Summary: For steady shear flows, elongated micellar solutions show shear stress saturation above a critical shear rate due to the formation of shear bands that results in non-homogeneous flow. Long transients and oscillations accompany this stress plateau. When measurements are done with a controlled stress rheometer, frequently a metastable branch is observed. At higher shear rates, a second upturn is observed above a second critical shear rate, which indicates that homogeneous flow is recovered.
Here, a model consisting of codeformational Maxwell constitutive equation coupled to a kinetic equation to account for the breaking and reformation of micelles is presented to reproduce the features described above in steady shear flows. The model also predicts a second metastable branch and long transients at higher shear rates, and the existence of inflexion point in stress-shear rate plots, above which no shear banding behavior is detected.