Vertical vibration effect on stability of conductive state of two-layer system with deformable interface

Abstract

The effect of high-frequency small-amplitude vertical vibrations on the stability of a conductive state of a two-layer system of immiscible fluids with a constant vertical heat flux imposed at external boundaries is studied within the framework of the generalized Boussinesq approximation taking into account the interface deformation. It is found that the long-wave instability is not affected by vibrations of small and moderate intensity. The impact of vibrations on the stability to the perturbations of finite wavelength is analyzed for the model system of fluids which have identical properties except densities and for the real system “formic acid – transformer oil”. For model system it is found that the stability boundary to the oscillatory finite-wavelength perturbations has the segment where vibrations make stabilizing effect and the segment of the destabilizing effect of vibrations. For real system “formic acid – transformer oil” vibrations reduce the conductive state stability to the monotonic finite-wavelength perturbations and increase the stability to the oscillatory finite-wavelength perturbations. As a result, the monotonic finite-wavelength perturbations become the most dangerous at high enough values of the vibrational Rayleigh number.