Long-wave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect: Linear theory

We investigate the long-wave Marangoni instability in a binary-liquid layer in the limit of a small Biot number B. The surface deformation and the Soret effect are both taken into account. It is shown that the problem is characterized by two distinct asymptotic limits for the disturbance wave number k, k∼B1∕4 and k∼B1∕2, which are caused by the action of two instability mechanisms, namely, the thermocapillary and solutocapillary effects. The asymptotic limit of k∼B1∕2 is novel and is not known for pure liquids. A diversity of instability modes is revealed. Specifically, a new long-wave oscillatory mode is found for sufficiently small values of the Galileo number.