THE COMBINED EFFECT OF ELECTRIC FIELD AND VIBRATIONS ON THE STABILITY OF THE INTERFACE BETWEEN HEAVY AND LIGHT FLUIDS

The combined effect of a normal electric field and normal vibrations on the stability of the base state of a system consisting of two dielectric fluids separated by an interface, which in the base state is flat and horizontal, is being studied. It is assumed that the density of the upper fluid is small compared to that of the lower fluid. It is also assumed that the viscosity is small in a certain sense. A multiscale method is used to study the instability. A fast vertical coordinate is introduced to describe the viscous boundary layer. The influence of the normal electric field on subharmonic and synchronous resonance modes of instability is considered. The dependence of the critical dimensionless vibration amplitude on the dimensionless parameter describing the electric field intensity and on the dimensionless wave number has been derived. The influence of normal vibrations on the Tonks-Frenkel instability has been investigated. The dependence of the critical dimensionless parameter, describing the electric field intensity, on the dimensionless vibration amplitude has been obtained.