Abstract

A continuum-level model for non-isothermal polymer crystallization following a complex flow is presented, along with a fundamental rule that may be employed to determine if the flow will influence the ensuing crystallization dynamics. This rule is based on two dimensionless parameters: the (Rouse) Weissenberg number, and an inverse Deborah number de�ned by the ratio between the time taken to cool to the melting point versus the stretch relaxation time, which determines the time available for flow-enhanced crystallization. Moreover, we show how the time to reach the melting point can be derived semi-analytically and expressed in terms of the processing conditions in the case of pipe
flow - ubiquitous in polymer processing. Whilst the full numerical model is required to quantitatively predict induction times and spherulite-size distributions, the proposed fundamental rule may be used practically to ensure, or
eliminate, flow-enhanced structures by controlling the processing conditions or material properties. We discuss how
ow-enhanced structures may be revealed only after post-processing annealing, and finally examine previous works that have successfully applied the model to extrusion-based three-dimensional (3D) printing.