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.