Maximum velocity of a liquid metal drop driven by a time-dependent electrocapillary excitation

Gallium alloys are promising materials in biomedical engineering, electronics, and wireless communications, thanks to their good conductivity, non toxicity and their ability to sustain large deformations. They can be transported in capillaries using purely electric means by continuous electrowetting (CEW). Current models of CEW-driven flows do not address the transient response to fast changes in the excitation, crucial in many applications. Here, we present a theory that describes the CEW-driven oscillatory motion of a drop of Eutectic Gallium-Indium alloy inside a capillary. We consider inertia, viscosity and the transient response of the electrical circuit consisting of the drop plus the electrolyte where it is immersed. The theory describes fairly well the experimental drop velocity and explains the existence of an optimal frequency that maximizes the velocity.