Computational Rheology with Integral Constitutive Equations

Abstract

AbstractComputational rheology deals with the formulation and solution of constitutive equations for non-Newtonian materials. From these the emphasis is put on polymeric materials, which exhibit both viscous and elastic behaviour in flow and deformation. These materials are often called viscoelastic materials. Polymer solutions and melts (e.g. commercial plastics and rubber) are good examples of viscoelastic materials. Their processing under continuous (e.g. extrusion) or batch (e.g. injection molding) operations is the main occupation of the plastics and rubber industries, but the corresponding modelling and numerical simulation is a difficult task and a relatively recent undertaking.The present work reviews modelling aspects of viscoelasticity and shows how the complex rheology of these materials is best captured through integral constitutive equations with a spectrum of relaxation times. Using such constitutive equations and the Finite Element Method (FEM), the solution of some benchmark problems of rheology becomes feasible. Examples will be shown from the flow of polymer melts and solutions in a 4:1 axisymmetric contraction encountered in standard capillary rheometry, as well as the flow around a sphere falling in a cylindrical tube. The emphasis will be on demonstrating the flow patterns via streamlines and predicting such viscoelastic phenomena as vortex growth, extrudate swell, and reduction of the drag coefficient, which are of particular interest to the rheological community as test cases of computational results.