Korteweg stresses and admissibility criteria for shear banded flows

•Korteweg stresses are proposed as a selection mechanism for shear banding transitions, as an alternative to stress diffusion.•It is shown that Korteweg stresses lead to a version of the equal area rule in steady shear banded flows.•The precise form which this equal area rule takes depends on the specific interfacial energy.

Nonmonotone constitutive behavior leading to shear banding occurs in a number of fluids, such as wormlike micelles and clay suspensions. In general, shear banded flows are not unique. Higher order terms in the governing equations are often introduced to distinguish a preferred solution that arises as a steady state in the long term. In the literature on wormlike micelles, stress diffusion has been widely considered for this purpose.In this paper, we discuss a different physical mechanism, based on interfacial energies and Korteweg stresses associated with them. It is shown how this criterion leads to a form of “equal area” rule.