A non-monotonic constitutive model is not necessary to obtain shear banding phenomena in entangled polymer solutions

TL;DR

This paper demonstrates that shear banding in entangled polymer solutions can occur without a non-monotonic constitutive model, showing that simple models can capture complex flow instabilities under certain conditions.

Contribution

The study shows that shear banding phenomena can be explained using a simple, modern constitutive model without requiring non-monotonic stress behavior, challenging previous assumptions.

Findings

Shear banding is captured by the non-stretching Rolie-Poly model with solvent viscosity.

Shear banding occurs in flow geometries with inhomogeneous shear stress.

Transient inhomogeneities can resemble shear banding even in weakly stable fluids.

Abstract

In 1975 Doi and Edwards predicted that entangled polymer melts and solutions can have a constitutive instability, signified by a decreasing stress for shear rates greater than the inverse of the reptation time. Experiments did not support this, and more sophisticated theories incorporated Marrucci's idea (1996) of removing constraints by advection; this produced a monotonically increasing stress and thus stable constitutive behavior. Recent experiments have suggested that entangled polymer solutions may possess a constitutive instability after all, and have led some workers to question the validity of existing constitutive models. In this Letter we use a simple modern constitutive model for entangled polymers, the non-stretching Rolie-Poly model with an added solvent viscosity, and show that (1) instability and shear banding is captured within this simple class of models; (2) shear banding phenomena is observable for weakly stable fluids in flow geometries that impose a sufficiently inhomogeneous total shear stress; (3) transient phenomena can possess inhomogeneities that resemble shear banding, even for weakly stable fluids. Many of these results are model-independent.