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

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.

Automated summary

The anti-gravity self-climbing behavior of a barrel-shaped droplet with low surface tension on a vertical conical surface was studied. Analytic expressions of the gas-liquid interface were established, and the positions of the advancing and receding ends were numerically determined. The results showed that the droplets exhibited increased apparent dynamic contact angles with volume, and the highest self-climbing height of the droplet increased with decreasing surface tension. The presence of a pre-wetting film on the conical surface reduced the contact line pinning force, facilitating the self-climbing of the droplet when the pinning force dominated over gravity. Compared to other interface shapes, the parabolic shape provided more accurate predictions of droplet thickness and self-climbing height, with relative differences of less than 20% between theoretical and experimental results. The findings have significant implications for manipulating low surface tension droplets in various applications.