Weightless experiments to probe universality of fluid critical behavior

Near the critical point of fluids, critical opalescence results in light attenuation, or turbidity increase, that can be used to probe the universality of critical behavior. Turbidity measurements in ${\mathrm{SF}}_6$ under weightlessness conditions on board the International Space Station are performed to appraise such behavior in terms of both temperature and density distances from the critical point. Data are obtained in a temperature range, far (1 K) from and extremely close (a few $\mu \mathrm{K})$ to the phase transition, unattainable from previous experiments on Earth. Data are analyzed with renormalization-group matching classical-to-critical crossover models of the universal equation of state. It results that the data in the unexplored region, which is a minute deviant from the critical density value, still show adverse effects for testing the true asymptotic nature of the critical point phenomena.

Figure 1

A lin-log plot of turbidity $\tau$ (expressed in ${\mathrm{m}}^{-1}$) as a function of $T-T_{\mathrm{coex}}$ (expressed in $\mathrm{mK}$) obtained from the present ALI DECLIC and previous ALICE2 light transmission measurements in ${\mathrm{SF}}_6$ (symbols are defined in the legend) and compared to the predicted turbidity from Eq. (2), using the CMM equation-of-state model with calculated parameters from column 3 of Table 1. The black dashed curve represents Eq. (2) for $\langle \delta \tilde{\rho }\rangle =0$ (exact critical isochore). The additional four (red solid, red double-dot–dashed, blue dotted, blue dot-dashed) curves represent Eq. (2) for $\langle \delta \tilde{\rho }\rangle$ covering the $0.7\%–1.0\%$ range, by using $0.1\%$ steps, respectively. The typical $30\text{−}\mu \mathrm{K}$ temperature error bar is only indicated by a horizontal red bar for the closest data point ($T-T_{\mathrm{coex}}\sim 3\mu \mathrm{K}$).

Figure 2

Joint fit result for the free parameters $l_0$, $m_0$, and $\overline{u}$ of the CPM fitting the ${\mathrm{SF}}_6{\chi }_T^{*}={\kappa }_T{p}_c$, $c_V^{*}$, and $\mathrm{\Delta }{\tilde{\rho }}_{LV}$ measurements of Refs. [22], [4], and [23], respectively, as functions of $|\mathrm{\Delta }{\tau }^{*}|$ along the critical isochore (see Ref. [18] for the amplitude notation and inserted labels for the curves and the symbols).