A One-Dimensional Model for Polypropylene Fiber Formation in Spunbonding Based on Airflow-Coupled Thermally Dominated Crystallization

Abstract

We propose a practical semi-empirical one-Dimensional (1D) elongational rheology and crystallization model for fiber formation within the spunbonding drawing region. The model predicts fiber diameter variations resulting from feed rate and drawing variations, which are common in the spunbonding process. To simplify the simulation of the polymeric phase, we introduce a method that reduces the need for extensive experimental fitting by a series of rapid simulations, among which the fitting case is selected by comparing the final fiber diameters. Fitting is based solely on the final fiber diameter at the conveyor, which is more accessible than the calorimetric or in-situ crystallization data required by conventional methods. This process consists of two steps: (1) performing a detailed Computational Fluid Dynamics (CFD) simulation to model the airflow within a large domain of the drawing region and determine the airflow being drawn from the surroundings toward the spinline, and (2) using the resulting air velocity profile as a boundary condition for our 1D fiber formation model. Alternatively, the air velocity in step (1) can be measured experimentally at various locations and incorporated as a boundary condition, enhancing the method's generalizability across different drafter geometries and operating conditions. Inspired by the Kanai et al. correlation framework, our 1D model in step (2) integrates heat transfer rates and extensional-thickening behavior within a thermally dominated crystallization framework: the relative crystallinity ξ(T) is expressed as a function of temperature alone, and the influence of Flow-Induced Crystallization (FIC) on melt rheology is captured indirectly through G_K. The model relies on a single empirical constant, G_K, requiring only one experimental fitting parameter per operating regime. G_K is not a material constant but a system-dependent effective parameter—equal to the logarithm of the total viscosity amplification from die to conveyor—whose value varies with throughput and drawing conditions. Since fiber Reynolds numbers remain of order unity, the airflow and fiber phases are one-way coupled; this allows a detailed air velocity profile to serve as a boundary condition, shifting computational complexity from crystallization kinetics to the more tractable airflow dynamics. We conducted a series of experiments using cryogenic Nitrogen (LN₂) to freeze molten fiber samples at various positions between the die and conveyor of a lab-scale spunbonding machine for comparison with the simulated data. We also performed X-Ray Diffraction (XRD) analysis of crystallized samples, which provided further insight into G_K, the effective crystallization index introduced in this study. The model reproduces measured diameter profiles across all tested feed and draw conditions, with the fitted G_K values reflecting the coupled influence of throughput and drawing force on effective crystallization rate.