Linear stability analysis on the onset of Soret-driven motion in a nanoparticles suspension

The onset of Soret-driven instability in binary mixture heated from above is analysed using the linear stability theory. The horizontal fluid layer placed between two plates is in a thermally stable state but the Soret diffusion can induce buoyancy-driven convection in the case of a negative Soret coefficient. It is well known that convective motion sets in from both boundaries if the Rayleigh number exceeds its critical value. For the case of highly unstable density stratification the buoyancy-driven motion sets in during the transient diffusion stage. The new stability equations are derived and are solved analytically and numerically. Here the stability limits which are related to the onset time of instabilities and wave number are presented as a function of the Rayleigh number, Lewis number and the separation ratio. The present stability criteria are compared with the existing experimental data.