Stability of viscous lubricated thin film down an inclined plane beneath ambient lighter non miscible static liquid

Abstract

This paper considers the stability of a thin film propagating beneath a large quantity of ambient static non miscible lighter liquid and over a sloping plane. Such configuration that has never been considered earlier can model the spill of a heavy hydrocarbon into the ocean by a tanker. Equations of conservation of the mass and the momentum were appropriately made non dimensional and a similar solution is proposed in this paper. In this way, an analytical expression of the hydrodynamic field, say velocity field and pressure field is provided. Then, the equation governing the spatiotemporal evolution of the water-oil interface was built and solved by a perturbation method. Also, the time evolution of the wave front position along the inclined plane was built. Finally, the effect of the control parameters on the linear stability of the flow was investigated.