Ultrasonic dispersion and attenuation near the liquid-gas critical point of ³He

We report ultrasonic dispersion and attenuation measurements near the liquid-gas critical point of ³He at frequencies from 0.5 to 5.0 MHz and densities from 0.89ϱ _c to 1.15ϱ _c . The singular part of the sound attenuation and the dispersion on the critical isochore ϱ _c = 0.0414 g/cm³ are analyzed in terms of the Kawasaki-Mistura theory. If the Ornstein-Zernike order parameter correlation function is assumed in the analysis, good agreement with our data is achieved, except close to the critical temperature T _cin the high-frequency region, where ω^* = ω/ω_D ^≫ 1. Here Ω _D is the characteristic relaxation rate of the critical fluctuations. From a fit of the theory to our data, and assuming the inverse correlation length κ is expressed by κ = κ₀ɛ^Ν, where ɛ = (T−T_c)/T_c with Ν = 0.63, we obtain κ₀ = (3.9 ± 0.4) × 10⁹ m⁻¹. It is found that a more realistic form of the correlation function, as proposed by Fisher and Langer and calculated by Bray, yields even poorer agreement with out data than does the classical Ornstein-Zernike form for Ω^* > 10. The same difficulties appear in the analysis of the available data for xenon. Thus, the present mode coupling theory is unable to satisfactorily describe the acoustic experiments on fluids near the liquid-vapor critical point over a large range of reduced frequencies Ω^*. In the appendix, we reanalyze previously reported ultrasonic data in ⁴He, taking into account the nonsingular term of the thermal conductivity. Using Ν = 0.63, we obtain a good fit of the experiment to the theory in the hydrodynamic region with κ₀ = (5.5 ± 1) × 10⁹ m⁻¹.