Interfacial hoop stress and instability of viscoelastic free surface flows

Viscoelasticity can dramatically exacerbate free surface flow instabilities. It is shown here that this destabilization arises, at least in part, from the combination of large tangential tension and curvature along a concave free surface. Tension and curvature generically lead to an unstable stress gradient at the free surface; a perturbation that locally thickens a fluid layer leads to a local accumulation of hoop stress, which drives further thickening of the layer. A simple theory based in this observation captures several features of experimental observations of coating flows, specifically the correlation between destabilization and extensional viscosity and the increase in wavenumber with viscoelasticity. In a particular model situation, instability of flow with a concave free surface can be reduced to a viscoelastic Rayleigh-Taylor problem, which is amenable to analytical treatment. In this situation the growth rate can be very large, because the stored elastic energy cannot balance the surface work associated with interface deformation. Application of the theory to the instability of filament stretching flow yields a prediction of the Weissenberg number below which instability does not occur that agrees well with experimental observations. © 2003 American Institute of Physics. @DOI: 10.1063/1.1568340#