Viscoelastic fluids include every-day materials that are all around us. Examples include molten plastics (or polymeric liquids), paints and biological fluids. The way these fluids behave can be surprisingly different from the way more familiar fluids such as water behave. For example, during industrial processes, these fluids are subjected to shearing and elongation. It is well known that under these conditions, the flow may undergo unusual instabilities that have unexpected consequences with economic implicatiions. It is therefore important for us to understand the factors that cause these flow instabilities and what the effect will be so that they can be prevented. There are also stabilizing effects of polymers, for example in drag reduction in turbulent flows, and in preventing or delaying the breakup of filaments, which are of major practical use. Over the past fifteen years, we have provided answers to these issues by studying and analyzing the partial differential equations that describe the flows of viscoelastic fluids in model geometries that are characteristic of typical industrial processes.
These papers examine the Johnson-Segalman model for plane Couette flow. This model has a non-monotone shear-stress-shear rate curve. The model problem leads to a two-layer spurted arrangement with a thin layer of the higher shear rate fluid at the wall and the bulk of the fluid in a lower shear rate. In this case, the theory predicts interfacial instabilities for short waves, which would manifest itself as loss of gloss in extrudates.