Slippage and Polymer Migration in a Model of Dilute Polymer Fluid
Date
2003-04-23
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
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.