Helical Instability of an Eccentric Coated Fiber

We study the destabilization of a gravity-driven viscous flow coating a vertical fiber. Numerous studies have focused on the transition of a liquid thread into a downward traveling train of beads along a fiber, a phenomenon known as Rayleigh-Plateau instability, in the limit of small Bond numbers, $Bo$, where the surface tension dominates over gravity. We here explore the limit of large $Bo$, i.e. centimetric radial sized liquid column. The experiments are carried out using highly viscous silicone oils to focus on inertialess flows (large Ohnesorge number, $Oh$). We observe the formation of a helical interface, coiling around the thin fiber, in this limit of high $Oh$ and $Bo$. We address theoretically the physical mechanism underlying the observed interface coiling and its associated geometric and hydrodynamic thresholds, by means of the linear stability analysis of a unidirectional flow along a rigid eccentric fiber. The asymmetry of the drainage velocity (shear distribution) above a certain threshold induces coiling. Overall, small fiber radius and large eccentricity tend to promote the coiling of the interface ($m=1$ modes), while reducing $Bo$ tends to preserve an axisymmetric interface ($m=0$ modes). We will compare the predictions of our model with experimental results.