Liu Jianxin, Feng Zhicheng, Ouyang Wengen, Shui Langquan, Liu Ze
Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China.
ACS Omega. 2022 Jun 7;7(24):20975-20982. doi: 10.1021/acsomega.2c01713. eCollection 2022 Jun 21.
Experiments and simulations have shown that a droplet can move spontaneously and directionally on a conical substrate. The driving force originating from the gradient of curvatures is revealed as the self-propulsion mechanism. Theoretical analysis of the driving force is highly desirable; currently, most of them are based on a perturbative theory with assuming a weakly curved substrate. However, this assumption is valid only when the size of the droplet is far smaller than the curvature radius of the substrate. In this paper, we derive a more accurate analytical model for describing the driving force by exploring the geometric characteristics of a spherical droplet on a cylindrical substrate. In contrast to the perturbative solution, our model is valid under a much weaker condition, i.e., the contact region between the droplet and the substrate is small compared with the curvature radius of the substrate. Therefore, we show that for superhydrophobic surfaces, the derived analytical model is applicable even if the droplet is very close to the apex of a conical substrate. Our approach opens an avenue for studying the behavior of droplets on the tip of the conical substrate theoretically and could also provide guidance for the experimental design of curved surfaces to control the directional motion of droplets.
实验和模拟表明，液滴可以在锥形基底上自发地定向移动。源自曲率梯度的驱动力被揭示为自推进机制。对驱动力进行理论分析非常有必要；目前，大多数分析基于微扰理论，且假设基底曲率较弱。然而，该假设仅在液滴尺寸远小于基底曲率半径时才成立。在本文中，我们通过探究圆柱形基底上球形液滴的几何特征，推导出一个更精确的描述驱动力的解析模型。与微扰解不同，我们的模型在弱得多的条件下有效，即液滴与基底之间的接触区域与基底曲率半径相比很小。因此，我们表明，对于超疏水表面，即使液滴非常靠近锥形基底的顶点，所推导的解析模型也适用。我们的方法为从理论上研究锥形基底尖端上液滴的行为开辟了一条途径，也可为控制液滴定向运动的曲面实验设计提供指导。
