Oxidation-Mediated Fingering in Liquid Metals

We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a gallium-based liquid metal alloy to values approaching zero, thereby inducing drastic shape changes, including the formation of fractals. The measured fractal dimension ($D=1.3\pm 0.05$) places the instability in a different universality class than other fingering instabilities. By characterizing changes in morphology and dynamics as a function of droplet volume and applied electric potential, we identify the three main forces involved in this process: interfacial tension, gravity, and oxidative stress. Importantly, we find that electrochemical oxidation can generate compressive interfacial forces that oppose the tensile forces at a liquid interface. The surface oxide layer ultimately provides a physical and electrochemical barrier that halts the instabilities at larger positive potentials. Controlling the competition between interfacial tension and oxidative (compressive) stresses at the interface is important for the development of reconfigurable electronic, electromagnetic, and optical devices that take advantage of the metallic properties of liquid metals.

Figure 1

(a) Schematic of apparatus, and experimental images of a $30\mu \mathrm{L}$ EGaIn droplet undergoing the fingering instability (see Movies 1–4 [23]). (b) Box-counting plot shown as a function of time for this same droplet, spreading at 1.3 V. The upper curves are box-counting plots for droplets with $V=10\mu \mathrm{L}$, $30\mu \mathrm{L}$, and $100\mu \mathrm{L}$ (see images), both analyzed immediately before the first branch breaks off.

Figure 2

(a) Representative images taken at the maximum area for all four regimes, and their dynamics characterized by (b) area $A(t)$ and (c) the electrical resistance measured from $[\mathcal{E}/I(t)]$. The star indicates the time at maximum area. All panels show data from the same four trials with $V=30\mu \mathrm{L}$ and $\mathcal{E}=0.8\mathrm{V}$ (regime A), $\mathcal{E}=1.8\mathrm{V}$ (regime B), $\mathcal{E}=2.8\mathrm{V}$ (regime C), and $\mathcal{E}=4.0\mathrm{V}$ (regime D). The run-to-run variations in area $A$ are $\pm 0.07,12.7,26.5$, and $2.12{\mathrm{mm}}^2$ for regimes A, B, C, and D, respectively.

Figure 3

Phase diagram for droplets of volume $V$ subject to an applied electric potential $\mathcal{E}$. The dashed black lines correspond to the regime boundaries. Regime A: smooth sessile droplets. Regime B: fractal morphology. Regime C: undulated spreading, followed by contraction. Regime D: spreading followed by contraction. Inset: for each $V$, the electric potential ${\mathcal{E}}_{\max }$ at which the maximum spreading extent occurs. Vertical bars represent the width of the $\mathcal{E}(A)$ curves shown in Fig. 4.

Figure 4

(a) Scaled area $\tilde{A}\equiv A/V^{2/3}$ as a function of applied electric potential $\mathcal{E}$. (b) The data from (a) with a rescaled horizontal axis: $(\mathcal{E}-{\mathcal{E}}_{\max })/{\mathcal{E}}_w$ to show similarity of results, with (${\mathcal{E}}_{\max }$, ${\mathcal{E}}_w$) measured from (a) for each droplet volume.