Two-dimensional perturbations in a scalar model for shear banding.
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.
Dubbeldam
J L A
JL
Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. j.l.a.dubbeldam@ewi.tudelft.nl
Olmsted
P D
PD