Implications of the Marangoni effect on the onset of Rayleigh–Benard convection in a two-layer system with a deformable interface

Abstract

The paper deals with the investigation of the implications of the Marangoni effect on the onset of Rayleigh-Benard convection in a two-layer system with deformable fluid interface. The study of the conductive state stability to the longwave perturbations shows that in the case of heating from above the thermocapillary effect leads to the increase of instability domain to the monotonic longwave perturbations. In the case of heating from below, the thermocapillarity makes stabilizing effect on the longwave perturbations and at some values of the parameters the configuration where more dense fluid is located above less dense one turns out to be stable. However, the analysis of the perturbations with finite wavelength in the presence of thermocapillary effect shows that in the case of heating from below the Rayleigh-Taylor instability is not suppressed. For any values of the parameters the perturbations with finite wavelength turn out to be more dangerous. In this situation the instability domain becomes wider with the increase of the Marangoni number modulus. In the case of heating from above, for any values of the Marangoni number, at the Rayleigh numbers small in the modulus, long-wave monotonic perturbations are most dangerous whereas at the Rayleigh numbers large in the modulus, the most dangerous mode is cellular monotonic instability.