The role of oscillation in ellipsoidal drop impact on a solid surface

Liquid droplet impact on a sonically excited thin membrane

The characteristics of droplet impact on hydrophobic surfaces can be altered by introducing surface oscillations. The contact duration, spreading, retraction, and rebounding behaviors of the impacting water droplet are examined at various sonic excitation frequencies of the hydrophobic membrane. Membrane oscillation and droplet behavior are analyzed by utilizing a high-speed camera. The restitution coefficient and membrane dynamics are formulated and the findings are compared with those of the experiments. It is found that the mode of membrane oscillation changes as the sonic excitation frequency is changed. The droplet spreading and retraction rates reduce while the rebound height and restitution coefficient increase at a sonic excitation frequency of 75 Hz. However, further increase of the excitation frequency results in reduced rebound height because of the increased energy dissipation on the impacted surface. The droplet contact (transition time) duration reduces as the excitation frequency increases. Increasing droplet Weber number enhances the droplet contact period on the membrane, which becomes more apparent at low frequencies of sonic excitation.

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=ρU_i²D₀/γWe = ρUi2D0/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.