Electrokinetic behavior of an individual liquid metal droplet in a rotating electric field

The interfacial tension gradient forms tangential stress that drives fluid flow at a liquid-liquid interface, known as the Marangoni convection. In this study, we report on the electrocapillary-driven Marangoni flow at the polarizable interface between a gallium-based liquid metal droplet (LMD) and electrolytes, activated by the rotating electric field. When the electric field frequency exceeds 50 Hz, the amplitude of the oscillatory movement of LMD decays to zero, resulting in a stationary droplet. Utilizing micrometer-resolution particle image velocimetry (micro-PIV), we investigate the flow patterns around the LMD in detail. The visualized flow fields reveal two distinct flow patterns in the surrounding fluid at the central cross section of LMD, which vary with changes in frequency: normal flow (50-200 Hz) and tangential flow (300-1000 Hz). To reveal this flow mechanism, we first analyzed the fluid configuration in a linear electric field. Subsequently, we employ the stream functions to theoretically derive the slip velocity of the Marangoni flow in a rotating electric field. By combining this with the numerical simulations, we arrive at the following conclusions: At high frequencies (f >= 50 Hz), the time-averaged part of the interfacial tension gradient dominates the in-phase Marangoni flow, leading to normal flow; while the frequency increases (f >= 300 Hz), the electrorotation due to the out-of-phase charging accounts for the transformation of the flow pattern. Our work systematically studied the Marangoni flow under linear and rotating electric fields, which is vital in electrokinetic flows and of fundamental interest for the fluid dynamics society.