Self-propulsion dynamics of small droplets on general surfaces with curvature gradient

We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computations for the capillary energy and the viscous dissipation in the system. The model describes quantitatively the spontaneous motion of a liquid droplet on general surfaces. In particular, it recovers previous models for droplet motion on the outside surface of a cone. In this case, we derive a scaling law of the displacement s similar to t(1/3) of a droplet with respect to time t by asymptotic analysis. Theoretical results are in good agreement with experiments in previous literature without adjusting the friction coefficient in the model.

Automated summary

Theoretical study on the self-propulsion dynamics of a small droplet on general curved surfaces leads to a new reduced model that quantitatively describes the motion of droplets. The model includes a scaling law for droplet displacement with respect to time on the outside surface of a cone. The theoretical results are in good agreement with experimental data without adjusting the friction coefficient in the model.