Electrohydrodynamic interaction of a tandem unequal-size droplet pair under the non-reciprocal effect

Tandem identical drops subjected to a uniform electric field (an over-idealized model in view of practical application) exhibit the simple electrocoalescence or repulsion because of the electric dipole–dipole interaction and the flow-induced electrohydrodynamic interaction. However, the unequal-size droplet pair creates a non-equilibrium dynamic system driven by the non-reciprocal interactions, where drops are expected to exhibit more complex dynamic behaviors. In addition, the Quincke rotation, a novel electrohydrodynamic behavior, converts the stresslet-quadrupole flow structure into the rolet structure. The bifurcation of the hydrodynamic interaction nature undoubtedly induces the unidentified yet pair dynamics. Motivated by these, a systematic numerical analysis is carried out by tuning R at the fixed viscosity ratio λ (=μi/μo) = 10.0, S = 0.5, and CaE = 0.4 (=εiE02aL/γ, represents the ratios of electric stress and surface tension stress) to identify the behavior diversity under the non-reciprocal effect and Quincke-rotation effect, and reveal the implied mechanisms. In this work, six dynamic patterns are discovered by varying R at e = 0.5: planet-like orbital rotation at R < 0.4; electrocoalescence at 0.4 ≤ R < 0.65; stationary state at R = 0.65; expulsion model at 0.65 < R ≤ 0.8; repulsion at 0.8 < R < 2; Quincke-like rotation model at R ≥ 2. Furthermore, the e-dependent transition feature of motion models is investigated. Two droplets always remain stationary at R = 0.65 regardless of the size ratio e. For e > 0.8, the expulsion pattern disappears. When e is reduced, the critical R needed to initiate Quincke-like rotation of the drop pair rises, until this dynamic activity stops happening at e ≤ 0.1.