A new oscillatory instability in Rayleigh–Bénard convection of a binary mixture with positive separation ratio

Abstract

It is well-known that for the onset of Rayleigh–Bénard (RB) convection in a binary mixture with Soret effect and negative separation ratio, the competitions between temperature and concentration gradients can lead to oscillatory instability. In this paper, through linear stability analysis, a new oscillatory instability is discovered in a binary mixture with positive separation ratio, thanks to the rich physics of a near-critical binary mixture, i.e., a binary mixture under supercritical pressure near the pseudo-critical state. The rich physics includes cross-diffusion effects (i.e., Soret and Dufour effects) and gravity-related effects (i.e., adiabatic temperature gradient and gravitational diffusion). The linear stability problem is governed by six dimensionless parameters, and the positive separation ratio is shown to be general. It is revealed that there are monotonic and oscillatory instabilities, corresponding to the monotonic and oscillatory growths of small perturbations. The conditions for the unexpected oscillatory instability can be interpreted as there are large enough stabilizing concentration gradient, and total diffusivity rate of concentration is less than that of temperature. Under a positive separation ratio, the stabilizing concentration gradient is a result of gravity-related effects. Besides, based on the physical properties of the reference fluid, when oscillatory instability occurs, gravity-related effects have already been the dominant obstacle for instability. This work provides analytical equations to predict the RB instability. More importantly, the newly discovered oscillatory instability overturns the stereotype of the conceptual connection between oscillatory instability and negative separation ratio.