The influence of thermocapillary effect on the onset of convection in a two-layer system with deformable interface and perfectly conductive boundaries

Abstract

The work is devoted to studying the excitation of the Rayleigh-Benard-Marangoni convection in a two-layer system of immiscible fluids with a deformable interface and rigid perfectly heat-conductive external boundaries. The influence of thermocapillary effect on the linear stability of the conductive state of the system under vertical temperature gradient is analyzed. The problem is solved in the framework of the generalized Boussinesq approximation, which allows us to correctly take into account the deformations of the interface. It has been found that, depending on the properties of fluids, a thermocapillary effect can either stabilize or destabilize the longwave mode of instability associated with the deformations of the interface. In the case of a two-layer system of formic acid and transformer oil, strong destabilization takes place. Numerical calculations performed for this pair of fluids at arbitrary values of wave number have shown that the influence of thermocapillary effect on finite-wavelength monotonic and oscillatory instability modes is also destabilizing. However, the lowering of instability threshold to oscillatory finite-wavelength perturbations due to the thermocapillary effect is much weaker than that for both longwave and finite-wavelength monotonic instability modes. As the result, at sufficiently large values of the Marangoni number the conductive state becomes unstable only with respect to monotonic perturbations. Further enhancement of the thermocapillary effect gives rise to a thermocapillary finite-wavelength oscillatory instability mode, which occurs at Galileo numbers large in absolute value (Ga<-80). Good agreement between the results of calculations and available experimental data has been obtained.