(352c) "Not So" Simple Shear Flow of Polymer Solutions (Shear Banding)

We consider the problem of shear banding. Recent experimental work by Wang and coworkers suggests that the phenomenon of shear banding can occur in polymer solutions. These observations are, however, at odds with the usual expectation that shear banding is due to a constitutive instability associated with a range of shear rates where the shear stress decreases with increasing shear rate. This behavior is believed to occur in solutions of wormlike micelles, and these fluids do exhibit shear banding. However, polymer solutions exhibit a monotonic increase of shear stress with shear rate, and thus (according to common wisdom) should not exhibit shear banding. Indeed, other investigators have had difficulty reproducing Wang’s experimental results.  In this talk, we show that a commonly accepted, monotonic constitutive model for polymers (the "Rolie-Poly" model) exhibits a linear instability that leads to a steady shear banding solution, provided that we treat the polymer concentration profile as an unknown, in addition to the velocity profile. We further show that many of the observations of Wang and coworkers are at least qualitatively reproduced, such as multiple steady states at certain shear rates, and elastic recoil during the startup flow that leads to the steady shear banded solutions.