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

YQ Li and HA Wu and FC Wang, JOURNAL OF PHYSICS D-APPLIED PHYSICS, 49, 085304 (2016).

DOI: 10.1088/0022-3727/49/8/085304

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.

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