Linear stability analysis of nonisothermal glass fiber drawing

Abstract

The draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocities, exceeds a critical value. In many cases, inertia, gravity, and surface tension cannot be neglected, and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. Additionally, it is also known that cooling can have a highly stabilizing effect on the draw resonance instability. However, a detailed analysis encompassing the effect of inertia, gravity, surface tension, and temperature is still lacking. Due to a destabilizing effect induced by geometry in the heat equation, we first show that the maximum critical draw ratio for fiber drawing can be two orders of magnitude lower than the one for the film casting problem when the heat transfer coefficient is assumed constant. By introducing a scaling making the fiber aspect ratio an independent parameter, we next show that the high value of the critical draw ratio encountered in industrial applications could be rationalized only if we consider that the heat transfer coefficient is not constant but depends on both the velocity and the cross-section area of the fiber. Within this framework, we show how the practical stability window is affected by the five control parameters: the draw ratio, the fiber aspect ratio, the inlet temperature, the convective heat transfer coefficient, and the stiffness of the non-homogeneous ambient temperature. We finally discuss the influence of radiative heat transfer on the stability.

Stability of drawing of microstructured optical fibres

“…Although this problem has a long history, it remains an active area of research, and important new stability results have been obtained by Bechert & Scheid (2017) and Philippi et al. (2022), who showed that the combined effects of surface tension, inertia and gravity can give rise to non-monotonic stability behaviour, and that surface tension can completely destabilise the flow. All of these studies considered the stability of axisymmetric thread with no internal holes.…”

“…For solid axisymmetric threads, this work has been extended to include the effects of inertia, surface tension, gravity and heating by various authors (Shah & Pearson 1972a,b;Geyling 1976;Geyling & Homsy 1980;Yarin 1986;Forest & Zhou 2001;Wylie, Huang & Miura 2007;Suman & Kumar 2009;Taroni et al 2013). Although this problem has a long history, it remains an active area of research, and important new stability results have been obtained by Bechert & Scheid (2017) and Philippi et al (2022), who showed that the combined effects of surface tension, inertia and gravity can give rise to non-monotonic stability behaviour, and that surface tension can completely destabilise the flow. All of these studies considered the stability of axisymmetric thread with no internal holes.…”