Criterion for purely elastic Taylor-Couette instability in the flows of   shear-banding fluids
  In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapted to shear-banding flows. We derive three categories of shear-banding flows with curved streamlines, depending on their stability. 
M.A. Fardin, T.J. Ober, C. Gay, G. Gr\'egoire, G.H. McKinley and S.   Lerouge
cond-mat.soft physics.flu-dyn