Unsteady electrorotation of a viscous drop in a uniform electric field

Abstract

A dielectric drop suspended in an immiscible dielectric fluid of higher conductivity can spontaneously generate the so-called Quincke rotation (a rotating activity that a weakly conducting drop/solid particle displays in an electric field) subjected to sufficiently strong electric field strength. The steady tilt has been extensively studied and is well elucidated now. However, the unsteady electrorotation of drop remains a largely unclear, complex issue. Motivated by this, we examine the unsteady drop electrorotation in this work with the required integrated convective bulk charge transport effect. First, for the steady rotation, the transient evolution to a steady droplet tilt from the symmetric Taylor state is analyzed in-depth. Here we discover several new phenomena, including the evolving equatorial charge jets. For unsteady rotation, based on a drop's interfacial charge variation, deformation, and tilt angle, the study reports the growth of three distinct rotating patterns in the viscosity ratio range 0.2≤λ=μi/μo≤20.0 and electric field strength E0≤25 kv/cm at a fixed conductivity ratio Q ( = σi/σo) = 0.026 and permittivity ratio S (= ϵi/ϵo) = 0.566. A low-viscosity drop ( λ≤2.5) exhibits only the periodic rotation. For the viscosity ratio 2.5<λ<7.0, the increased electric intensity creates two new unsteady rotation modes: the pseudo-periodic tumbling and the irregular one. For λ≥7, the periodic mode remains absent; instead, the drop displays the electric intensity-dependent tumbling and irregular rotation patterns. Our study shows that the rotation reduces a drop's transitory interfacial charge. At this stage, the drop rotation behavior is controlled by competing charge convection due to fluid flow and charge supply by conduction. The resulting varying electric Reynolds number ReE (the time ratio of charge relaxation and charge convection) explains the created different rotation mechanisms. For ReE>1, owing to lacking enough interfacial charge to sustain rotation, the drop's transition to a temporary non-rotating Taylor state occurs until the interface recharges. The resultant mechanism supports the periodic batch-type rotation for a low-viscosity drop and the irregular rotation for a high-viscosity drop in a higher electric field. In contrast, for ReE<1, the drop timely acquires sufficient charge to support continuous tumbling electrorotation.