Constitutive equation for polymer liquids: application to shear flow

Abstract

A constitutive equation for describing the nolinear viscoelastic behaviour of polymer systems is proposed. It is based on the concept of structural kinetics. The suggested model is a modification of the one presented by Acierno et al. It differs from the latter by the kinetic equation.The model is applied to various types of equilibrium and transient shear flows. Transient elongational flow will be dealt with in a separate paper. The equilibrium experiments include viscosity and first normal stress difference, linear dynamic moduli, parallel and orthogonal superposition moduli. Three transient experiments are included. Two of them have been used before: relaxation of shear stress upon cessation of flow and shear stress overshoot as a function of rest time. The third technique is a new one and consists of superimposing orthogonally a vibration on relaxation after cessation of flow. The transient experiments prove the necessity to introduce a new kinetic equation in Acierno's model.In the experiments two fluids are used: a polyisobutylene solution in decaline and a polyacrylamide solution in a mixture of glycerine and water. For one system the kinetic model parameter is derived from shear flow data. For the other this parameter is derived from elongatinal flow data. The purpose is to develop a model where a single set of material parameters describes both shear flow and elongational flow data.