Rayleigh–Bénard instability in nonreactive binary fluids. II. Results

TLDR

For stationary convection, the critical Rayleigh number depends only on a single parameter ψ, which is proportional to the thermal diffusion ratio and incorporates other transport and thermodynamic coefficients.

Abstract

The hydrodynamic stability of binary, Boussinesq fluids in Bénard geometry, with both the Soret and Dufour effects included has been studied. For stationary convection, the critical Rayleigh number Rcr, depends only on a single parameter ψ which is proportional to the thermal diffusion ratio and depends on other transport and thermodynamic coefficients. For ψ⩾0 (’’normal’’ Soret effect) the instability sets in only when the fluid is heated from below; for ψ<−1 only when the fluid is heated from above; and for −1<ψ< 0 convection may occur for either sign of the imposed temperature gradient. The critical wave vector kcr becomes vanishingly small in the system with two rigid boundaries; for ψ≳4(ψ<0) when the fluid is heated from below (above). When kcr∼0, Rcr is independent of the Dufour effect and the convective heat flux is proportional to (kcr)2 so that heat flux measurements are impractical in this limit. Oscillatory instability occurs only in fluids with ψ<0 which are heated from below. The dependence of Rcr on the mass density gradient and on the separation of time scales for the relaxation of temperature and concentration fluctiations is discussed.