Abstract
We discuss the extraordinary growth in the attenuation of sound αλ and in the dispersion in the speed of sound c, which occurs near all liquid-vapor critical points. The attenuation and dispersion have been measured over 5 orders of magnitude in frequency. Remarkably, the data collapse onto universal, theoretically predicted curves. The theory considers equilibrium density fluctuations near the critical point where the fluctuations are large compared with the particle spacing. These density fluctuations have a distribution of sizes characterized by the correlation length ξ and a distribution of lifetimes characterized by the relaxation time τ. As the critical point is approached, ξ and τ diverge with the universal power laws ξ ∝ r−0.63 and τ ∝ r−1.93, where r is a measure of the distance from the critical point. [At the critical density ρc, r ≡ (T − Tc)/Tc.] In the low-frequency limit (ωτ ≪ 1), the attenuation grows as αλ ∝ r−1.93 and the speed of sound approaches zero as c ∝ r0.055. When ωτ ≫ 1, αλ approaches a maximum, non-universal limit and strong dispersion is present. Low-frequency sound waves reach the condition ωτ = 1 closer to Tc and deeper into the asymptotic critical regime than do high-frequency sound waves. In Earth's gravity, we show that stirring a near-critical fluid reduces stratification and enables measurements closer to the critical point. We compare the attenuation and dispersion for pure fluids near the liquid-vapor critical point with that of binary liquid mixtures near the consolute point.
Published Version
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