Eur. Phys. J. E 29, 363-378 (2009)
DOI: 10.1140/epje/i2009-10501-0

Two-dimensional perturbations in a scalar model for shear banding

J. L. A. Dubbeldam¹ and P. D. Olmsted<sup>2

1</sup>  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

j.l.a.dubbeldam@ewi.tudelft.nl

Received 20 March 2009 / Revised version 8 May 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.

PACS
47.50.-d - Non-Newtonian fluid flows.
47.20.-k - Flow instabilities.
47.57.Ng - Polymers and polymer solutions.

Correspondence: j.l.a.dubbeldam@ewi.tudelft.nl


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009