Dynamic-scaling theory of critical ultrasonic attenuation in binary liquids

The critical slowing down that sets in near the critical point of a second-order phase transition is manifested in fluids by a diverging relaxation time for the long-wavelength order-parameter fluctuations. This divergence has a profound effect on all of the transport properties. In sound propagation, the adiabatic compressions and dilations produce temperature swings which the order-parameter fluctuations can follow fully only if the sound frequency is smaller than the relaxation rates in the fluid. As the critical point is approached this condition is violated and a lagging, or hysteretic, response results. As demonstrated by Clerkeet al., the known amplitude of the temperature swings leads to a prediction of ultrasonic attenuation at the critical point that agrees, in magnitude, exactly with that found by Harada et al. The theoretically predicted scaling function that describes how the attenuation and dispersion vary as the critical point is approached is in good agreement with the experimental findings of Garland and Sanchez.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.