Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions

TL;DR

This paper introduces an analytical model that predicts acoustic relaxation absorption in gas mixtures by identifying dominant energy transfer processes, enabling the extraction of composition-specific relaxation contributions.

Contribution

The model uniquely combines parallel and series relaxation theories to clarify how individual gas compositions influence acoustic relaxation absorption.

Findings

Model accurately predicts relaxation absorption spectra for various gases.

Simulation results align well with experimental data.

The approach isolates composition-specific relaxation contributions.

Abstract

The existing molecular relaxation models based on both parallel relaxation theory and series relaxation theory cannot extract the contributions of gas compositions to acoustic relaxation absorption in mixtures. In this paper, we propose an analytical model to predict acoustic relaxation absorption and clarify composition relaxation contributions based on the rate-determining energy transfer processes in molecular relaxation in excitable gases. By combining parallel and series relaxation theory, the proposed model suggests that the vibration-translation process of the lowest vibrational mode in each composition provides the primary deexcitation path of the relaxation energy, and the rate-determining vibration-vibration processes between the lowest mode and others dominate the coupling energy transfer between different modes. Thus, each gas composition contributes directly one single relaxation process to the molecular relaxation in mixture, which can be illustrated by the decomposed acoustic relaxation absorption spectrum of the single relaxation process. The proposed model is validated by simulation results in good agreement with experimental data such as $\mathrm{N_2}$, $\mathrm{O_2}$, $\mathrm{CO_2}$, $\mathrm{CH_4}$ and their mixtures.