Nonlinear three-dimensional electrohydrodynamic interactions of viscous leaky dielectric drops

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McDougall, Michael and Wilson, Stephen and Das, Debasish (2026) Nonlinear three-dimensional electrohydrodynamic interactions of viscous leaky dielectric drops. Physical Review Fluids. ISSN 2469-990X (In Press) (https://doi.org/10.1103/lrkw-739x)

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Abstract

When a drop of a leaky dielectric fluid is suspended in another fluid and subjected to a uniform DC electric field, it becomes polarized, leading to tangential electric stresses that drive fluid motion both inside and outside the drop. In the presence of a second drop, the dynamics of the first drop are altered due to electrohydrodynamic interactions with the second, causing the drops to trans- late due to dielectrophoretic forces and hydrodynamic interactions. We present a semi-analytical nonlinear three-dimensional small deformation theory for a pair of identical, widely-separated leaky dielectric drops suspended in a weakly conducting fluid. This theory is valid under conditions of large drop separation, high drop viscosity, and high surface tension, ensuring that the drops remain nearly spherical. The resulting model is semi-empirical, with selected higher-order terms retained rather than obtained through a systematic asymptotic expansion. For the first time, we develop a model within the Taylor–Melcher leaky dielectric framework that incorporates both transient charge relaxation and convection. This allows the model to capture the transition to Quincke rotation, a symmetry-breaking phenomenon in which drops begin to spontaneously rotate in sufficiently strong fields. We derive and numerically integrate coupled nonlinear ordinary differential equations for the dipole moments, shapes, and positions of the drops. Our results show good quantitative agreement with previous numerical and experimental work in the limit of zero charge relaxation and convec- tion, and the model reduces to existing models for isolated drops and interacting solid spheres in the relevant limits. We also discuss the hysteresis in the onset of Quincke rotation of isolated drops observed in experiments. Various trajectories for pairs of drops undergoing Quincke rotation are presented, along with results for fixed drops, including their shape, the nature of electrohydrody- namic interactions (attractive or repulsive), and the conditions leading to Quincke rotation. In particular, it is shown that the onset of Quincke rotation for a pair of drops is qualitatively different from that for an isolated drop due to electrohydrodynamic interactions and from that for a pair of solid spheres due to straining flows present only in drops.

ORCID iDs

McDougall, Michael, Wilson, Stephen ORCID logoORCID: https://orcid.org/0000-0001-7841-9643 and Das, Debasish ORCID logoORCID: https://orcid.org/0000-0003-2365-4720;
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