A. Podolny, A. Nepomnyashchy, A. Oron
Mathematical Modelling of Natural Phenomena
We have explored the combined long-wave Marangoni and Rayleigh instability of the quiescent state of a binary- liquid layer heated from below or from above in the presence of the Soret efiect. We found that in the case of small Biot numbers there are two long- wave regions of interest k » Bi 1=2 and k » Bi 1=4 . The dependence of both monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers has been investigated. The complete linear stability analysis reveals the diversity of instability types in the long-wave region, and a need in the development of the nonlinear theory of the discovered phenomena becomes obvious.