Resonance induced instability for surface tension measurement part 2, extension to terrestrial environments and limitations

This study extends a method for extracting multiple surface tension measurements from a single experiment by leveraging resonant spatial modes generated during the Faraday forcing of a levitated droplet. The prior phase of this work demonstrated that, under sufficiently strong forcing, secondary modal responses emerge through nonlinear interactions with the primary mode as observed from experiments performed aboard the International Space Station (ISS) in the electrostatic levitation furnace (ELF) of the Japan Aerospace Exploration Agency. By comparing the primary droplet response with its secondary responses, a self-consistent method for determining surface tension could be achieved. However, due to experimental conditions, only the first principal mode (mode 2) was realized. The present study extends this approach by focusing on target modes higher than the principal mode in ground-based experiments conducted at Marshall Space Flight Center’s Electrostatic Levitation Laboratory (ESL). Results show that higher-order modes are preferable because they minimize interference from harmonics of the forcing frequency. Alternatively, when surface deformation remains below 10% of the resting radius for the first principal mode, the true modal frequencies of subordinate modes can still be distinguished from harmonic responses. Other nonlinear behaviors that appear during drop oscillation, where the natural frequency can be extracted, are discussed as well. Here, we report measurements obtained for platinum, gold, and tin, which exhibit strong agreement between experimentally measured and theoretically predicted natural frequency ratios in ground-based environments, underscoring the capability of the method.