Non Linear Rheology of Wormlike Micelles
The motivation of this study is a recent work of Porte et al. (1997) on shear induced inhomogeneous flows of solutions of giant micelles. The authors proposed a phenomenological analysis based on a effective potential that accounts for the free energy stored in a viscoelastic material under steady shear conditions. In such a scheme, mechanical flow instabilities have been described by a non-monotonic constitutive relation for the shear stress as a function of the shear rate. The model accounts for the existence of a stress plateau in which the set of stationnary states is highly degenerate in a shear rate controlled experiment. As a consequence, hysteresis is predicted but not observed experimentally.