Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation

Abstract

Based on a single integral constitutive equation with a strain-dependent memory function, a relation between the primary normal stress functionθ and the shear viscosity functionη is proposed. According to this theory, the primary normal stress functionθ can be obtained from viscosity data by simple differentiation of the viscosity functionη with respect to the shear rate $$\dot \gamma$$ , and multiplication by a factor (−1/n). The material parametern is thereby associated with the strain dependence of the memory function. This relation was compared with the viscosity and primary normal stress data of six polymer melts, three polymer solutions, and an aluminium-soap solution, which were measured by several research groups and are available in the literature. In spite of the vast differences in physical constitution and chemical structure of the melts and solutions considered, agreement between predicted and measured values was encouraging.