The hydrodynamic instability of a two layer system consisting of insul
ating and conducting immiscible liquids subjected to a unipolar inject
ion is examined. A theoretical model taking into account the slight de
formation of the interface is developed. The effect of deformation is
accounted for by the Bond number and by a new non dimensional paramete
r P proportional to the surface tension. The preliminary results show
that, with surface deformation, the instability criterion strongly dep
ends on the P number. For some values of P, two instability mechanisms
bulk and interfacial ones take place. When strongly decreasing the st
rength of surface tension or the liquid thickness, the critical number
tends to a value such that the system is very close to interfacial in
stability.