  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.
