Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids

¹ Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université Paris Diderot 10 rue Alice Domont et Léonie Duquet, 75205 Paris Cédex 13, France, EU
² Department of Mechanical Engineering, Massachusetts Institute of Technology - 77 Massachusetts Avenue, MA 02139-4307 Cambridge, USA

^a sandra.lerouge@univ-paris-diderot.fr

Received: 12 August 2011
Accepted: 5 October 2011

Abstract

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.