Surface tension effects an the nonlinear behavior of long waves in a two layer flow

Abstract

The propagation of long waves of finite amplitude at the interface of two viscous fluids in the presence of interfacial tension is examined. The effect of capillarity on the shape of the waves at the interface of two superposed fluids is investigated for a wide range of density differences, viscosity ratios and imposed pressure gradients. It is found that in planar geometry surface tension stabilizes the interfacial disturbances. Attention is given to the case in which the upper fluid is more dense and comprises a thin film above the lower fluid. With the heavier fluid on the top the flow pattern is always unstable when surface tension effects are neglected. In this case the interfacial waves do not grow forever and reach a finite amplitude only when the interfacial tension is greater than a critical value.