How fast can a liquid metal drop respond to a time-dependent electrocapillary excitation?

TL;DR

The paper addresses the transient response of a liquid Ga–In drop confined in a capillary under time-varying electrocapillary excitation. It develops a minimal model that couples inertia and viscosity with the circuit’s transient response, treating the drop as a surface capacitor and including a thin-film resistance, to predict the drop’s velocity in response to oscillatory voltage. The theory, validated by experiments across multiple drop lengths and frequencies, reveals an optimal excitation frequency that maximizes the peak velocity and demonstrates how mechanical and electrical transfer functions shape the response. This insight enables more rapid and controllable CEW-driven drop transport, with potential impact on liquid-metal microfluidic devices and dynamic reconfigurable antennas. The framework also clarifies the role of interfacial capacitance and drop-film resistance in limiting high- and low-frequency performance, providing design guidelines for CEW-based applications.

Abstract

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.

Figures (8)

• Figure 1: (a) Sketch of the experimental setup and (b) equivalent electric circuit.
• Figure 2: Experimental sample corresponding to a drop of length $L_{d0} = 10.9$ mm at rest. (a) Excitation $E(t)$, measured current, $I(t)$, and velocity, $V(t)$, for an excitation of $f = 1$ Hz and amplitude $E_0=0.5$ V. (b) Peak current $I_{\rm max}$. (c) Peak speed $V_{\rm max}$. Colorbar represents drop length, $L_{\mathrm{d}0}$, in (b) and (c).
• Figure 3: Dimensionless peak velocity, $V_\mathrm{max}/V_\mathrm{d}$ as a function of the dimensionless frequency $\Omega$. The solid line corresponds to the model predictions for a drop of typical length $L_\mathrm{d} = 8$ mm. Colorbar shared with Fig. \ref{['fig:expMeas']}.
• Figure S1: Comparison between the impedance predicted by the model (brown line) and the experimental one (symbols). The cyan line is a fitting to the experimental impedance of the circuit with no drop, $Z_\mathrm{c}$.
• Figure S2: Experimental setup and workflow control.