Estimation of the elongational viscosity of polyethylene blends at high deformation rates

Abstract

The Binding and Cogswell entry flow analyses were used to model the flow of low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), and a 50 50 blend of LLDPE with LDPE through a sudden contraction. The entrance angle of the converging stream is estimated by using the two previous analyses and compared to the flow visualization experiments. The entrance angle was well predicted, being more accurate in the case of the Binding analysis, when the entrance angle was small (large vortices). An approximate sink flow analysis is proposed which gave better predictions when the entrance angles were large. Since experimental results of the elongational viscosity at high deformation rates are not available, the elongational viscosity predicted from three previous entry flow analyses were compared to the predictions of the Larson (PEC) model. It was shown that both the strain hardening parameter of the PEC model and the distribution of the relaxation moduli and relaxation times determine the power-law indices t and n of the elongational viscosity and the viscosity, respectively, and therefore control the generation of lip vortices upstream of a contraction. The entrance pressure was shown to have the same dependence on deformation rate for both the Cogswell and Binding analyses. All three models predicted vortex growth if t is greater than n. Complex flow patterns were generated by the flow of the 50 50 blend at high deformation rates whereby a minimum in the entrance angle was observed.