on their own, yielding a maximum breakup rate of 20% for cutoff scales slightly larger than the droplet diameter. In contrast, large-scale structures (low-pass cases) consistently drive the droplet to fragmentation in 100% of the runs, compared to a baseline rate of 60% in the unfiltered reference turbulence. This demonstrates that the inertial-range eddies larger than the droplet scale are the primary source of the hydrodynamic strain required to overcome the stabilizing capillary pressure, which is generated by small-scale velocity fluctuations. Further- more, statistical analysis of the post-breakup droplet size distribution confirms the emergence of sub-Hinze (d−10/3 ) and super-Hinze (d−3/2 ) scaling laws. Additionally, a scale-by-scale energy budget analysis reveals that the interface acts as a dynamic energy buffer, absorbing kinetic energy from the large-scale forcing eddies and subsequently releasing it at smaller scales dur- ing fragmentation. These findings provide a physical foundation for developing scale-aware subgrid-scale models. Our results reveal a fundamental asymmetry in the scale-dependent breakup dynamics. Isolated small-scale turbulent fluctuations (HP cases) are shown to be incapable of triggering droplet breakup on their own, yielding a 0% breakup rate for cutoff scales smaller than or equal to D, and only 20% for the 1.2D case. In contrast, large-scale structures (LP cases) consistently drive the droplet to fragmentation in 100% of the runs, compared to a baseline rate of 60% in the unfiltered reference turbulence. This clear discrepancy demonstrates that the inertial-range eddies larger than the droplet scale are the primary source of the hydrodynamic strain required to overcome the stabilizing capillary pressure. Furthermore, statistical analysis of the post-breakup droplet size distribution (DSD) confirms the emergence of the classic sub-Hinze d^(-10/3) and super-Hinze d^(-3/2) scaling laws. Additionally, a scale-by-scale (SBS) energy budget analysis reveals that the liquid-liquid interface acts as a dynamic energy buffer (or flywheel), absorbing kinetic energy from the large-scale forcing eddies, storing it as surface potential energy, and subsequently releasing it at smaller scales during the fragmentation process. These findings provide a physical foundation for developing scale-aware subgrid-scale (SGS) models in multiphase turbulence simulations.