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

Abstract

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 $s\sim t^{1/3}$ 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.

arXiv comment30 pages,15 figures

References in corpus (9)

• Self Running Droplet: Emergence of Regular Motion from Nonequilibrium Noise
• Ultrafast Spontaneous Motion of Nanodroplets
• Ring to Mountain Transition in Deposition Pattern of Drying
• Wetting hysteresis induced by nanodefects
• Chemo-Sensitive Running Droplet
• Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems
• Directional spreading of a viscous droplet on a conical fibre
• Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces
• Solid-state dewetting on curved substrates