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arXiv · 0908.1878

Two-dimensional perturbations in a scalar model for shear banding

Johan L. A. Dubbeldam·P. D. Olmsted
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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.

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Johan L. A. Dubbeldam, P. D. Olmsted. 2009-08-13. Two-dimensional perturbations in a scalar model for shear banding. https://doi.org/10.1140/epje%2Fi2009-10501-0

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