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

Abstract

We have considered for binary fluids the universal dynamic amplitude ratio $R$ which connects the typical frequency $\Gamma$ of the order-parameter fluctuations to the viscosity $\overline{\eta }$ and to the correlation length $\xi$. We have analyzed the mode-coupling (MC) approach and the renormalization-group (RG) theory. The mode-coupling approach accounts for background terms in both $\overline{\eta }$ and $\Gamma$, whereas RG includes corrections to scaling in the transport coefficients with an effective exponent $\overline{\Delta }\simeq 0.7$. We emphasize that the two approaches are similar in formulation, the correction terms from MC showing a leading exponent $\nu =0.63\mathrm{}$, close to $\overline{\Delta }$. The correction amplitudes $a_{\Gamma }$ (linewidth) and $a_{\overline{\eta }}$ (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: $\frac{a_{\overline{\eta }}}{a_{\Gamma }}=2\mathrm{}{x}_{\overline{\eta }}$, with $x_{\overline{\eta }}\simeq 0.06$, the critical viscosity exponent. We also define an amplitude factor $\tilde{R}\mathrm{}(q,t)\mathrm{}$, 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 $\tilde{R}$ 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.