par- 6 avril 2009
Jorge E. PUIG Chemical Engeneering dpt, Université de Guadalajara MEXIQUE
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Under steady shear flow, elongated micellar solutions show shear stress saturation above a critical shear rate due to the formation of shear bands that result 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 the Bautista-Manero-Puig (BMP) model consisting of the codeformational Maxwell constitutive equation coupled to a kinetic equation to account for the breaking and reformation of the micelles is presented to reproduce the features described above in steady shear flow. The model also predicts a second metastable branch and long transients at higher shear rates and the existence of an inflexion point in stress-shear rate plots above which no shear banding behavior is detected. The stress plateau is set in our model by the criterion of equal extended Gibbs free energy of the bands. Moreover, 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.
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