Effects of vibration amplitude and volume on resonance characteristics of supercooled sessile droplets

Supercooled sessile droplets on cold surfaces exist widely in industry and easily experience freezing/frosting subjected to external vibrations. Existing research, however, has predominantly focused on droplet vibration under ambient conditions. This study investigates the resonance characteristics of such droplets under varying vibration amplitudes (200–1000 μm) and volumes (25–75 μL), employing a low-temperature vibration platform. The experiments show that the harmonic resonance response of the droplets shares the same period as the excitation signal but exhibits a half-period phase lag. Supercooling has a minor effect on the resonance frequencies of the droplet's second-, third-, and fourth-order modes. However, supercooling suppresses droplet deformation by increasing viscosity and contact radius. For the second- and third-order modes, the normalized peak height of 50 μL supercooled droplets increases approximately linearly with amplitude, showing increments of 19.82% and 10.90%. In the fourth-order mode, high amplitudes induce Faraday instability, resulting in a normalized peak height significantly lower than that of an ambient-temperature droplet. The node angles on the droplet surface are weakly affected by volume, whereas the normalized peak height in the second-order mode decreases with increasing volume due to the enhanced restraining effect of gravity on deformation. A modified spherical harmonic model, applicable under pinned contact line conditions, is established and accurately captures droplet shapes at the peak, valley, and equilibrium states. The findings clarify the coupling mechanism between vibration and supercooling, providing insights for vibration-accompanied icing processes and de-icing strategies.