Rayleigh-Bénard convection in binary mixtures with separation ratios near zero

We present an experimental study of convection in binary mixtures with separation ratios Ψ close to zero. Measurements of the Hopf frequency for Ψ0, we found that the pattern close to onset consisted of squares. Our data give the threshold of convection ${\mathit{r}}_{\mathit{c}}$≡${\mathit{R}}_{\mathit{c}}$/${\mathit{R}}_{\mathit{c}0}$ (${\mathit{R}}_{\mathit{c}}$ is the critical Rayleigh number of the mixture and ${\mathit{R}}_{\mathit{c}0}$ that of the pure fluid) from measurements of the refractive-index power of the pattern as revealed by a very sensitive quantitative shadowgraph method. Over the range Ψ≲0.011, corresponding to ${\mathit{r}}_{\mathit{c}}$≳0.2, these results are in good agreement with linear stability analysis. The measured refractive-index power varies by six orders of magnitude as a function of r and for r≳0.55 is in reasonable agreement with predictions based on the ten-mode Lorenz-like Galerkin truncation of Müller and Lücke [H. W. Müller and M. Lücke, Phys. Rev. A 38, 2965 (1988)]. For smaller r, the model predicts a cancellation between contributions to the refractive index from concentration and temperature variations, which does not seem to occur in the physical system. Determinations of the wave numbers of the patterns near onset are consistent with the theoretically predicted small critical wave numbers at positive Ψ. As r approaches one, we find that q approaches the critical wave number ${\mathit{q}}_{\mathit{c}0}$≃3 of the pure fluid. (c) 1995 The American Physical Society