A new scaling number reveals droplet dynamics on vibratory surfaces

Mingkai Song; Hongwei Zhao; Ting Wang; Shunbo Wang; Jie Wan; Xuezhi Qin; Zuankai Wang

doi:10.1016/j.jcis.2021.10.165

A new scaling number reveals droplet dynamics on vibratory surfaces

J Colloid Interface Sci. 2022 Feb 15;608(Pt 3):2414-2420. doi: 10.1016/j.jcis.2021.10.165. Epub 2021 Oct 29.

Authors

Mingkai Song¹, Hongwei Zhao², Ting Wang³, Shunbo Wang¹, Jie Wan¹, Xuezhi Qin⁴, Zuankai Wang⁵

Affiliations

¹ School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, PR China.
² School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, PR China; Key Laboratory of CNC Equipment Reliability, Ministry of Education, Changchun 130025, PR China. Electronic address: hwzhao@jlu.edu.cn.
³ Department of Mechanical Engineering, City University of Hong Kong, Hong Kong 999077, PR China.
⁴ School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, PR China; Department of Mechanical Engineering, City University of Hong Kong, Hong Kong 999077, PR China.
⁵ Department of Mechanical Engineering, City University of Hong Kong, Hong Kong 999077, PR China. Electronic address: zuanwang@cityu.edu.hk.

PMID: 34753623
DOI: 10.1016/j.jcis.2021.10.165

Abstract

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=ρU_i²D₀/γ, we define the vibration Weber number We^*=ρU_v²D₀/γ to quantitively analyze the vibration-induced dynamic pressure on droplet behaviors on vibratory surfaces, where ρ,γ,D₀,U_iandU_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\2sin(θ/2)], leading to (D_m - D_m0)/D_m0 ∝ We^*/[We^1\2sin(θ/2)], where θ 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.

Keywords: Droplet spreading; Dynamic pressure; Scaling relation; Vibratory surfaces.