Lattice Boltzmann simulations of droplet dynamics and break-up in generic time-dependent and turbulent flows*

We study the behaviour of droplet break-up in generic time-dependent shear flows via a multicomponent Lattice Boltzmann algorithm. Our work can be seen as an extension to studies on the influence of inertia on droplet break-up (Y.Y. Renardy, V. Cristini, Phys. Fluids 13, 7 (2001)), whereas we deal with cases of time-dependent droplet break-up, which arise when the temporal rate of change of the shear intensity is of comparable size to the droplet relaxation time. This work is a continuation to a previous study on stable time-dependent droplet dynamics (F. Milan, M. Sbragaglia et al., Eur. Phys. J. E 41, 6 (2018)). Furthermore we investigate a more realistic model enabling the study of fully resolved dilute droplet suspension dynamics under the influence of turbulent fluctuations via multicomponent Lattice Boltzmann simulations, which we compare with previous studies containing non fully resolved droplets (L. Biferale, C. Meneveau, R. Verzicco, J. Fluid Mech. 754, 184 (2014)).