Electrohydrodynamic deformation of a confined droplet in an alternating current electric field: An analytical study.

This article presents an analytical solution for the mean and time-periodic deformation of a neutrally buoyant, leaky dielectric droplet confined within a spherical domain and subjected to a uniform alternating current (AC) electric field. The study introduces a confinement parameter dependent on the droplet-to-domain size ratio, permittivity ratio, conductivity ratio, and frequency, and analyzes how confinement influences electric potential, surface charge density, Maxwell stresses, fluid flow, and droplet deformation. Validation against established theories confirms the model's accuracy for unbounded and confined droplets under DC and AC fields. Key findings include that confinement can either increase or decrease electric potential and surface charge density depending on conductivity and permittivity ratios, alters fluid flow strength at the interface, affects the critical frequency for shape transitions between oblate and prolate forms, and modifies the sensitivity of deformation to viscosity ratio. These insights are relevant for microfluidic applications requiring precise droplet manipulation under oscillating electric fields.