Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: Drops more conductive than the suspending fluid

Abstract

Direct numerical simulation is used to examine the rheological properties of an emulsion of leaky dielectric fluids when an electric field is applied to the system. The emulsion consisting of neutrally buoyant drops is immersed in a simple shear flow where an electric potential difference is applied between the plates. It is assumed that drops are more conductive than the suspending fluid and that the electrical conductivity ratio between the drops and the suspending fluid, R=σi∕σo, is larger than the dielectric permittivity ratio, S=εo∕εi. If a single leaky dielectric drop is immersed in an electric field, this combination of properties leads to a viscous fluid motion from the equator to the poles. The response of an emulsion depends on the competition between the electrical forces and the fluid shear. This relation is quantified by the Mason number, Mn=(3λ+2)μγ̇∕6(λ+1)ε0β2E∞2. The significance of drop deformability is measured through the electric capillary number, Ce=ε0β2E∞2a∕γ. The microstructure and properties of an emulsion depend mainly on Mn, Ce, and R. An emulsion immersed in an electric field exhibits three different regimes for increasing Mn. When the electrical forces are substantially larger than the fluid shear, Mn<0.02, the drops aggregate in structures oriented parallel to the electric field that dictate the response of the system. At intermediate shear rates, 0.02<Mn<0.2, the competition between the electrical forces and the fluid shear results in a continuous rearrangement of the aggregated structures. When the shear rate is increased further, Mn>0.2, the aggregated structures are broken up, and the effect of the electrical interaction weakens. The application of an electric field leads electrorheological emulsions to exhibit an increase in their effective viscosity for the range of properties examined here, 0.001<Mn<10.0. However, this variation is strongly nonlinear and depends on the microstructure of the emulsion. The deformation and aggregation of the drops caused by the electric field also modifies the elastic properties of the systems. When the strength of the electrical forces is larger than that of the viscous forces, Mn<O(1), the electrorheological emulsions exhibit negative values for the first normal stress difference. The electric field causes the drops to deform into a prolate shape in the direction parallel to the electric field. The prolate deformation leads to stronger interfacial stresses in the direction normal to the applied shear, which results in negative values of the first normal stress difference. The dependency of the microstructure and rheological properties on the drop deformability, the electrical conductivity ratio, and the drop volumetric fraction is also discussed. Results for emulsions with a drop volumetric fraction of up to 0.56 are presented.