The effect of a high-frequency progressive vibration on the convective instability of a two-layer fluid

The influence of a high-frequency progressive vibration on the onset of thermal convection in a two-layer system of viscous immiscible fluids is investigated. The interface is deformable, the outer walls are rigid, and heat-transfer conditions of a general form are assigned on them. The starting equations are taken in the generalized Oberbeck–Boussinesq approximation. An averaging method is employed. It is shown that the averaged problem contains a vibrogenic external force and vibrogenic stresses that are proportional to the square of the amplitude of the vibration rate. A quasi-equilibrium solution that satisfies the closure condition is found, and its stability is investigated. It is established that, unlike the case of a single-layer fluid, the horizontal component of the vibration influences the onset of convection and have a destabilizing effect. The vertical component stabilizes the two-layer system by increasing the surface tension. The long-wavelength asymptotic is investigated. Calculations are performed for the silicone oil–Fluorinert and acetonitrile–n-hexane systems.