The stability of gravity driven viscoelastic film-flow at low to moderate Reynolds number
The hydrodynamic stability of a film of viscoelastic fluid falling under its own weight down an inclined surface is considered. As a first step, the stability to infinitesimal disturbances (linear stability) is studied. The equations governing the growth of small, two dimensional disturbances in the parallel base state are derived and solved numerically for the Oldroyd-B fluid model as well as the multiple-mode Rouse model over a wide range of the relevant viscoelastic parameter - the Deborah number. Our results demonstrate that for small Reynolds number, although viscoelastic effects are destabilizing as predicted by other authors, the growth rate of the resulting purely elastic waves remains very small and, therefore, these waves are presumably of little consequence in practical situations. On the other hand, at moderate Reynolds numbers, viscoelastic effects are primarily stabilizing. Both results suggest that the perturbation analyses employed by previous authors are simply too limited in their scope to describe the complex nature of the instability in this viscoelastic, free-surface flow.
scientific article; zbMATH DE number 4078985