Shear-banding and Taylor-Couette instability in thixotropic yield stress fluids

In the present work, we study the flow of thixotropic yield stress fluids between two concentric cylinders. In order to take into account the thixotropy, the constitutive relation uses a structural parameter which is driven by a kinetic equation. Here, the Houska's model is considered. Depending on the breakdown rate of the structural parameter, localization or shear-banding are observed. We show that for fragile structures, a shear-banding flow may be observed although for stronger structures, only localisation of the flow is observed such as in Bingham fluids. Physical explanations of the shear-banding discussed by several authors in the literature highlight that the shear-banding may be associated with a discontinuity into the structure of the material and a non-monotonic evolution of the stress according to the constitutive relation with the strain rate. Solving numerically the flow, we show that such a rheological model based on the existence of a structural parameter is able to predict shear-banding. Moreover, the consequences of the thixotropy on the linear stability of the azimuthal flow is studied in a large range of parameters. Although the thixotropy allows shear banding for the base flow, it does not modify fundamentaly the stability of the Couette flow compared to a simple yield stress fluid. The apparent shear-thinning behaviour depends on the thixotropic parameters of the fluid and the results about the onset of the Taylor vortices in shear-thinning fluids are retrieved. Nevertheless, the shear-banding modifies the stratification of the viscosity in the flowing zone such that the critical conditions are mainly driven by the width of the flowing region.