Spreading dynamics of droplets impacting on oscillating hydrophobic substrates

Droplet impact on oscillating substrates is important for both natural and industrial processes. Recognizing the importance of the dynamics that arises from the interplay between droplet transport and substrate motion, in this work, we present an experimental investigation of the spreading of a droplet impacting a sinusoidally oscillating hydrophobic substrate. We focus particularly on the maximum spread of droplets as a function of various parameters of substrate oscillation. We first quantify the maximum spreading diameter attained by the droplets as a function of frequency, amplitude of vibration, and phase at the impact for various impact velocities. We highlight that there can be two stages of spreading. Stage I, which is observed at all impact conditions, is controlled by the droplet inertia and affected by the substrate oscillation. For certain conditions, a Stage II spreading is also observed, which occurs during the retraction process of Stage I due to additional energies imparted by the substrate oscillation. Subsequently, we derive scaling analyses to predict the maximum spreading diameters and the time for this maximum spread for both Stage I and Stage II. Furthermore, we identify the necessary condition for Stage II spreading to be greater than Stage I spreading. The results will enable optimization of the parameters in applications where substrate oscillation is used to control the droplet spread, and thus heat and mass transfer between the droplet and the substrate.