Self-climbing of a low surface tension droplet on a vertical conical surface

Abstract

The anti-gravity self-climbing behavior of an axisymmetric barrel-shaped droplet with low surface tension on a vertical conical surface was investigated. Parabolic equations, circular equations and linear equations were proposed to build the analytic expressions of the two-dimensional gas-liquid interface, the final advancing-/receding-end positions were solved numerically. The results showed that the apparent dynamic contact angles of the droplets became greater with the increase of volume, and were larger than the Young’s contact angle. The realizable highest self-climbing height of the droplet was increased monotonically with the decrease of the surface tension. The deposited pre-wetting film on the conical surface reduced the contact line pinning force of the droplet, which could dramatically facilitate the self-climbing of the droplet when the contact line pinning force played a more important role in the resistance than the gravity. Compared to the circle-shaped and cone-shaped gas-liquid interface of the droplet at the final self-climbing position, the droplet thickness and the self-climbing height of the droplet in a parabolic shape were much closer to that of experiments, and the relative differences between the theoretical results and the experimental results were lower than 20%. Moreover, the surface free energy of the droplet calculated based on a parabolic shape was close to that form SE simulations. The findings in this work help to manipulate the self-climbing behavior of low surface tension droplets in various potential applications.