Stability analysis of stratified Rayleigh–Bénard–Poiseuille convection. Part II: Influence of thermocapillary forces

Abstract

The development of convective cells in horizontal stratified systems can be induced by buoyancy or thermocapillary forces (Marangoni effect). When both mechanisms of instability are present it is expected a non-trivial influence of one over the other, with the main characteristics based primarily on the ratio between the buoyancy forces acting in each layer. In this study, linear stability analysis is used to investigate the influence of the thermocapillary effect in double layer stratified systems confined between two solid walls and heated from below, including cases where a pressure gradient induces fluid flow parallel to the walls. To simplify the analysis, it is assumed that the fluids in both layers have similar properties and the interface deformation is neglected. The presence of thermocapillary forces acting on the interface generates a complex behavior, particularly when the upper layer is deeper than the lower layer, which causes the convective cells to emerge initially in the upper layer. In this case, oscillatory states can appear as a result of the competition between the mechanisms of instability. This behavior is not observed if the thermocapillary forces are neglected; therefore, in order to obtain a complete picture of the system stability, it is important to include the Marangoni effect. The increases in the Reynolds and Prandtl numbers showed a similar effect. For low Re or Pr values, the thermocapillary forces initially stabilize the system, however, after a certain threshold the increase in the Marangoni number tends to destabilize the system. The presence of parallel flow also hinders the formation of oscillatory states. When the convective cells emerge initially on the lower layer, the increase in the Marangoni number facilitates the development of the cells, since the thermocapillary forces always act in the same direction as the buoyancy forces at the interface.