The fastest drop climbing on a wet conical fibre

We use high-speed video imaging to study the capillary-driven motion of a micro-droplet along the outside of a pre-wetted conical fiber. The cones are fabricated on a glass-puller with tip diameters as small as 1 μm, an order of magnitude smaller than in previous studies. The liquid is fed through the hollow fiber accumulating at the fiber tip to form droplets. The droplets are initially attached to the opening as they grow in size before detaching and traveling up the cone. This detachment can produce a transient oscillation of high frequency. The spatial variation of the capillary pressure drives the droplets towards the wider side of the cone. Various liquids were used to change the surface tension by a factor of 3.5 and viscosity by a factor of 1500. Within each droplet size and viscous-dissipation regime, the data for climbing speeds collapse on a single curve. Droplets traveling with and against gravity allow us to pinpoint the absolute strength of the driving capillary pressure and viscous stresses and thereby determine the prefactors in the dimensionless relationships. The motions are consistent with earlier results obtained from much larger cones. Translation velocities up to 270 mm/s were observed and overall the velocities follow capillary-viscous scaling, whereas the speed of the fastest droplets is limited by inertia following their emergence at the cone tip.