Normal Stress Ratio Predicted by Viscoelastic Constitutive Equations

The first and second normal stress differences, N 1 and N2 in steady shear flow are calculated using differential constitutive equations proposed by Leonov and Giesekus. At low shear rates, the Leonov model gives -N2/ N1=0.25 for both single and multiple relaxation modes. In the Giesekus model, −N2/ N1 increases with increasing anisotropy mobility parameter α. Both models predict that −N2/N1 is a decreasing function of the shear rate at high shear rates. The shear rate dependence of −N2/N1 becomes weaker with increasing width of relaxation time distribution. The BKZ type integral constitutive equation is employed to investigate the effect of a model parameter b (=N2/N 1) on steady planar, uniaxial and biaxial extensional flows. It is found that the strain rate dependences of planar2 and biaxial extensional viscosities are very sensitive to the parameter b, where 2 in planar extension denotes the direction of constant width.