Role of viscosity in turbulent drop break-up

We investigate drop break-up morphology, occurrence, time and size distribution, through large ensembles of high-fidelity direct-numerical simulations of drops in homogeneous isotropic turbulence, spanning a wide range of parameters in terms of the Weber number $We$, viscosity ratio between the drop and the carrier flow $\mu _r=\mu _d/\mu _l$, where d is the drop diameter, and Reynolds ($Re$) number. For $\mu _r \leq 20$, we find a nearly constant critical $We$, while it increases with $\mu _r$ (and $Re$) when $\mu _r > 20$, and the transition can be described in terms of a drop Reynolds number. The break-up time is delayed when $\mu _r$ increases and is a function of distance to criticality. The first break-up child-size distributions for $\mu _r \leq 20$ transition from M to U shape when the distance to criticality is increased. At high $\mu _r$, the shape of the distribution is modified. The first break-up child-size distribution gives only limited information on the fragmentation dynamics, as the subsequent break-up sequence is controlled by the drop geometry and viscosity. At high $We$, a $d^{-3/2}$ size distribution is observed for $\mu _r \leq 20$, which can be explained by capillary-driven processes, while for $\mu _r > 20$, almost all drops formed by the fragmentation process are at the smallest scale, controlled by the diameter of the very extended filament, which exhibits a snake-like shape prior to break-up.