Electrohydrodynamic instabilities in freely suspended viscous films under normal electric fields

TL;DR

This paper investigates the stability and nonlinear dynamics of three-layer viscous films under electric fields, revealing mechanisms for pattern formation and droplet generation relevant to microfluidic applications.

Contribution

It introduces a comprehensive model combining linear stability analysis and boundary element simulations to understand electrohydrodynamic instabilities in multilayer films.

Findings

Identification of different instability modes

Demonstration of tip streaming and droplet formation

Analysis of nonlinear effects on long-term dynamics

Abstract

Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study the stability and dynamics of a system of three superimposed layers of two immiscible fluids subject to a normal electric field. Following the Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a net charge accumulates on the interfaces. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a linear stability analysis and identify different modes of instability, and we characterize the behavior of the system as a function of the relevant dimensionless groups in each mode. Further, we perform numerical simulations using the boundary element method in order to study the effect of nonlinearities on long-time interfacial dynamics. We demonstrate how the coupling of flow and surface charge transport in different modes of instability can give rise to nonlinear phenomena such as tip streaming or pinching of the film into droplets.