Influence of process and material parameters on the draw resonance instability

In film casting and fiber spinning processes, liquid material is extruded through a die with predefined speed and taken up by a rotating chill roll in order to fabricate thin films and slender fibers. The main control parameter is the so-called draw ratio, defined as the ratio of the inlet to the take-up velocity. Exceeding a critical draw ratio results in steady oscillations of both the velocity field and film or, respectively, fiber geometry, which is commonly known as draw resonance and which leads to inhomogeneous product properties and possible breakdown of the process.
 
In this talk, a linear stability study of draw resonance is presented. The first part concentrates on the influence of practical relevant control parameters on the onset of draw resonance. For this purpose, a simple one-dimensional Newtonian model is used to investigate the effects of inertia and gravity. The neck-in effect, which describes the reduction of film width along the stretching direction, and the influence of surface tension in fiber spinning are discussed as well. Stability maps give a comprehensive overview of the stability behavior of the system and enable the identification of various regimes, including regions of unconditional stability and unconditional instability.
 
In the second part of the talk, the influence of viscoelastic properties is discussed. This is accompanied by a small experimental study on the dependence of the critical draw ratio on the Deborah number. Necessary properties of an appropriate viscoelastic constitutive equation are evaluated and underlying stability mechanisms are revealed.
Finally, the theoretical prediction is compared to the experimental findings.

References
[1] M. Bechert, D. W. Schubert and B. Scheid, Practical mapping of the draw resonance instability in film casting of Newtonian fluids, European Journal of Mechanics B/Fluids 52, 68-75 (2015).