A DIFFERENTIAL CONSTITUTIVE EQUATION FOR ENTANGLED POLYMER-SOLUTIONS

A simple and computationally tractable constitutive equation is develo ped for concentrated and entangled polymer systems, based upon a singl e vector description of the polymer configuration. The constitutive eq uation is intended to mimic the DEMG model, and allows the vector to s tretch and orient on different time scales. The constitutive equation is shown to yield steady material functions in homogeneous, extension- dominated flows that are in excellent qualitative and quantitative agr eement with the DEMG model. The constitutive equation is shown to exhi bit less shear thinning than the Doi-Edwards reptation model, and ther efore also shows a shear viscosity in better agreement with experiment . In simple shear flow the model predicts chain stretch at large shear rates, in contrast to the DEMG model, but in qualitative agreement wi th recent experimental studies (Bercea et al., Macromolecules 26 (1993 ) 7095-7096). In start up of simple shear, the model predicts an under shoot in the orientation angle, and over; and undershoots in the biref ringence in qualitative agreement with experiments. (C) 1999 Elsevier Science B.V. All rights reserved.