Constitutive equations for fiber suspensions in viscoelastic media

The kinetic theory of elastic dumbells with a friction factor that depends on the fiber orientation is used to obtain constitutive equations for fiber suspensions in a polymer matrix. We followed the approach of Fan (X.J. Fan, in P. Moldenaers and R. Keunings (Eds.), Theoretical and Applied Rheology, Proceedings XIth International Congress on Rheology, Brussels, Elsevier, Amsterdam, 1992, pp. 850-852), and derived equations for polymer solutions based on the FENE-P, FENE-CR, and Giesekus models. Start-up and steady-state free shear flows are studied to explore the effects of the fiber-polymer coupling as well as the fiber volume fraction. Predictions based on different types of closure approximations for the fourth-order fiber orientation tensor are also discussed.