Whirling instability of an eccentric coated fibre

Abstract

We study a gravity-driven viscous flow coating a vertical cylindrical fibre. The destabilisation of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh–Plateau and Kapitza instabilities in the limit of small Bond numbers $Bo$ . Here, we focus on quasi-inertialess flows (large Ohnesorge number $Oh$ ) and conduct a linear stability analysis on a unidirectional flow along a rigid eccentric fibre for intermediate to large $Bo$ . We show the existence of two unstable modes, namely pearl and whirl modes. The pearl mode depicts asymmetric beads, similar to that of the Rayleigh–Plateau instability, whereas a single helix forms along the axis in the whirl mode instability. The geometric and hydrodynamic thresholds of the whirl mode instability are investigated, and phase diagrams showing the transition thresholds between different regimes are presented. Additionally, an energy analysis is carried out to elucidate the whirl formation mechanism. This analysis reveals that despite the unfavourable capillary energy cost, the asymmetric interface shear distribution, caused by the fibre eccentricity, has the potential to sustain a whirling interface. In general, small fibre radius and large eccentricity tend to foster the whirl mode instability, while reducing $Bo$ tends to favour the dominance of the pearl mode instability. Finally, we compare the predictions of our model with the results of some illustrative experiments, using highly viscous silicone oils flowing down fibres. Whirling structures are observed for the first time, and the measured wavenumbers match our stability analysis prediction.

Bead-on-fibre morphology in shear-thinning flow

“…However, in this case, the viscosity is independent of shear rate; thus asymmetry must arise from a different mechanism. Recent work by Eghbali et al (2022) showed that shear along the liquid-gas interface of a Newtonian liquid can sustain asymmetric flows for thick, viscous films flowing down a fibre using an energy balance analysis. However, the asymmetry of a Newtonian bead-on-fibre pattern remains an open topic for investigation, and the mechanism responsible for amplifying and sustaining it has yet to be determined.…”

“…Eghbali et al. (2022) performed experiments on highly viscous Newtonian flow down a fibre, and observed two asymmetric modes: pearl and whirl. They altered the initial eccentricity of the liquid about the fibre, showing that the morphology depends on the Bond number and eccentricity, and rationalized these observations using an energy analysis that showed that shear at the liquid–gas interface can sustain the whirling mode instability.…”

“…The asymmetric morphology results in azimuthally asymmetric bead profiles like the 'clamshell' profile observed for static beads on a fibre; however, they are also axial asymmetric, resulting in a wide range of shapes. Eghbali et al (2022) performed experiments on highly viscous Newtonian flow down a fibre, and observed two asymmetric modes: pearl and whirl. They altered the initial eccentricity of the liquid about the fibre, showing that the morphology depends on the Bond number Bo and eccentricity, and rationalized these observations using an energy analysis that showed that shear at the liquid-gas interface can sustain the whirling mode instability.…”

Research on online monitoring and anti-dance technology of transmission line dance based on wide-area information transmission

“…P.Yu's eccentric inertia coupling instability mechanism that the lateral and torsional motions may be stable only due to the eccentric inertia effect caused by the angle of attack change so that the response of the lift on the lateral vibration to form a positive feedback exacerbated the lateral vibration, and gradually accumulating energy, and finally the formation of a substantial dance. Theoretically speaking, vertical self-excitation or torsional self-excitation of a single degree of freedom is possible, but in fact, the wire dance belongs to the motion of three degrees of freedom, and in the vast majority of cases, three kinds of vibration, vertical, horizontal and torsional, will occur at the same time [23]. This is due to the presence of eccentric inertia of the wire over ice, where one motion may induce another.…”