Shape oscillation and detachment conditions for a droplet on a vibrating flat surface.

In this study, we obtain experimental understanding of the mode characteristics of a droplet placed on a flat surface under periodic forced vibrations. The detachment conditions for the droplet on the surface were also studied. In order to estimate the resonance frequency of a droplet placed on a hydrophobic surface, theoretical modelling was combined with experimental approaches. Two high speed cameras were used to observe droplet characteristics, including mode shape, detachment, occurrence of secondary droplet breakup, and horizontal torsional motion. Two cameras were installed to the right above the droplet and at the side of the droplet. There was no more than an 18% discrepancy between the theoretical and experimental resonance frequencies. This discrepancy was likely caused by several factors such as contact line friction, nonlinear wall adhesion, and experimental uncertainty. When applying a relatively low voltage to a speaker, the contact line of a droplet was pinned and shape oscillations of the droplet appeared in a bilaterally symmetric way. In contrast, at higher voltages, the contact line depinned and the shape oscillations became more active. For excitation frequencies identical to the mode frequency, the lobe size of the droplet was relatively larger than that at neighbouring frequencies. The experimental results also indicate that the generation and complete detachment of small-scale droplets occur only at the 2nd mode.

Mode pattern of internal flow in a water droplet on a vibrating hydrophobic surface.

The objective of this study is to understand the mode pattern of the internal flow in a water droplet placed on a hydrophobic surface that periodically and vertically vibrates. As a result, a water droplet on a vibrating hydrophobic surface has a typical shape that depends on each resonance mode, and, additionally, we observed a diversified lobe size and internal flows in the water droplet. The size of each lobe at the resonance frequency was relatively greater than that at the neighboring frequencies, and the internal flow of the nth order mode was also observed in the flow visualization. In general, large symmetrical flow streams were generated along the vertical axis in each mode, with a large circulating movement from the bottom to the top, and then to the triple contact line along the droplet surface. In contrast, modes 2 and 4 generated a Y-shaped flow pattern, in which the flow moved to the node point in the lower part of the droplet, but modes 6 and 8 had similar patterns, with only a little difference. In addition, as a result of the PIV measurement, while the flow velocity of mode 4 was faster than that of model 2, those of modes 6 and 8 were almost similar.