Buckling instabilities in models of viscoelastic free surface flows

We study here some theoretical model problems, with the goal of obtaining a better understanding of viscoelastic free surface flows and their unique f low instabilities. The first analysis examines the stability of inward radi al flow of an Oldroyd-B fluid in a washer-shaped domain, showing that the a zimuthal compression in this flow leads to a free surface instability - a c rinkling or buckling in the azimuthal direction. This instability is suppre ssed by surface tension at large wave numbers, and growth rates are strongl y attenuated by solvent viscosity. A second analysis shows how thin stress boundary layers can develop in free surface flows, and the final analysis t akes the stress localization idea literally, using a thin elastic membrane as a model of stress boundary layer. Under elongation at constant enclosed volume, initially axisymmetric membranes with fixed circular ends, e.g. tru ncated cones, become unstable with respect to nonaxisymmetric disturbances, again due to azimuthal compressive stresses. The resulting configurations appear similar to those observed in filament stretching experiments. (C) 20 00 Elsevier Science B.V. All rights reserved.