Waves at the interface between a clear liquid and a mixture in a two-phase flow

Abstract

In the two-dimensional sedimentation process beneath an inclined wall, the mixture of the participate and liquid phases is separated from the wall by a boundary layer of the clear liquid. This paper contains a simple mathematical model giving waves on the interface between the clear liquid and the mixture. These waves are caused by a discontinuity in the gradient of the tangential velocity of the clear liquid, across the interface. In the limiting case of small concentration of the particulate phase in the mixture, the model gives a dispersive wave running upward along the interface in the direction of the flow in the boundary layer. The effect of finite concentration is to introduce a damping.