Interactions Between Coupled Transfer and Gravity: Rayleigh-Bénard Instability

Abstract

AbstractThis chapter enters the second part of this thesis, where a hydrodynamic instability problem is studied and coupled heat and mass transfer exists through cross-diffusion effects. In this chapter, theoretical tools are implemented to study the Rayleigh-Bénard instability in a binary mixture at supercritical pressures, which is characterized by gravity-related effects and cross-diffusion effects with positive separation ratio. Analytical criteria are derived for ideal stress-free boundary conditions, and an unusual oscillatory instability is discovered. Analyses regarding the origin of oscillatory instability reveal that it requires a sufficiently large stabilizing concentration gradient and the total diffusivity rate of concentration is less than that of temperature, where the stabilizing concentration gradient is a result of gravity-related effects. Discussions concerning the relative importance of gravity-related effects reveal that for the reference fluid under near-critical states, gravity-related effects become dominate when the thickness of fluid layer is at the centimeter level.