Speed of sound in dense simple liquids

Abstract

The speed of sound of simple dense fluids is shown to exhibit a pronounced freezing temperature scaling of the form $c_{\mathrm{s}}/v_{\mathrm{T}}\simeq \sqrt{\gamma }+\alpha (T_{\mathrm{fr}}/T{)}^{\beta }$, where $c_s$ is the speed of sound, $v_{\mathrm{T}}$ is the characteristic thermal velocity, $\gamma$ is the ideal gas heat capacity ratio, $T$ is the temperature, $T_{\mathrm{fr}}$ is the freezing temperature, and $\alpha$ and $\beta$ are dimensionless parameters. For the Lennard-Jones fluid we get $\gamma =5/3$, $\alpha \simeq 7$ with a weak temperature dependence, and $\beta =1/3$. Similar scaling works in several real liquids, such as argon, krypton, xenon, nitrogen, and methane. In this case, $\alpha$ and $\beta$ are substance-dependent fitting parameters. A comparison between the prediction of this freezing temperature scaling and a recent experimental measurement of the speed of sound in methane under conditions of planetary interiors is presented and discussed. The results provide a simple practical tool to estimate the speed of sound in regimes where no experimental data are yet available.

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Cited by in corpus (2)

• Variational approach to Yukawa fluids. II. Instantaneous elastic moduli and sound velocities
• Variational approach to Yukawa fluids. I. Thermodynamics