Role of inertia in two-dimensional deformation and breakup of a droplet

TL;DR

This study uses Lattice Boltzmann simulations to show that inertia is essential for droplet breakup in two dimensions, revealing two distinct breakup pathways and a sharp transition between them.

Contribution

It demonstrates that inertia is necessary for droplet breakup in two-dimensional flows and identifies two different breakup routes with a transition between them.

Findings

Inertia is necessary for droplet breakup in 2D.

Two breakup pathways: two-lobed and three-lobed structures.

A sharp transition exists between the two routes.

Abstract

We investigate by Lattice Boltzmann methods the effect of inertia on the deformation and break-up of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is {\em necessary} for break-up, so that at zero Reynolds number the droplet deforms indefinitely without breaking. We identify two different routes to breakup via two-lobed and three-lobed structures respectively, and give evidence for a sharp transition between these routes as parameters are varied.