Critical sound propagation in mixtures

Abstract

We calculate critical effects in the sound propagation in mixtures near consolute or plait points within a non-asymptotic renormalization group theory and derive general expressions for the frequency-dependent sound velocity and sound attenuation. The critical non-asymptotic time scale in the sound mode in mixtures is set by an effective order parameter Onsager coefficient containing a dynamical parameter related to the enhancement of the thermal conductivity in the mixture, not considered so far. The differences in the critical behavior near the consolute and plait point are due to the different non-asymptotic behavior of the zero-frequency sound velocity. We compare our predictions for the sound velocity and sound absorption near the plait point in 3 He-4 He mixtures.

Non-asymptotic approach to ultrasonic attenuation in nitroethane isooctane critical mixture

“…Recently, an extensive analysis of sound propagation both in pure fluids and critical mixtures has been performed by Folk and Moser [14][15][16][17]. They studied non-asymptotic transport coefficient (viscosity, diffusion and thermal conductivity) and sound mode within the dynamical equations of model H of the renormalization group theory [19].…”

“…Ferrell and Bhattacharjee [13] proposed a simple correction procedure-based on the use of an effective reduced temperature-to clearly reveal the underlying universal scaling. Recently, Folk and Moser [14][15][16][17] have proposed a new model of sound propagation in pure fluids and critical mixtures. They analysed non-asymptotic transport coefficients (viscosity, mass diffusion and thermal diffusion) and sound propagation in the nonasymptotic limit using renormalization group theory.…”

Sound attenuation near the demixing point of binary liquids: interplay of critical dynamics and noncritical kinetics

“…It should be noted that the binary mixture can exhibit a kind of gas-liquid transition as the temperature and concentration are varied. This is the plait point [2,3] where some of the dynamic features are the same as in the pure fluid critical point and the binary liquid consolute point, but the sound attenuation is different [4][5][6]. The interest in the strong correlations of fluctuations, promoting the striking similarity and thus the universal characteristics, has stimulated theoretical as well as experimental investigations [7][8][9][10][11].…”

Dynamical Crossover at the Liquid-Liquid Transformation of a Compressed Molten Alkali Metal

“…It is well documented that the adiabatic sound velocity reflects the combined critical behavior of structure and thermodynamics, namely γ/S(k → 0), being S(k) the static structure factor [35]. Furthermore, according to the theory of dynamic critical phenomena [36,37], it is possible to observe a reduction in the adiabatic speed of sound by approaching the liquid-gas transition or the demixing limit in binary liquids. Remarkably, we show in Fig.4 a slope discontinuity in the pressure behavior of the instantaneous, hypersonic sound velocity as determined by GCM applied to the AIMD data, which can not be simply traced back to the above mentioned structural and thermodynamical criticalities.…”