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 τ _c 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 τ _c . This means that the growth period of initiated instabilities is needed for convective motion to be detected experimentally. It seems evident that during τ _c ≤ τ ≤ 3 τ _c convective motion is relatively very weak and the primary diffusive transfer is dominant. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.