A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

TL;DR

This paper introduces a volume-based hydrodynamic model for sound wave propagation in monatomic gases, accurately capturing phase speed and damping across all Knudsen numbers, including high-frequency regimes where traditional models fail.

Contribution

The study develops a novel hydrodynamic model incorporating mass-density diffusion and volume terms, improving predictions of sound wave behavior in rarefied gases over existing models.

Findings

Accurately predicts sound wave phase speed and damping across all Knudsen numbers.

Reproduces experimental observations of standing waves in high Knudsen number regimes.

Suggests sound waves at high frequencies are better described as mass-density waves.

Abstract

We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.