Stability of a material interface in a two-phase system with a free surface

This study examines the stability of a motionless two-phase fluid layer when the interface incorporates surface properties and interacts with a free surface located above. We introduce the exact jump conditions at the interface and solve the associated boundary eigenvalue problem by means of analytical and numerical methods. This analysis demonstrates the onset of a new interfacial instability when the free surface and the material properties of the interface are present simultaneously. Remarkably, this instability takes place within the domain of stability of the Rayleigh–Taylor mechanism, i.e. when the acceleration due to gravity acts from the lighter to the heavier fluid.