Criteria for shear banding in time-dependent flows of complex fluids

TL;DR

This paper develops a universal criterion for predicting shear banding onset in complex fluids under various time-dependent flow protocols, based solely on measurable rheological response functions, independent of specific fluid models.

Contribution

It introduces a general, fluid-universal criterion for shear banding onset in time-dependent flows, applicable across different experimental protocols and independent of specific constitutive models.

Findings

Derived a criterion for shear banding onset in step stress, step strain, and shear startup.

Validated the criterion with simulations of multiple fluid models.

Established the criterion's independence from internal fluid variables.

Abstract

Within a highly generalised theoretical framework for the flow properties of complex fluids, we study the onset of shear banding in the three most common time-dependent experimental protocols: step stress, step strain and shear startup. By means of a linear stability analysis we derive a fluid-universal criterion for the onset of banding, separately for each protocol, that depends only on the shape of the experimentally measured time-dependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs. shear rate). We support them with simulations of the rolie-poly model of polymeric fluids, the soft glassy rheology model, and a fluidity model.