The European Physical Journal E

, Volume 29, Issue 4, pp 363–378 | Cite as

Two-dimensional perturbations in a scalar model for shear banding

  • J. L. A. DubbeldamEmail author
  • P. D. Olmsted
Regular Article


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.


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


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Delft University of TechnologyCD DelftThe Netherlands
  2. 2.Polymer IRC and School of Physics & AstronomyUniversity of LeedsLeedsUK

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