2021/06/14 by Manuel Ettmüller, Ettmüller, Manuel, Walter Arne +5
Chemical Engineering · Materials Science · Physics and Astronomy · #34Bxx #34E15 #65L10 #76-XX #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Rheology and Fluid Dynamics Studies #Textile materials and evaluations #msc:34Bxx #msc:34E15 #msc:65L10 #msc:76-XX #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2106.07525
arxiv created 2021/06/14 · openalex publication_date 2021/06/14 · arxiv updated 2021/06/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.