Electric-field-induced transitions from spherical to discocyte and lens-shaped drops

When a poorly conducting drop that is surrounded by a more conducting exterior fluid is subjected to an electric field, the drop can deform into an oblate shape at low field strengths. Such drops become unstable at high field strengths and display two types of dynamics, dimpling and equatorial streaming, the physics of which is currently not understood. If the drop is more viscous, dimples form and grow at the poles of the drop and eventually the discocyte-shaped drop breaks up to form a torus. If the exterior fluid is more viscous, the drop deforms into a lens and sheds rings from the equator that subsequently break into a number of smaller droplets. A theoretical explanation as to why dimple- and lens-shaped drops occur, and the mechanisms for the onset of these instabilities, are provided by determining steady-state solutions by simulation and inferring their stability from bifurcation analysis. For large drop viscosities, electric shear stress is shown to play a dominant role and to result in dimpling. For small drop viscosities, equatorial normal stresses (electric, hydrodynamic and capillary) become unbounded and lead to the lens shape.