Drop fragment distributions under shear with inertia

Abstract

A numerical investigation is conducted for a drop of viscous liquid, suspended in another liquid of the same density and viscosity, and undergoing breakup due to simple shear. The computational domain is a three-dimensional box, with spatial periodicity on the sides, and no-slip conditions at the top and bottom walls. The full Navier–Stokes equations are solved, with a volume-of-fluid algorithm to track the interface, a continuous surface force or surface stress formulation for modeling interfacial tension, and a semi-implicit Stokes solver to treat order one Reynolds numbers. We focus on trends for the drop fragment distribution when the flow strength is fixed and the mother drop size is increased. Just above the critical capillary number, the drop evolves to a dumbbell, and breaks according to the end-pinching mechanism. The daughter drops take almost all the mother drop volume; the neck then spawns small moons of less than 1% the critical volume. When the mother drop size increases, there is repeated end-pinching for the elongated neck region. The fragments consist of large satellites with radii that are two to three times that of the effective neck radius, alternating with small moons. At higher capillary numbers, much of the neck becomes cylindrical and breakup produces large satellites of roughly monodispersed size and volumes in the range 10–17% of the critical volume, alternating with small moons. The large mother drops result in daughters that scale with the critical size (and are always the largest fragments produced), together with satellites that also scale with the critical size, and moons which make up a small percentage of the volume. Such scalings allow to predict the fragment size distribution. Our results are consistent with recent experimental observations for Stokes flow. The effect of inertia is a reduction in the size of the fragments.