Elastic memory governed cross-sectional evolution of non-circular viscoelastic jets: A critical role of the first normal stress difference

The precise control of cross-sectional morphology in profiled fibers remains a challenge due to the non-uniform extrusion swell, a phenomenon insufficiently elucidated by existing models. To overcome this, we develop a predictive, multi-velocity center coupled extrusion model for dry-jet wet spinning that explicitly resolves the coupling between velocity field rearrangement and elastic recovery. This model identifies the first normal stress difference as the key quantitative indicator of the elastic memory effect, which dominates cross-sectional deformation under low draw conditions. A critical threshold of 4.7 × 103 Pa for this stress difference, driving extrusion swell, is established. Simulation results, validated by experiments, provide a practical guideline for spinneret design and process control, enabling the precise fabrication of profiled fibers with tailored shapes.