Critical phenomenon analysis of shear-banding flow in polymer-like micellar solutions. 1. Theoretical approach.

The shear-banding flow in polymer-like micellar solutions is examined here with the generalized Bautista-Manero-Puig model. The coupling between flow and diffusion naturally arises in this model, which is derived from the extended irreversible thermodynamic formalism. The limit of an abrupt interface is treated here. The model predicts a dynamic master steady-flow diagram, in which all data collapse at low shear rates. Moreover, the model predicts that a nonequilibrium critical line is reached upon decreasing the shear-banding intensity parameter of the model, which corresponds to increasing temperature, increasing surfactant concentration, or varying salt-to-surfactant concentration ratio. By employing nonequilibrium critical theory and the concept of dissipated energy (or extended Gibbs free energy), a set of symmetrical reduced stress versus reduced shear-rate curves are obtained similar to gas-liquid transitions around the critical point. In addition, the nonequilibrium critical exponents are derived, which follow the extended Widom's rule and the extended Rushbroke relationship, but they are nonclassical.