A new scaling number reveals droplet dynamics on vibratory surfaces

Abstract

HypothesisDroplet spreading on surfaces is a ubiquitous phenomenon in nature and is relevant with a wide range of applications. In practical scenarios, surfaces are usually associated with certain levels of vibration. Although vertical or horizontal modes of vibration have been used to promote droplet dewetting, bouncing from immiscible medium, directional transport, etc., a quantitative understanding of how external vibration mediates the droplet behaviors remains to be revealed. MethodsWe studied droplets impacting on stationary and vibratory surfaces, respectively. In analogy to the Weber number We=ρUi2D0/γ, we define the vibration Weber number We*=ρUv2D0/γ to quantitively analyze the vibration-induced dynamic pressure on droplet behaviors on vibratory surfaces, where ρ,γ,D0,UiandUv are liquid density, surface tension, initial droplet diameter, impact velocity of the droplet, and velocity amplitude of vibration, respectively. FindingsWe demonstrate that the effect of vibration on promoting droplet spreading can be captured by a new scaling number expressed as We*/[We1\\2sin(θ/2)], leading to (Dm − Dm0)/Dm0 ∝ We*/[We1\\2sin(θ/2)], where θ is the contact angle, and Dm0 and Dm are the maximum diameter of the droplet on stationary and vibratory surfaces, respectively. The scaling number illustrates the relative importance of vibration-induced dynamic pressure compared to inertial force and surface tension. Together with other well-established non-dimensional numbers, this scaling number provides a new dimension and framework for understanding and controlling droplet dynamics. Our findings can also find applications such as improving the power generation efficiency, intensifying the deposition of paint, and enhancing the heat transfer of droplets.