Viscoelastic Dean flow serves as a simple model for more complicated flows found in polymer processing operations. It may be generated by applying an azimuthal pressure drop to a polymer solution confined between two concentric cylinders. The resulting flow profile has an unstable radial stratification of hoop stress beyond the centerline of the gap between the cylinders. As a result of this, if the pressure drop exceeds a certain critical value, the axially homogenous base flow becomes unstable, and an axially periodic flow is produced. The movie above shows how applying a small oscillatory axial flow can stabilize this instability.

The first frame after the title shows a density plot of the perturbation hoop stress (i.e., the deviation of the hoop stress from its value in the base state) on an azimuthal cross-section just at the onset of instability. The white rectangle in the upper right corner of the image shows the true aspect ratio of the geometry. After a short delay, an oscillatory axial flow is generated by moving the inner cylinder. The perturbation hoop stress decays in a few oscillations and the base flow is recovered, thus showing that the flow can be stabilized. We expect that the stabilization method shown here carries over to more complex and industrially important flows as well.