Stability of shear banded flow for a viscoelastic constitutive model with thixotropic yield stress behavior

A viscoelastic constitutive model which combines the partially extending strand convection model and a Newtonian solvent is used in the regime of large relaxation time. Prior work on one dimensional time-dependent solutions at prescribed shear stress predicts some of the features expected of thixotropic yield stress fluids, such as delayed yielding. In this paper, we present the linear stability analysis of two-dimensional plane Couette flow, for parameter regimes that support a two-layer arrangement consisting of an unyielded layer and a yielded layer. Asymptotic analysis and computational techniques are applied. We find that the one layer yielded flow can have bulk instabilities which also emerge in the two-layer flow. Bulk instabilities in the yielded phase appear not to have been observed in prior literature. For some parameters, an interfacial mode is unstable and is driven by the normal stress difference across the interface. The yielded zone has the higher first normal stress difference, as for the well-studied Johnson-Segalman model. In order to assess the importance of the sign of the first normal stress difference at the interface, we specifically design a modification to the model to reverse the sign. It is found that instabilities still occur.