Scaling laws of droplets on vibrating liquid-infused surfaces

Droplets oscillating on vibrating substrates are very interesting scientifically, with applications such as anti-icing, droplet transportation, and measuring dynamic surface tension. Reported here are the dynamics of droplets with different volumes on a vibrating smooth surface infused with liquid of different viscosities. The movement of the three-phase droplet contact line is used to quantify the droplet dynamics, and it is found that this movement is linearly proportional to the amplitude of the substrate and inversely proportional to the viscosity of the liquid infused therein. When the substrate viscosity is relatively low, the droplet volume also affects the contact-line movement. Scaling laws for the contact-line movement are derived involving the Ohnesorge number and the reciprocal of the capillary number. Also elucidated is the relationship between the resonance frequency and the substrate viscosity, and the characteristic droplet morphology under different substrate viscosities is extracted to describe the contact-line movement. Interestingly, the substrate viscosity is controlled in an innovative way to achieve almost the same contact-line movement on the present surface as on superhydrophobic and hydrophilic surfaces.