Three-dimensional extrudate swell experimental and numerical study of a polyethylene melt obeying a memory-integral equation

The present work deals with the experimental and numerical features of the flow of a linear low-density polyethylene melt (LLDPE) at 160°C at the exit of a die of square cross-section. The rheological properties of the fluid are fitted by a Wagner's memory-integral constitutive equation. The characteristics of the extrudate jet are determined by optical means at different flow rates. The stream-tube analysis, already applied to two-dimensional extrudate swell problems involving rate and integral constitutive equations, is considered to simulate the flow field. The method avoids particle tracking problems related to integral models and allows computation of the unknown free surface by considering only a `peripheral stream tube' limited by the wall and the jet surface and an inner stream surface. Those boundary surfaces are determined by considering the conservation equations together with boundary condition equations, solved by the Levenberg–Marquardt optimization algorithm. The method leads to a considerable reduction in the number of degrees of freedom and the storage area. The numerical results are found to be generally consistent with the experimental data and highlight the growing importance of stress peaks due to the singularity at the exit when the flow rate increases.