Description of uniaxial, biaxial, and planar elongational viscosities of polystyrene melt by the K-BKZ model

Abstract

The three types of Kaye–Bernstein–Kearsley–Zapas (K-BKZ) equations: Wagner–Demarmels (WD) model, Papanastasiou–Scriven–Macosko (PSM) model, PSM–Luo–Tanner (PSMLT) model have been examined to describe experimental results of uniaxial, biaxial, and planar elongational viscosities of polystyrene (PS) melt. In these equations, the viscosity was calculated from the relaxation spectrum and damping function. The relaxation spectrum was determined by dynamic shear experiment. The damping functions were obtained by stress relaxation experiments under biaxial, planar and shear deformations. The shear and biaxial damping functions were described better by the PSM and PSMLT models than by the WD model. However, the experimental planar damping function was not described well. This poor fitting to the planar damping function came from the result that the planar damping function gave more strain-softening than shear. In the theoretical predictions, the damping function of shear and planar elongations should be identical with each other. Our result is inconsistent with this prediction. The elongational viscosities were calculated from the relaxation spectrum and the damping functions, and then compared to experimental data. Elongational viscosities for planar and biaxial deformations were measured by the lubricated squeezing method. In the case of uniaxial deformation, it was measured by a Meissner-type rheometer. Experimental results of uniaxial and biaxial elongational viscosities agreed with the prediction of the PSMLT model. Although the PSMLT model under-predicted the planar elongational viscosity, it was concluded that this model was the best of three models.