Critical deformation state of binary droplet breakup in turbulence

The deformation and breakup of drops in turbulent flows play a key role in a variety of industrial processes and natural situations. Literature reviews link the breakup of a droplet into two droplets (known as binary breakup) to a critical deformed state (CDS). Based on the droplet static pressure distribution, the CDS is defined as a level of deformation beyond which binary breakup is assumed to be inevitable and deterministic, i.e. even if no further external stresses act on the droplet. This study examines this CDS concept and identifies how sensitive rupture dynamics are to external stresses. These points are addressed using direct numerical simulations of individual droplets evolving in turbulence from their initially spherical state up to fragmentation. A scale-by-scale analysis is employed to describe droplet shape and deformation. It ensures an objective determination of the relevant scales involved in the CDS. The analysis of many simulated droplets shows that binary rupture is always preceded by the formation of a neck, whose narrowing until rupture is predicted by the CDS criterion of the literature. Supplementary simulations show that, depending on the shape of the droplets at the CDS, the turbulence has a negligible, contributory or essential effect on rupture. Thus, the binary breakup of droplets in a turbulent environment depends on the shape of the droplets and on their Ohnesorge number (ratio of viscous forces to capillary and inertial forces). These results suggest that the study should be supplemented with a comprehensive description of droplet morphology.