Absolute instabilities in two-layer gravitiy driven film flow with a free surface

We investigate on the basis of a linear analysis the stability of a gravity driven laminar, stratified film flow of two superposed fluids which are a clear liquid and a suspension of solid particles below. The study is based on the assumption that the concentration remains constant within the suspension layer. This assumption is justified because of the base-state results for shear induced resuspension for even moderate flow-rates. The numerical solutions display the existence of two different instabilities: waves at the free surface and interfacial waves. Here we concentrate on the latter instabilities and show that such a gravity driven two-layer film flow with a free surface is absolutely unstable.