Stability analysis of shear banding flow with the BMP model

The Bautista–Manero–Puig (BMP) model, consisting of the upper-convected Maxwell constitutive equation coupled to a kinetic equation that takes into account structural changes induced by flow, predicts the basic features of shear banding flow in polymer-like micellar solutions. In this work, the Lyapunov stability analysis applied to this model is used to determine the regions of stability and instability under conditions of shear banding flow. Results indicate that the steady state is reached very slowly within the meta-stable regions and quite rapidly in the homogeneous flow regions as well as in the unstable region where the slope of the constitutive flow curve is negative. Moreover, the Lyapunov stability criterion suggests the locus of the spinodal curve and the existence of a critical point for specific values of temperature and surfactant concentration. In addition, a criterion to set the stress plateau is derived from Extended Irreversible Thermodynamic (EIT) that consists in the equality of the minima in extended Gibbs free energy of the stable flow branches. This approach relates the EIT criterion for the stress plateau to the stability analysis for shear banding flow.