Mechanism for drop formation on a coated vertical fibre

Abstract

Rayleigh instability on an axisymmetric viscous film around a vertical fibre produces localized wave structures (pulses) on a flat substrate film that can grow by an order of magnitude to form large capillary drops. We show that this drop formation process is driven by a unique mechanism in the form of an ever-growing pulse which leaves behind a trailing film thinner than the one it advances into. In addition to accumulating liquid from the film, the growing pulse also captures smaller and slower pulses in coalescence cascades. We construct this supercritical growing pulse by matched asymptotics and show that it will eventually evolve into a capillary drop if the local film thickness h is larger than hc=1.68R3H−2 where R is the fibre radius and H the capillary length. We also show that subcritical pulses with h<hc will equilibrate into stationary pulses that do not grow or coalesce readily to form drops.