Measuring Liquid Metal Interfacial Tension by Faraday Wave Dispersion and Zero-Padded FFT

We present a benchtop Faraday wave dispersion method for measuring the interfacial tension of room-temperature liquid metals. A GaInSn layer covered by NaOH solution is vertically vibrated (30-70 Hz) to excite subharmonic standing waves at the GaInSn-NaOH electrochemical interface. Wavelengths are extracted from time-averaged images via zero-padded spatial FFT (2048 px) with a meniscus-excluding mask. A nonlinear least-squares fit of the two-layer dispersion relation over seven frequencies and 41 individual measurements yields σ = 0.488 N/m (R2 = 0.990). Including all experimental uncertainty sources, the final result is σ = 0.488 ± 0.027 N/m. Independent pendant-drop measurements on the same GaInSn-NaOH interface give σ = 0.444 N/m, consistent with published pendant-drop and microfluidic tensiometry values spanning 0.40-0.50 N/m. The method requires no transmission through the working fluid, making it suitable for opaque liquid metals where conventional optical tensiometry is precluded.