Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

Abstract

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Electrorheology of a dilute emulsion of surfactant-covered drops

“…Later, they also observed that a similar phenomenon influences the migration characteristics of a drop in Poiseuille flow (Mandal et al, 2016b). The coupling of an external flow field and electrohydrodynamics can exhibit various non-intuitive flow physics in and around an individual drop (Allan & Mason, 1962;Maehlmann & Papageorgiou, 2009) and thus has the ability to drastically alter the bulk rheology of emulsions (Ha & Yang, 2000;Fernndez, 2008). Vlahovska (2011) established a theoretical understanding of the impact of drop-level flow dynamics and deformation on the electrorheology of a dilute emulsion.…”

Uniform electric-field-induced lateral migration of a sedimenting drop

“…From this discussion one would expect that a background flow field may also significantly affect the drop dynamics. However, there is very little study (Xu & Homsy 2006;Vlahovska 2011;Xu 2007;Mahlmann & Papageorgiou 2009;He et al 2013) in the present literature which considers the electrohydrodynamic motion of a single drop or bubble in the presence of an imposed background flow, which is very common in modern microfluidic devices. Xu & Homsy (2006) have shown the influence of surface charge convection on the velocity of a sedimenting leaky dielectric drop in the presence of uniform axial electric field for nearly spherical drop and small charge relaxation time scale.…”

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] [14][15][16][17][18][19][20]. Each implicit technique to represent the interface has its own advantages and drawbacks.…”