Vibration of submillimeter-size supported droplets

We study the fundamental vibration mode of supported submillimeter-size droplets. Using an analogy with a simple oscillator we derive a semianalytical expression for the eigenfrequency and the scaling law of the energy dissipation within the droplet. The experimental results obtained for mercury drops deposited on glass are compared with the model. The agreement is satisfactory for the eigenfrequencies on the whole range of size we considered (from 0.04 to 0.9 mm). The scaling law for the dissipation is recovered for radii larger than 0.1 mm but fails for smaller droplets. We finally discuss possible applications related to the use of vibrations to effectively reduce the hysteresis of the wetting angle and therefore increase the mobility of the supported droplets.