Electrohydrodynamics in leaky dielectric fluids using lattice Boltzmann method

The application of an electric field on a multi-component leaky dielectric fluid system leads to an electric stress at the fluid-fluid interface. To capture the effect of these electric stresses, we report a new method to couple the electrostatics and hydrodynamics of leaky dielectric fluids within the framework of the lattice Boltzmann method. The developed methodology relies on obtaining time invariant solution to the equation governing the divergence of current density in the flow domain using a time marching lattice Boltzmann equation or through a finite-difference formulation. The coupling between the low spurious velocity hydrodynamics model and the leaky dielectric counterpart is also illustrated through the use of three case studies involving interaction of single or multiple droplets suspended in an outer fluid under the action of an external electric field. The results obtained from the developed methodology are shown to be in excellent agreement with earlier published analytical and numerical results. Further, the numerical experiments demonstrate that the developed methodology is applicable for both steady- and time-dependent flows. (C) 2018 Elsevier Masson SAS. All rights reserved.