Slippage and Migration in Taylor-Couette Flow of a Model for Dilute Wormlike Micellar Solutions

Abstract

In this paper we explore a model, most appropriate for dilute or semi-dilute worm-like micellar solutions, in an axisymmetric circular Taylor-Couette geometry. This study is a natural continuation of earlier work on rectilinear shear flows. The model, based on a bead-spring microstructure with nonaffine motion, reproduces the pronounced plateau in the stress strain-rate flow curve as observed in laboratory measurements of steady shearing flows. 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 profiles obtained in numerical solutions show strong qualitative agreement with those of laboratory experiments.