Marangoni Fingering Instabilities in Oxidizing Liquid Metals

TL;DR

This study investigates Marangoni fingering instabilities in oxidizing liquid metals, specifically EGaIn, revealing how voltage-induced oxide formation causes spreading and tip-splitting, with a phase diagram mapping stability conditions.

Contribution

It provides the first detailed phase diagram of Marangoni fingering instabilities in oxidizing liquid metals, linking current density and initial finger width to stability and splitting behavior.

Findings

Identified two critical current densities affecting finger stability.

Mapped the phase diagram of instability regimes.

Determined the minimum finger width for tip-splitting to occur.

Abstract

Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, oxides deposit on the surface of the metal, which leads to a lowering of the interfacial tension, allowing spreading under gravity. Understanding the spreading dynamics of room temperature liquid metals is important for developing soft electronics and understanding fluid dynamics of liquids with extreme surface tensions. When the applied voltage or the oxidation rate becomes too high, the EGaIn undergoes fingering instabilities, including tip-splitting, which occur due to a Marangoni stress on the interface. Our experiments are performed with EGaIn droplets placed in an electrolyte (sodium hydroxide); by placing the EGaIn on copper electrodes, which EGaIn readily wets, we are able to control the initial width of EGaIn fingers, setting the initial conditions of the spreading. Two transitions are observed: (1) a minimum current density at which all fingers become unstable to narrower fingers; (2) a current density at which the wider fingers undergo a single splitting event into two narrower fingers. We present a phase diagram as a function of current density and initial finger width, and identify the minimum width below which the single tip-splitting does not occur.