Whirling instability of an eccentric coated fiber*

The destabilization of the gravity-driven flow of a viscous liquid thread coating a vertical cylindrical fiber into a downward moving train of beads has been linked to the conjunction of the Rayleigh-Plateau and Kapitza instabilities when the surface tension dominates over gravity (small Bond numbers, $Bo$). We focus on the limit of large $Bo$ by means of experiments with highly viscous silicone oils flowing down fibers, forming centimeter-diameter threads, and linear stability analyses (LSA) of quasi-inertialess flows (large Ohnesorge number, $Oh$). Relaxing the concentricity of the fiber and the liquid thread, we show the existence of two unstable modes: pearl (P) and whirl (W) modes. The P mode depicts asymmetric beads, whereas a helical interface forms around the fiber in the W mode instability. Detailed LSA of a unidirectional flow along a rigid eccentric fiber is conducted to determine the geometric and hydrodynamic thresholds of the W mode instability. Additionally, energy analysis is carried out to elucidate the whirl formation mechanism. Despite its capillary cost, the asymmetric shear distribution around a small eccentric fiber has the potential to sustain the interface whirl, at sufficiently large $Bo$. We compare the predictions of our model to experimental results.