Electrohydrodynamics of viscous drops in strong electric fields: Numerical simulations

TL;DR

This paper develops a 3D boundary element method to simulate the complex behavior of dielectric liquid drops in electric fields, capturing charge convection effects and validating against experiments and theories.

Contribution

It introduces a comprehensive 3D numerical simulation framework for the leaky dielectric model, including charge convection and non-axisymmetric drop dynamics.

Findings

Simulation results agree with experimental data.

Charge convection enables modeling of electrorotation.

The method captures symmetry-breaking bifurcations.

Abstract

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviors contingent on field strength and material properties. These phenomena are best described by the Melcher-Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop-fluid interface and prescribes a balance between charge relaxation, the jump in Ohmic currents from the bulk and charge convection by the interfacial fluid flow. Most previous numerical simulations based on this model have either neglected interfacial charge convection or restricted themselves to axisymmetric drops. In this work, we develop a three-dimensional boundary element method for the complete leaky dielectric model to systematically study the deformation and dynamics of liquid drops in electric fields. The inclusion of charge convection in our simulations permits us to investigate drops in the Quincke regime, in which experiments have demonstrated a symmetry-breaking bifurcation leading to steady electrorotation. Our simulation results show excellent agreement with existing experimental data and small-deformation theories.