Speed of sound in dense simple liquids

TL;DR

This paper presents a universal scaling law for the speed of sound in dense simple liquids and real fluids, linking it to temperature and freezing point, validated by experiments and applicable for estimating sound speeds in unmeasured regimes.

Contribution

It introduces a new freezing temperature scaling law for the speed of sound in dense fluids, applicable to both simple and real liquids, with validation against experimental data.

Findings

Scaling law accurately describes sound speed near freezing in simple and real liquids.

Parameters $eta$ and $ ext{ extalpha}$ are substance-dependent but follow a universal form.

The model predicts sound speeds in planetary interior conditions where data is lacking.

Abstract

The speed of sound of simple dense fluids is shown to exhibit a pronounced freezing temperature scaling of the form $c_{\rm s}/v_{\rm T}\simeq \sqrt{\gamma} +\alpha (T_{\rm fr}/T)^{\beta}$, where $c_s$ is the speed of sound, $v_{\rm T}$ is the characteristic thermal velocity, $\gamma$ is the ideal gas heat capacity ratio, $T$ is the temperature, $T_{\rm fr}$ 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.