EHD instability of two liquid layer system with deformable interface

The hydrodynamic instability of a two layer system consisting of insulating and conducting immiscible liquids subjected to a unipolar injection is examined. A theoretical model taking into account the slight deformation of the interface is developed. The effect of deformation is accounted for by the Bond number and by a new non dimensional parameter P proportional to the surface tension. The preliminary results show that, with surface deformation, the instability criterion strongly depends on the P number. For some values of P, two instability mechanisms bulk and interfacial ones take place. When strongly decreasing the strength of surface tension or the liquid thickness, the critical number tends to a value such that the system is very close to interfacial instability.