A New Scaling Number Reveals Droplet Dynamics on Vibratory Surfaces.

Hypothesis: Droplet 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. Methods: We studied droplets impacting on stationary and vibratory surfaces, respectively. In analogy to the Weber number We = rho(UiD0/gamma)-D-2, we define the vibration Weber number We* = rho(UvD0/gamma)-D-2 to quantitively analyze the vibration-induced dynamic pressure on droplet behaviors on vibratory surfaces, where rho, gamma, D-0, U-i and U-v are liquid density, surface tension, initial droplet diameter, impact velocity of the droplet, and velocity amplitude of vibration, respectively. Findings: We demonstrate that the effect of vibration on promoting droplet spreading can be captured by a new scaling number expressed as We*/[We(1) sin(theta/2)], leading to (D-m - D-m0)/D-m0 proportional to We*/[We(1) sin(theta/2)], where theta is the contact angle, and D-m0 and D-m 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. (C) 2021 Elsevier Inc. All rights reserved.