Rayleigh-Bénard convection in binary-gas mixtures: Thermophysical properties and the onset of convection

We present an experimental investigation of Rayleigh-Bénard convection in binary-gas mixtures. In order to interpret the results quantitatively, we determined the necessary thermodynamic and transport properties for six mixtures (He-${\mathrm{CO}}_2$, He-${\mathrm{SF}}_6$, He-Xe, Ne-Ar, Ar-${\mathrm{CO}}_2$, and ${\mathrm{H}}_2$-Xe) by a combination of data from the literature, molecular-theory calculations, and thermal-conductivity measurements. All six mixtures have positive separation ratios Ψ. The Lewis number L (the ratio of the mass to the thermal diffusivity) is of O(1), in contrast to liquid mixtures where L=O(${10}^{\mathrm{-}2}$). An important feature of the gas mixtures is that their Prandtl number (the ratio of the kinematic viscosity to the thermal diffusivity) can be lower than those of the two pure components. We discuss the physical reason for this and show that the minimum Prandtl number reached by using binary-gas mixtures is about 0.16. The critical temperature difference Δ${\mathrm{T}}_{\mathrm{c}}$ for the onset of convection is determined from measurements of the Nusselt number N (the effective thermal conductivity) and from the contrast of shadowgraph images as a function of ΔT. The results agree well with the prediction of linear stability analysis. In contrast to convection in binary-liquid mixtures with Ψ>0, N for the gas mixtures increases significantly with ε≡ΔT/Δ${\mathrm{T}}_{\mathrm{c}}$-1 as soon as the convection starts at the Soret onset and is qualitatively similar to the Nusselt number of pure fluids. However, the critical Rayleigh number ${\mathrm{R}}_{\mathrm{c}}$ is lower than the value ${\mathrm{R}}_{\mathrm{c}0\mathrm{}}$=1708 of pure fluids. The pattern at onset in the gas mixtures initially consists of parallel straight rolls, in contrast to binary-liquid mixtures where the pattern consists of squares. Based on the gas-mixture properties, we find that the Dufour effect (the reciprocal process of the Soret effect) is relatively weak. The slope dN/dε of N at onset is found to be consistent with that predicted by an eight-mode Galerkin truncation.