Instability of a planar fluid interface under a tangential electric field in a stagnation point flow

Mohammadhossein Firouznia, Michael J. Miksis, Petia M. Vlahovska, David Saintillan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The interface between two immiscible fluids can become unstable under the effect of an imposed tangential electric field along with a stagnation point flow. This canonical situation, which arises in a wide range of electrohydrodynamic systems including at the equator of electrified droplets, can result in unstable interface deflections where the perturbed interface gets drawn along the extensional axis of the flow while experiencing strong charge build-up. Here, we present analytical and numerical analyses of the stability of a planar interface separating two immiscible fluid layers subject to a tangential electric field and a stagnation point flow. 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 local linear stability analysis in the vicinity of the stagnation point to study the behaviour of the system in terms of the relevant dimensionless groups of the problem. The local theory is complemented with a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. Our analysis demonstrates the subtle interplay of charge convection and conduction in the dynamics of the system, which oppose one another in the dominant unstable eigenmode. Finally, numerical simulations of the full nonlinear problem demonstrate how the coupling of flow and interfacial charge dynamics can give rise to nonlinear phenomena such as tip formation and the growth of charge density shocks.

Original languageEnglish (US)
Article numberA25
JournalJournal of fluid Mechanics
StatePublished - Jan 25 2022


  • electrohydrodynamic effects

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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