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

TL;DR

This paper derives asymptotically justified boundary conditions for a stiff viscoelastic two-phase fiber model, improving numerical stability and efficiency in simulating flow-enhanced crystallization during fiber spinning.

Contribution

It introduces asymptotic boundary conditions for a singularly perturbed model, reducing artificial effects and enhancing numerical robustness in fiber crystallization simulations.

Findings

Boundary conditions prevent artificial boundary layers.

Numerical methods become faster and more robust.

Facilitates process design and material optimization.

Abstract

For flow-enhanced crystallization in fiber spinning, the viscoelastic two-phase fiber models by Doufas et al. (J. Non-Newton. Fluid Mech., 2000) and Shrikhande et al. (J. Appl. Polym. Sci., 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.