PROBLEMS ORIGINATING FROM THE USE OF THE GORDON-SCHOWALTER DERIVATIVE IN THE JOHNSON-SEGALMAN AND RELATED MODELS IN VARIOUS SHEAR-FLOW SITUATIONS

The predictions of the Johnson-Segalman model have been compared to experimental results in some simple flows, namely steady state shearing flow and stress growth in shear, for various molten polyethylenes having different molecular characteristics as far as their molecular weight level, polydispersity index and branching degree are concerned. Attention has been focused on this particular model because it has been shown to be an approximation of the Phan-Thien-Tanner equation in simple shear flows, the later model being frequently used in numerical calculations for complex flows. The Johnson-Segalman model is a codeformational rheological equation of state, which allows non-affine motion of the network junctions by introduction of a single parameter (a) named the slip factor. This assumption provides a great improvement in the predictions of non-linear response to flows involving large deformations, either in shear or in elongation. However, the determination of the slip parameter from the various experiments has shown that a single value of the slip factor can not be used to describe both tangential stresses (tau12) and normal stresses (tau11 - tau22) in polyethylene melts. This has been related to a discrepancy of the model concerning the violation of the Lodge-Meissner rule as a consequence of the use of the Gordon-Schowalter derivative. Similar discrepancy can be expected in the case of the Phan-Thien-Tanner equation. Nevertheless, the slip factor, that can be determined either by fitting tangential stresses or normal stresses, is found to be nearly constant for a particular material, whatever the flow regime is (transient or steady). Moreover, for the various linear polymers (high density or linear low density polyethylenes), these parameters appear to be nearly independent of the molecular weight distribution. In this case, the differences in the non-linear behaviour in shear can only be attributed to differences in the linear relaxation modulus. On the other hand, a highly branched material (low density polyethylene) shows very different values of the slip parameters.