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

Abstract

Direct numerical simulations of the effects of an electric field on an emulsion of drops are presented. A simple shear flow configuration is adopted where the electric field is applied perpendicular to the sliding plates. Both the drops and the suspending fluid are assumed to behave as leaky dielectric fluids. Here, drops less conductive than the suspending fluid with an electrical conductivity ratio smaller than the dielectric permittivity ratio are considered. This combination of electrical properties leads to a viscous fluid motion from the poles to the equator. The response of an emulsion is governed by the competition between the electrical forces, the fluid shear, and the capillary forces. The Mason number [Mn=(3λ+2)μγ̇∕6(λ+1)ε0β2E∞2] and the electric capillary number [Ce=ε0β2E∞2a∕γ] are used to describe the response of the systems. As previously observed in experiments at low shear rates, Mn<0.2, the drops aggregate in chains that tilt under a shear. The competition between the electrical forces and the fluid shear results in shorter chains at intermediate shear rates, 0.2<Mn<2.0. As the fluid shear becomes stronger than the electrical attraction, Mn>2.0, the chains of drops break up. The rheological properties mainly depend on the emulsion microstructure. The effective viscosity exhibits a strong shear-thinning response because the chains of drops, which appear at low shear rates, increase the resistance of the system to shear. As the chains shorten and break up, the effective viscosity decreases. The elastic properties of the emulsion are also affected by the presence of the electric field. Normal stress differences arise as a consequence of the deformation of the drops and the surface tension acting on the interface between the fluids. The shape of the drops is determined by the deformation caused by the viscous forces and the deformation due to the electric stresses. At low shear rates, the electric effects are predominant and the application of an electric field leads the drops to deform into oblate shapes. The oblate deformation results in higher stresses in the direction parallel to the shearing motion than perpendicular to it, which results in a significant increase in the first normal stress difference. As the shear rate is increased, the oblate deformation is supplemented by the deformation due to the fluid shear. The deformation caused by the electric field is also responsible for the negative magnitude of the second normal stress difference in three-dimensional emulsions.

Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs

“…While the prototypical problem of an isolated drop in a uniform electric field has been extensively studied (see for a recent review (Vlahovska 2019)), investigations of the collective dynamics of many drops are scarce (Fernandez 2008 a , b ; Casas et al. 2019) and mainly focused on the near-contact interaction preceding electrocoalescence (Anand et al.…”

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field

“…Fernandez and Trygvasson [28] incorporated finite-volume and front-tracking methods to study the behavior of an emulsion of leaky dielectric droplets in an electric field generated by parallel plate electrodes. Fernandez [29,30] did a similar study to investigate the response of an emulsion of a leaky dielectric droplet in a shear flow by employing the same formulation. Hua et al [31] also utilized a front-tracking and finite-volume method to solve the full Navier-Stokes equations and studied the motion of a droplet suspended in a viscous medium under the influence of an electric field.…”

Analysis of Partial Electrocoalescence by Level-Set and Finite Element Methods

“…Explicit approaches, such as boundary integral and front-tracking methods, track discrete points on the interface surface. The motion and deformation of droplets under the presence of an electric field [8][9][10][11][12] and electro-T e been reproduced using this type of techniques. However, their implementation is not straightforward as the addition of surface-marker points is usually needed in order to obtain sufficient interface 3 resolution when stretching, coalescence and pinching occur .…”