Slippage and Polymer Migration in a Model of Dilute Polymer Fluid

Abstract

This paper introduces a new mathematical model for a dilute complex fluid based on a Hookean bead-spring mechanism. The new model couples constitutive equations with number density and includes bead slippage which manifests itself in higher- order corrections. In the case of simple shear flows, we compute steady solutions and determine the linear stability of this model along the flow curve. The linear stability indicates a selection mechanism for multi-valued regions of the flow curve in stress- controlled experiments. We find that the model provides a physically reasonable extension to existing models and exhibits desirable properties such as shear thinning and shear banding. Finally, it predicts hysteretic behavior in the effective viscosity qualitatively similar to that which has been observed in laboratory experiments.