Experimental determinations of universal amplitude combination for binary fluids. II. Dynamics

We have considered for binary fluids the universal dynamic amplitude ratio R which connects the typical frequency Γ of the order-parameter fluctuations to the viscosity η and to the correlation length ξ. We have analyzed the mode-coupling (MC) approach and the renormalization-group (RG) theory. The mode-coupling approach accounts for background terms in both η and Γ, whereas RG includes corrections to scaling in the transport coefficients with an effective exponent Δ0.7. We emphasize that the two approaches are similar in formulation, the correction terms from MC showing a leading exponent ν=0.63, close to Δ. The correction amplitudes a_Γ (linewidth) and a_η (viscosity) are essentially positive in the MC approach. Moreover, we claim that their ratio should be universal if we assume the Bhattacharjee-Ferrell crossover viscosity function: a_ηa_Γ=2x_η, with x_η0.06, the critical viscosity exponent. We also define an amplitude factor ̃ \~R(q,t), the asymptotic value of which is R. It allows the corrections to scaling, in the framework of the RG theory, to be taken into account. New viscosity measurements have been made with the isobutyric acid-water (I-W) and triethylamine-water (T-W) systems. New Rayleigh linewidth measurements have been performed in the T-W mixture. Analyses of the viscosity data in I-W, T-W, nitrobenzene-n-hexane (N-H), nitroethane-3-methylpentane (N-M), and chlorex-n-dodecane (C-D) systems have led us to introduce correction terms for the I-W and T-W systems, with an experimental exponent {}0.7. I-W corrections have been found negative. The linewidth data, analyzed in the N-H, I-W, C-D, N-M, and T-W systems, show that corrections are present in ̃ \~R for the N-M and T-W mixtures, with exponent ~ 0.7. T-W corrections have been found to be negative, when using negative statics corrections. Finally, the asymptotic values of R were found in the range 1.00-1.14, with a mean uncertainty of 7%. They are in agreement with both the recent MC (1.027) and RG (1.038) expectations.