Two-dimensional perturbations in a scalar model for shear bandingJ. L. A. Dubbeldam1 and P. D. Olmsted2
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
Received 20 March 2009 / Revised version 8 May 2009 / Published online 31 July 2009
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: email@example.com
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009