Onset of Soret convection in a nanoparticles-suspension heated from above

The onset of Soret-driven convection in a nanoparticles suspension heated from above is analyzed theoretically based on linear theory and relative instability concept. A new set of stability equations are derived and solved by using the dominant mode method. The dimensionless critical time τc to mark the onset of instability is presented here as a function of the Rayleigh number, the Lewis number and the separation ratio. Available experimental data indicate that for large Rayleigh number convective motion is detected starting from a certain time τ≈3 τc. This means that the growth period of initiated instabilities is needed for convective motion to be detected experimentally. It seems evident that during τc ≤ τ ≤ 3 τc convective motion is relatively very weak and the primary diffusive transfer is dominant.