Startup Steady Shear Flow from the Oldroyd 8-Constant Framework

Abstract

One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation, and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can, overshoot, and then, they can even undershoot. We call such responses nonlinear, and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviours of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rate, and otherwise, nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rate. The effect of salt concentration on the nonlinear parameters is explored.