Korteweg stresses and admissibility criteria for shear banded flows

Abstract

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.