A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops

TL;DR

This paper introduces a spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops, accurately capturing complex shape deformations and charge dynamics under electric fields.

Contribution

The paper develops a spectral boundary integral approach with spherical harmonic expansions for stable, high-accuracy simulations of electrohydrodynamics in viscous drops, including a comprehensive charge transport model.

Findings

Method accurately simulates droplet deformation and charge distribution.

Validation against experimental and analytical results confirms reliability.

Numerical techniques effectively handle steep charge gradients and artifacts.

Abstract

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling of interfacial charge transport and fluid flow can trigger electrohydrodynamic instabilities that lead to shape deformations and complex dynamics. We present a spectral boundary integral method to simulate droplet electrohydrodynamics in a uniform electric field. All physical variables, such as drop shape and interfacial charge density, are represented using spherical harmonic expansions. In addition to its exponential accuracy, the spectral representation affords a nondissipative dealiasing method required for numerical stability. A comprehensive charge transport model, valid under a wide range of electric field strengths, accounts for charge relaxation, Ohmic conduction, and surface charge convection by the flow. A shape reparametrization technique enables the exploration of significant droplet deformation regimes. For low-viscosity drops, the convection by the flow drives steep interfacial charge gradients near the drop equator. This introduces numerical ringing artifacts we treat via a weighted spherical harmonic expansion, resulting in solution convergence. The method and simulations are validated against experimental data and analytical predictions in the axisymmetric Taylor and Quincke electrorotation regimes.