Analysis of New Phenomena in Shear Flow of Non-Newtonian Fluids

Phase-plane and small-parameter asymptotic techniques are used to analyze systems of ordinary differential equations that describe the transient behavior of non-Newtonian fluids in shear flow. These systems approximate the partial differential equations that derive from three-dimensional balance laws and from differential constitutive models for highly elastic liquids. Two models are considered: one with a single relaxation time and small Newtonian viscosity; the other with two relaxation times and no Newtonian viscosity. Both possess the key feature that the variation of steady shear stress with strain rate is not monotone. The analysis shows that both models exhibit several distinctive phenomena: spurt, shape memory, hysteresis, latency, and normal stress oscillations. The predictions for the spurt phenomenon agree quantitatively with experimental results for polymer melts; the other new phenomena, which were discovered recently in numerical simulation, should also be observable in rheological experiments.