Stability Analysis of Marangoni Convection in Binary Mixtures Subjected to the Soret Effect

Abstract The linear stability of confined Marangoni convection in binary mixtures subjected to the Soret effect is examined. A two dimensional cavity filled with a non-reactive binary fluid is submitted to a constant heat flux across the undeformable upper free surface. The results are given by curves Ma¯c=Ma¯(ΨM) that depend only on the aspect ratio of the cavity where Ma¯ and ΨM are dimensionless numbers constructed from the Marangoni number Ma and the ratio SM of solutal to thermal contribution to the surface tractions. The instability thresholds are found to decrease when the aspect ratio or the destabilizing solutal contribution to the surface force increase, with changes in the critical flow structure. An interesting result is that when this solutal contribution is mainly responsible for driving the flow, the first bifurcation is a transition to a one roll structure independent of the aspect ratio of the cavity. But the presence of several modes close to the threshold can lead quickly to strong mode interactions.