Slippage and migration in taylor-couette flow of a model for dilute wormlike micellar solutions

We explore the rheological predictions of a constitutive model developed for dilute or semi-dilute wormlike micellar solutions in an axisymmetric Taylor-Couette °ow. This study is a natural continuation of earlier work on rectilinear shear °ows. The model, based on a bead-spring microstructure with nona±ne motion, reproduces the pronounced plateau in the stress strain-rate °ow curve that is observed in laboratory measurements of steady shearing °ows. We also carry out a linear stability analysis of the computed steady state solutions. The results show shear-banding in the form of sharp changes in velocity gradients, spatial variations in number density, and in alignment or stretching of the micelles. The velocity pro¯les obtained in numerical solutions show good qualitative agreement with those of laboratory experiments. Key words: Mathematical modeling, inhomogeneous °uids, dumbbell models with slippage, wormlike micellar solutions, Taylor-Couette °ow.