Pump-driven droplet electrohydrodynamics: deformation, pinch-off and recoalescence

We investigate pump-driven droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is developed that couples Nernst--Planck--Poisson electrodiffusion with incompressible Navier--Stokes--Cahn--Hilliard flow, and incorporates interfacial ionic pumps as prescribed surface fluxes. In the pump-free baseline, applied fields merely polarise the droplet and deformation is negligible. By contrast, surface-localised pumping drives the accumulation of positive ions within the droplet, elevates the interior potential, and generates non-uniform electric fields. The resulting Lorentz stresses stretch and displace the droplet, thin interfacial necks, and trigger pinch-off; the daughter droplets subsequently recoalesce, often after wall contact, yielding flattened remnants. In multiple-droplet settings, pump-induced charging produces lateral electrostatic repulsion and asymmetric deformation; under geometric confinement, crescent bending and star-like morphologies emerge. Shear-flow tests further show that a pumped droplet can be immobilised and ruptured while an unpumped neighbour is advected downstream, suggesting a route to sorting. Taken together, the results establish interfacial pumping as an internal actuation mechanism that robustly controls droplet morphology and dynamics across configurations.