Electro-hydrodynamics modeling of liquid-metal droplets with electrochemical oxidation

Eutectic Gallium-Indium (EGaIn) is a room-temperature liquid metal with tunable surface tension and complex interfacial dynamics under applied electric fields. Due to its high electrical conductivity, fluidity, and low toxicity, EGaIn has gained significant interest for applications in robotics, electronics, and biomedical devices. In this work, we consider the dynamics of an EGaIn droplet immersed in a NaOH electrolyte on a flat substrate. A one-dimensional lubrication model is developed for the film thickness of the liquid metal and the oxide concentration at the EGaIn/NaOH interface. This model incorporates Marangoni effects, bulk surface tension, modified intermolecular forces, and an electrochemical oxidation flux determined by a two-dimensional multiphase electric field model. Using the coupled model, we numerically study the spatiotemporal evolution of the droplet shape and the surface oxide concentration under various electric potential boundary conditions. We demonstrate fundamental droplet behaviors such as wetting, dewetting, and directional transport. Furthermore, the simulations reveal that complex dynamics, including droplet coalescence and splitting, can be achieved by altering boundary voltages over time, offering a potential framework for programmable liquid metal manipulation.