Non-Newtonian flow has been a topic of academic studies for over a hundred years and is highly relevant to many industrial processes, particularly in polymer processing. Various microstructure and/or continuum mechanics frameworks have been proposed in the literature to model the nonlinear effects of elasticitity in polymer flow. However, accurate modeling of 3-D viscoelastic flow with high Deborah number and Weissenburg number still remains a substantial challenge, and constitutive models with minimal number of fitting parameters are particularly desired in modeling of realistic flow problems in polymer processing. In this work, a hybrid microstructure/continuum formulation is developed for a finitely extensible polymer coil that interacts with surrounding molecules through entanglement and disentanglement. A polymer coil is considered as an ellipsoid in the continuum domain and its microstructural effects on relaxation and hardening are tackled through finite stretch. A rotational recovery process is additionally introduced to the evolution equation for the ellipsoidal conformation tensor using continuum mechanics principles so that the difference between rotational flow (such as shear) and purely extensional flow can be naturally handled in 3D flow. The resulting model contains 3 major parameters: one for finite stretch dictated by a ceiling stretch of the coil, a second one for rotational recovery, and a third one for adjusting stretch hardening of the rubbery coil. Each model parameter is linked to a corresponding physical process and can be readily determined from normal rheological plots. The new model, even in a single mode, is able to simultaneously predict practical material functions in simple shear and coaxial extension and to fit well to representative experimental data. Particularly in the steady-state (or quasi-steady state) flow case, a nearly closed-form stress to velocity gradient relationship can be derived with which shear thinning and elongational thickening can be simultaneously considered while computational advantages of a classical GNF model is retained.
About Lecturer: Donggang Yao is Professor in the School of Materials Science & Engineering at Georgia Institute of Technology. He received his Ph.D. and Master’s degrees both in Mechanical Engineering from University of Massachusetts Amherst, and his B.S. degree from Shanghai Jiao Tong University, China. He teaches and directs research in the broad area of polymer engineering. His current research focuses on processing of high-strength polymer fibers, single-polymer composites manufacturing, and constitutive modeling of rheologically complex materials. Dr. Yao was a recipient of the 2003 NSF Career Award. He currently serves as an associate editor for the ASME Journal of Manufacturing Science and as the Polymer and Soft Materials Technical Committee Chair of the Materials Division of ASME.