Dynamics bf Shear Flow of a Non-Newtonian Fluid*

Viscoelastic materials with fading memory, e.g., polymers, suspensions, and emulsions, exhibit behavior that is intermediate between the nonlinear hyperbolic response of purely elastic materials and the strongly diffusive, parabolic response of viscous fluids. Many popular numerical methods used in the computation of steady viscoelastic flows fail in important flow regimes, and thus do not capture significant non-Newtonian phenomena. A key to satisfactory explanation of these phenomena is the study of the full dynamics of the flow. This paper studies the dynamics of shear flow, presenting a description of non-Newtonian phenomena caused by a non-monotone relation between the steady shear stress and shear strain rate. Analytical results for such phenomena are surveyed, and three distinct numerical methods are developed to accurately compute the dynamics. The computations reproduce experimental measurements of non-Newtonian “spurt” in shearing flow through a slit die. They also predict related phenomena (such as hysteresis and shape memory); experiments are suggested to verify these predictions.