Uniform electric-field-induced non-Newtonian rheology of a dilute suspension of deformable Newtonian drops

Abstract

The rheological behavior of a dilute emulsion comprised of neutrally buoyant drops suspended in an immiscible medium under the combined influence of a uniform electric field and simple shear flow is analyzed. Considering the drops and suspending medium as Newtonian and leaky dielectrics, the effective emulsion stress tensor is obtained when the fluid motion is governed by the Stokes equations. The present study takes into account an arbitrarily oriented uniform electric field in the plane of shear flow. A small-deformation analysis is performed to study this coupled electrohydrodynamic problem considering weak imposed shear flow and weak surface charge convection. Analytical expressions are obtained for the effective shear viscosity and normal stress differences of the dilute emulsion. The tilt angle (orientation angle of the applied electric field relative to the direction of shear flow) is found to affect the emulsion rheology. Key results show that the dilute emulsion exhibits non-Newtonian behavior such as shear-rate-dependent effective viscosity and nonzero first and second normal stress differences. In the absence of shape deformation and charge convection, a dilute emulsion displays shear thinning or shear thickening behavior depending on the drop polarization and tilt angle. The effective viscosity of the dilute emulsion can be lower or higher than the viscosity of the suspending medium depending on the electrical property ratios, tilt angle, and relative strength of the electric stress as compared with viscous stress. Surface charge convection significantly affects the electrohydrodynamic flow and thereby modifies the effective viscosity and normal stress differences. The applied electric field significantly affects the drop shape and orientation angle and thereby modifies the effective viscosity and normal stress differences. Both the surface charge convection and shape deformation can increase or decrease the effective viscosity and normal stress differences. Notably, the presence of surface charge convection and shape deformation leads to the generation of electric torque, which further results in a nonzero antisymmetric component of the emulsion stress tensor. We establish that fine-tuned rheology of a dilute emulsion can be obtained by proper choices of the tilt angle.