RAYLEIGH-BENARD CONVECTION IN BINARY-MIXTURES WITH SEPARATION RATIOS NEAR ZERO

We present an experimental study of convection in binary mixtures with separation ratios psi close to zero. Measurements of the Hopf frequen cy for psi < 0 were used to determine the relationship between psi and the mass concentration x with high precision. These results are consi stent with but more precise than earlier measurements by conventional techniques. For psi > 0, we found that the pattern close to on-set con sisted of squares. Our data give the threshold of convection r(c)-R(c) /R(c0) (R(c) is the critical Rayleigh number of the mixture and Reo th at of the pure fluid) from measurements of the refractive-index power of the pattern as revealed by a very sensitive quantitative shadowgrap h method. Over the range psi less than or similar to 0.011, correspond ing to r(c) greater than or similar to 0.2, these results are in good agreement with linear stability analysis. The measured refractive-inde x power varies by six orders of magnitude as a function of r and for r R 0. 55 is in reasonable agreement with predictions based on the ten- mode Lorenz-like Galerkin truncation of Muller and Lucke [H. W. Muller and M. Lucke, Phys. Rev. A38, 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 th e patterns near onset are consistent with the theoretically predicted small critical wave numbers at positive psi. As r approaches one, we f ind that q approaches the critical wave number q(c0)similar or equal t o 3 of the pure fluid.