Inhomogeneous flows and shear banding formation in micellar solutions: Predictions of the BMP model

The shear-banding flow in polymer-like micellar solutions is examined here with the Bautista-Manero-Puig (BMP) model. The expressions derived from the constitutive equations of the model, in addition to the conservation equations, are formulated for the case of inhomogeneous simple-shear flow. The resulting system of equations is hyperbolic, the solution of which can be found with the method of the characteristics. The characteristic trajectories associated to the system encompass a set of equations that is solved numerically. Here the actual flow initiation in a parallel plate rheometer is mimicked for both strain-controlled and stress controlled conditions, i.e., starting from rest, the velocity of the upper plate is allowed to increase stepwise to allow fully-developed flow after each velocity increment. In another case, the upper-plate velocity is allowed to decrease stepwise from a high shear rate down to low shear rates. When band formation is predicted, two or multiple bands are generated. Results include the phase portraits around the flow curve and for the confined fluid, predictions are given for the velocity, stress and fluidity fields as functions of both space and time. Moreover, it is shown that the values of the stress plateau and of the critical shear rates approach same values independently of the initial conditions and shear history for a given applied shear rate or shear stress. This result is obtained without the inclusion of gradient terms. An important result is that the model predicts the same stress plateau for forward and backward sweeps under strain controlled conditions and a discontinuity at the shear plateau for stress-controlled conditions. (C) 2012 Elsevier B.V. All rights reserved.