A PHENOMENOLOGICAL VISCOSITY MODEL FOR POLYMERIC FLUID

A phenomenological viscosity model for steady-state flows of non-Newto nian polymeric fluids has been proposed based on the assumption of uni queness of viscosity. The separable dependences of viscosity on the se cond and third invariants of the rate of deformation tensor represent the key ingredient of the model, i.e. eta = eta(SH)(II(d))Tr(III(d)). The model fits experimental data of shear and extensional viscosities of various polymer melts and solutions. These data show shear-thinning , extension-thinning, extension-thickening, and extension-thickening w ith a maximum (and a minimum). The application of the viscosity model in numerical simulation of contraction flow predicts non-monotonically increasing vortex enhancement, which is in agreement with experiments . The third invariant dependence of viscosity which, in the current wo rk, is not introduced merely to give a large Trouton ratio, is discuss ed. It is found that the third invariant can vary significantly betwee n an unadulterated extensional flow and an adulterated one, a fact whi ch can affect viscosity dramatically.