The onset of elastically driven wavy motion in the flow of two viscoelastic liquid films down an inclined plane

The onset of wavy motion in the flow of two-layer viscoelastic liquid films with matched densities and viscosities down an inclined plane is studied by a linear stability analysis in the limit of zero Reynolds numbers. It is shown that an interfacial wave can be generated at any Weissenberg number due to a stratification in the first normal stress difference when the more elastic liquid lies next to the solid wall, independent of the depth ratio between the layers. A surface wave can also be generated when elastic stresses are large. Critical Weissenberg numbers for the onset of these elastically driven wavy motions are calculated for various depth ratios of the layers.