Soret effect and slow mass diffusion as a catalyst for overstability in Marangoni-Bénard flows

We study the onset of time dependent Marangoni-Bénard convection in binary mixtures subject to Soret effect by numerical computation of linear instability thresholds in infinite fluid layers and two-dimensional boxes. The calculations are done for positive Marangoni numbers (Ma > 0) and negative Marangoni Soret parameters SM = –(DSγc)/(DγT) where DS and D are the Soret and mass diffusion coefficients, respectively, and γT, γc are the first derivatives of the surface tension with respect to temperature and concentration. Our purpose is to understand why for particular choices of Prandtl and Schmidt numbers, the increase of the stabilizing solutal contribution leads to a decrease of the critical temperature difference, a phenomenon already reported by Chen & Chen [5] and Skarda et al. [12] For various choices of Prandtl and Schmidt numbers we analyze the evolution of the critical Marangoni number Mac, critical wavenumber kc and angular frequency ωc with SM and compute the corresponding eigenvectors. We next propose a physical mechanism which explains how the stabilizing solutal contribution acts as a catalyst for overstability. Finally, we extend our results to two dimensional boxes of small aspect ratio.