Inverse parameter estimation for the white–metzner equation using extrudate diameter measurements

Abstract This study presents a method to determine the elastic modulus of the White–Metzner (WM) viscoelastic model, which is used to describe polymer melt flow. In processes involving polymeric liquids, elastic effects are essential for accurate simulations. In particular, phenomena such as melt swelling after extrusion and upon gate passage in injection molding are critical to process simulation. However, systematic procedures for material characterization remain underdeveloped since implementation of an appropriate material model is challenging due difficulties inherent in parameter determination. In this work, to account for the shear thinning behavior, which is essential when handling polymeric liquids in current processes, while also incorporating elastic properties, the WM equation was employed. The method employs the post-extrusion swelling phenomenon where the diameter of the extruded material expands after exiting the capillary die. It integrates melt swell measurements with numerical simulations based on the WM equation and highlights the importance of considering gravity in the simulation. A laser scanning microscope is used to measure the extruded diameter while adaptive multi-objective optimization identifies unknown parameters in the model to align the simulation results with the measured diameter. This approach successfully determined the elastic modulus of the PET-PEN copolymer, establishing a system for determining the viscoelastic properties of polymer melts.