Eur. Phys. J. E (2009) 29: 363-378
https://doi.org/10.1140/epje/i2009-10501-0

Regular Article

Two-dimensional perturbations in a scalar model for shear banding

¹ Delft University of Technology, Mekelweg 4, 2628, CD Delft, The Netherlands
² Polymer IRC and School of Physics & Astronomy, University of Leeds, LS2 9JT, Leeds, UK

^* e-mail: j.l.a.dubbeldam@ewi.tudelft.nl

Received: 20 March 2009
Revised: 8 May 2009
Accepted: 17 June 2009
Published online: 31 July 2009

Abstract

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.