Polymer processing applications, especially coating processes, are
susceptible to instabilities that arise purely from the elasticity of the
polymeric liquid. We are working to gain a better fundamental
understanding of instabilities and nonlinear dynamics in polymeric flows,
as well as to develop strategies for suppressing them. Examples of our
recent work in this area are as follows:
- Prediction of the existence of stationary, spatially localized,
"point defect" vortex pair patterns in viscoelastic circular Couette flow.
These solutions are very strongly localized, are isolated in parameter
space from the trivial solutions in Couette flow, exist for large and even
infinite wavelengths, and show a hysteretic character in the Weissenberg
number, similar to experimentally observed "diwhirl" patterns. These
new patterns may comprise, along with oscillatory patterns arising via
linear instability, the fundamental building blocks of complex
spatiotemporal dynamics in polymeric flows.
- Theoretical prediction that addition of a relatively weak steady or
oscillatory flow in the direction transverse to the main flow can lead to
significant stabilization of flow. We have elucidated, using asymptotic
analysis and full numerical simulations, the detailed mechanism underlying
the stabilization. In effect, the very elasticity that drives instability
can also be used to suppress it.
- Elucidation of a novel mechanism for viscoelastic free surface
instabilities like those observed in the filament stretching rheometer, an
important new device for characterizing elastic polymer solutions. The
mechanism we have described may also play a role in other polymer flow
phenomena, such as the knife-edged shape of the rear of a bubble rising in
a viscoelastic fluid.
- Complete exact solution of the normal mode stability problem for
viscoelastic plane Couette flow, including the modes in the continuous
spectrum. The stress fields are not integrable, explaining some of the
numerical difficulties and spurious instabilities found in transient
computations of viscoelastic flows.
