Non-newtonian flow for concentrated polymer systems

The modified Graessley theory with the three-dimensional Maxwell model can well explain some of the nonlinear viscoelastic behavior of concentrated polymer systems at least qualitatively with the assumption of a box-type relaxation spectrum for the equilibrium state.

The relaxation spectrum of concentrated polymer systems in shear flow is obtained by means of Graessley's theory. It is assumed that the characteristic time for the entanglement formation is the same order as that for its breakage and that the spectral density of the relaxation spectrum in the flow system is proportional to the number of entanglements between two molecules. The spectral density decreases approximately proportionally to 1/γ for relaxation times larger than 1/γ The non-Newtonian viscosity and other viscoelastic properties, such as the so-called stress overshoot and the stress relaxation, are calculated by using the obtained relaxation spectrum. Our theory explains very well the experimental results in many cases. Good agreement with experimental results is found if we assume that the so-called box-type relaxation spectrum in the equilibrium state has a finite gradient of the order of ?0.5 in the edge region of larger relaxation time on log-log plots.