# Electrorheology of a dilute emulsion of surfactant-covered drops

## TL;DR

This paper investigates how surfactant coatings affect the electrohydrodynamic behavior of deformable drops in emulsions under shear and electric fields, revealing complex interactions influencing bulk viscosity and flow properties.

## Contribution

It introduces a comprehensive 3D analysis of surfactant effects on electrohydrodynamics of drops, highlighting conditions where surface tension gradients vanish and viscosity changes are minimized.

## Key findings

- Surfactant non-uniformity significantly alters flow disturbance.
- Critical shear rates depend on fluid permittivity and conductivity ratios.
- Charge convection influences shear thinning and thickening behaviors.

## Abstract

The effects of surfactant coating on a deformable viscous drop under the combined action of a shear flow and a uniform electric field, are investigated by solving the coupled equations of electrostatics, fluid flow and surfactant transport. Employing a comprehensive three-dimensional solution technique, the non-Newtonian shearing response of the bulk emulsion is analyzed in the dilute suspension regime. The present results reveal that the surfactant non-uniformity creates significant alterations in the flow disturbance around the drop, thereby influencing the viscous dissipation from the flowing emulsion. This, in effect, triggers changes in the bulk shear viscosity. It is striking to observe that the balance between electrical and hydrodynamic stresses is affected in such a way that surface tension gradient on the drop surface vanishes for some specific shear rates and the corresponding effective change in the bulk viscosity becomes negligible too. This critical condition hugely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also the physical mechanisms of charge convection of surface deformation play their role in determining this critical shear rate. The charge convection instigated shear thinning or shear thickening behavior of the emulsion gets reversed due to a coupled interaction of the charge convection and Marangoni stress. In addition, the electrically created anisotropic normal stresses in the bulk rheology, get reduced due to the presence of surfactants, especially when the drop viscosity is much lesser than the continuous fluid. A thorough description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion, may provide a fundamental understanding of a more complex emulsion system.