The stability characteristics of polymeric flows are often dramatically different from those of Newtonian flows. In some cases, polymers can stabilize Newtonian flows or significantly alter the nature of the instability, in other cases viscoelastic effects lead to new instabilities.
Shear flows with curved streamlines are used in a number of widely applied rheometers, such as the cone-and-plate, parallel plate or eccentric disc rheometer. Instabilities here are a major concern, since the use of the device for measurement presume a specific flow kinematics which no longer applies when an instability sets in. David Olagunju (University of Delaware) spent a sabbatical year at Virginia Tech is 1996/7. During this time, he and Yuriko Renardy collaborated on this topic. Their paper extends earlier work by including the effect of inertia and nonaxisymmetric modes.
In the final paper, a comparison is made between different approaches which simplify the equations of motion to varying degrees. Much of the work in the literature is based on a small gap approximation and an assumption of radially localized disturbances. The work keeps the small gap approximation but does not assume radial localization. The results are compared with numerical simulations of the full problem on the one hand, and the radially localized theory on the other hand.