# Numerical Simulations of Vorticity Banding of Emulsions in Shear Flows

## TL;DR

This study uses numerical simulations to investigate vorticity banding in emulsions under shear flow, revealing how droplet coalescence influences the stability of banded structures and the system's effective viscosity.

## Contribution

It provides new insights into the mechanisms of emulsion banding and the role of droplet coalescence through detailed interface-resolved simulations.

## Key findings

- Banded structures are stable with droplet merging, unstable without coalescence.
- Droplet coalescence reduces system energy dissipation and effective viscosity.
- Initial banded distributions can be stable or unstable depending on coalescence conditions.

## Abstract

Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding experimentally observed we have performed interface resolved simulations of the two-fluid system. The experiments were perfomed starting with a random distribution of droplets which, under the applied shear, evolves in time resulting in a phase separation. To numerically reproduce this process, the banded structures are initialized in a narrow channel confined by two walls moving in opposite direction. We find that the initial banded distribution is stable when droplets are free to merge and unstable when coalescence is prevented. In this case, additionally, the effective viscosity of the system increases, resembling the rheological behavior of suspensions of deformable particles. Droplets coalescence, on the other hand, allows emulsions to reduce the total surface of the system and hence the energy dissipation associated to the deformation, which in turn reduces the effective viscosity.