Choice of the Mathematical Models in the Simulation of Elongational Flow-Induced Crystallization (FIC) During Polymer Processing: A Review

Behrang Mohajer; Amirmahdi Salehi; Mohamad Kheradmandkeysomi; Amirjalal Jalali; Markus Bussmann; Chul B. Park

Abstract

This review examines mathematical models of elongational Flow-Induced Crystallization (FIC) from a computational modeling perspective, emphasizing their practical integration within transport-based simulation frameworks. The work targets researchers in computational fluid dynamics (CFD) who model the cooling stages of polymer processing operations such as melt spinning and injection molding. Rather than reiterating the extensive physics of FIC, the review focuses on the choice of mathematical formulation best suited for a given simulation objective. Existing approaches are classified into four model types distinguished by their complexity, required input data, and computational cost: Type 1 models introduce empirical crystallization terms within simplified rheological frameworks; Type 2 combine the Avrami formulation with correlations that account for flow-induced effects; Type 3 embed crystallization kinetics directly into constitutive equations through stress or strain tensors; and Type 4 represent molecular or atomistic simulations that resolve chain dynamics in detail. Each model type is critically evaluated in terms of predictive accuracy, implementation practicality, and suitability for different process scales. Comparative tables summarize these attributes, guiding the selection of an appropriate correlation strategy consistent with available data and computational resources. The review concludes by identifying current challenges—including polymer blends, non-isothermal effects, and anisotropic morphologies—and outlining promising directions for future research. Overall, this work serves as a concise reference for CFD practitioners seeking reliable FIC formulations that balance fidelity, efficiency, and applicability across polymer-processing simulations.

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