Stagnation of a droplet on a conical substrate determined by the critical curvature ratio

In this work, we studied the effect of the curvature ratio, which is defined as the ratio of the local substrate radii to droplet radii, on the spontaneous directed movement and stagnation of a droplet on a conical substrate. The stagnation phenomenon emerged when the ratio exceeded a critical value. We found that the moving process of the droplet from the tip to the base of the conical substrate can be divided into three stages based on the critical curvature ratio. In order, these comprise: the fast-moving stage (S1) where the droplet obtains large driving force and resistance force, which are resulted from large contact line and contact angle difference between the two opposite sides of the droplet, respectively; the short transition stage (S2) where the droplet morphology tends to be symmetry, both driving force and resistance force decrease rapidly to a low level; and the stagnation stage (S3) where the curvature ratio is much larger than the critical value. Both driving force and resistance force approach zero, the droplet stagnates at the local substrate instead of moving forward. The curvature ratio based theoretical analyses of free energy, driving force and resistance force are in good consistence with simulation results, and can well describe the moving process and the stagnation phenomenon of the droplet on the conical substrate.

在这项工作中，我们研究了曲率比（定义为局部基底半径与液滴半径之比）对液滴在锥形基底上的自发定向运动和停滞的影响。当该比值超过临界值时，出现停滞现象。我们发现，基于临界曲率比，液滴从锥形基底尖端向底部的移动过程可分为三个阶段。依次为：快速移动阶段（S1），在此阶段液滴获得较大的驱动力和阻力，这分别是由液滴两侧较大的接触线和接触角差异导致的；短暂过渡阶段（S2），在此阶段液滴形态趋于对称，驱动力和阻力迅速降低至较低水平；以及停滞阶段（S3），在此阶段曲率比远大于临界值，驱动力和阻力都趋近于零，液滴在局部基底上停滞而不向前移动。基于曲率比的自由能、驱动力和阻力的理论分析与模拟结果高度一致，能够很好地描述液滴在锥形基底上的移动过程和停滞现象。