On flow-enhanced crystallization in fiber spinning: Asymptotically justified boundary conditions for numerics of a stiff viscoelastic two-phase model

For flow-enhanced crystallization in fiber spinning, the viscoelastic two-phase fiber models by Doufas et al. (2000) and Shrikhande et al. (2006) are state of the art. However, the boundary conditions associated to the onset of crystallization are still under discussion, as their choice might cause...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2021-10, Vol.296, p.104636, Article 104636
Main Authors: Ettmüller, Manuel, Arne, Walter, Marheineke, Nicole, Wegener, Raimund
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Boundary layers
Boundary value problem of perturbed ordinary differential equations
Continuation-collocation method
Crystallization
Design optimization
Differential equations
Fiber spinning
Mathematical models
Ordinary differential equations
Parameters
Relaxation time
Robustness (mathematics)
Viscoelastic two-phase model
Viscoelasticity
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Summary:For flow-enhanced crystallization in fiber spinning, the viscoelastic two-phase fiber models by Doufas et al. (2000) and Shrikhande et al. (2006) are state of the art. However, the boundary conditions associated to the onset of crystallization are still under discussion, as their choice might cause artificial boundary layers and numerical difficulties. In this paper we show that the model class of ordinary differential equations is singularly perturbed in a small parameter belonging to the semi-crystalline relaxation time and derive asymptotically justified boundary conditions. Their effect on the overall solution behavior is restricted to a small region near the onset of crystallization. But their impact on the performance of the numerical solvers is huge, since artificial layering, ambiguities and parameter tunings are avoided. The numerics becomes fast and robust and opens the field for simulation-based process design and material optimization. •Asymptotic analysis of a viscoelastic two-phase fiber model for melt spinning.•Derivation of asymptotically justified boundary conditions.•The underlying ordinary differential equations become regularly perturbed.•Avoidance of artificial boundary layering, ambiguities and parameter tunings.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2021.104636