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Simulation-based High-Speed Elongational Rheometer for Carreau-type Materials

Lukas Kannengiesser, Walter Arne, Alexander Bier, Nicole Marheineke, Dirk W. Schubert, Raimund Wegener

TL;DR

The paper develops a simulation-based workflow to identify Carreau-type elongational viscosity parameters within a unified 1D fiber-spinning model. It combines a collocation-continuation numerical scheme for the boundary-value fiber equations with a gradient-based nonlinear least-squares optimization, using diameter data from multiple high-speed spinning experiments to infer $(n,\kappa)$ where $K=\exp(\kappa)$. The identified parameters, e.g., $(n,\kappa)=(0.8,11.71)$ giving $K_{opt}=1.22\times10^{5}$ Pa, demonstrate pronounced non-Newtonian behavior and provide a better fit to diameter and velocity profiles than Newtonian models. This work delivers a proof-of-concept for data-driven parameter identification in generalized Newtonian polymers and lays groundwork for extending to more complex rheologies and process designs, with potential impact on high-speed fiber spinning simulations and material characterization.

Abstract

For the simulation-based design of fiber melt spinning processes, the accurate modeling of the processed polymer with regard to its material behavior is crucial. In this work, we develop a high-speed elongational rheometer for Carreau-type materials, making use of process simulations and fiber diameter measurements. The procedure is based on a unified formulation of the fiber spinning model for all material types (Newtonian and non-Newtonian), whose material laws are strictly monotone in the strain rate. The parametrically described material law for the elongational viscosity implies a nonlinear optimization problem for the parameter identification, for which we propose an efficient, robust gradient-based method. The work can be understood as a proof of concept, a generalization to other, more complex materials is possible.

Simulation-based High-Speed Elongational Rheometer for Carreau-type Materials

TL;DR

The paper develops a simulation-based workflow to identify Carreau-type elongational viscosity parameters within a unified 1D fiber-spinning model. It combines a collocation-continuation numerical scheme for the boundary-value fiber equations with a gradient-based nonlinear least-squares optimization, using diameter data from multiple high-speed spinning experiments to infer where . The identified parameters, e.g., giving Pa, demonstrate pronounced non-Newtonian behavior and provide a better fit to diameter and velocity profiles than Newtonian models. This work delivers a proof-of-concept for data-driven parameter identification in generalized Newtonian polymers and lays groundwork for extending to more complex rheologies and process designs, with potential impact on high-speed fiber spinning simulations and material characterization.

Abstract

For the simulation-based design of fiber melt spinning processes, the accurate modeling of the processed polymer with regard to its material behavior is crucial. In this work, we develop a high-speed elongational rheometer for Carreau-type materials, making use of process simulations and fiber diameter measurements. The procedure is based on a unified formulation of the fiber spinning model for all material types (Newtonian and non-Newtonian), whose material laws are strictly monotone in the strain rate. The parametrically described material law for the elongational viscosity implies a nonlinear optimization problem for the parameter identification, for which we propose an efficient, robust gradient-based method. The work can be understood as a proof of concept, a generalization to other, more complex materials is possible.
Paper Structure (16 sections, 36 equations, 5 figures, 3 tables, 2 algorithms)

This paper contains 16 sections, 36 equations, 5 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Fiber Spinning Simulation Model
  3. Fiber model
  4. Collocation-continuation scheme
  5. Parameter dependence
  6. Gradient-based Parameter Identification
  7. Problem formulation
  8. Data and weighting strategies
  9. Algorithmic procedure
  10. Application and Results
  11. Test setting: Data and solver
  12. Identified material parameters and fiber behavior
  13. Solver performance
  14. Conclusion
  15. Model Closure
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Spinning apparatus with single die and aspirator, used in bier2022novel
  • Figure 2: Data of measured fiber diameters (top) and converted (velocity-like) counterparts (bottom) with associated fitted profiles along the spin-line for two different experimental settings (left and right)
  • Figure 3: Diameter profiles over spin-line in different experimental set-ups for PMMA7N: measured data and associated fit vs. simulated results with $\mathbf{p}_\mathrm{opt}$ as well as $n=1$ (Newtonian)
  • Figure 4: Velocity-like profiles over spin-line in different experimental set-ups for PMMA7N: converted measured data and associated fit vs. simulated results with $\mathbf{p}_\mathrm{opt}$ as well as $n=1$ (Newtonian)
  • Figure 5: Cost function $J$ for $n\in [0,1]$ and $\kappa \in [9,16]$

Theorems & Definitions (2)

  • Remark 1
  • Remark 2