  Small droplets on slender conical fibers spontaneously move along the fiber
due to capillary action. The droplet motion depends on the geometry of the
cone, the surface wettability, the surface tension, the viscosity, and the
droplet size. Here we study with experiments and numerical simulations, the
formation, spontaneous motion, and the eventual merger, of multiple droplets on
slender conical fibers as they interact with each other. The droplet size and
their spacing on the fibre is controlled by the Plateau-Rayleigh instability
after dip-coating the conical fiber. Once these droplets are formed on the
fiber, they spontaneously start to move. Since droplets of different size move
with different speeds, they effectively coarsen the droplet patterning by
merging on the fiber. The droplet merging process affects locally the droplet
speed and alters the spatiotemporal film deposition on the fiber.
