Calculating vibrational mode contributions to sound absorption in
excitable gas mixtures by decomposing multi-relaxation absorption
spectroscopy
Kesheng Zhang
a,b
, Yi Ding
c
, Ming Zhu
c,
⇑
, Mingzhe Hu
d
, Shu Wang
c
, Yingqun Xiao
a
a
Guizhou Key Laboratory of Electric Power Big Data, Guizhou Institute of Technology, Guiyang 550003, Guizhou, China
b
School of Information Engineering, Guizhou Institute of Technology, Guiyang 550003, Guizhou, China
c
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
d
Department of Physics and Electronics, Liupanshui Normal University, Liupanshui, Guizhou 553004, China
article info
Article history:
Received 2 August 2016
Received in revised form 19 September
2016
Accepted 21 September 2016
Keywords:
Sound absorption
Molecular vibrational relaxation
Mode contributions
Decomposing multi-relaxation absorption
spectra
abstract
Sound relaxational absorption spectroscopy of excitable gas mixtures is potentially applied for gas com-
position detection. The relaxation of vibrational modes of gas molecules determines the sound relax-
ational absorption. However, to our knowledge, the contribution of each vibrational mode available in
gas mixtures to sound multi-relaxation absorption has not been calculated in existing literature. In this
paper, based on the decoupled expression of the effective isochoric molar heat for a gas mixture, a sound
multi-relaxation absorption spectrum is decomposed into the sum of single-relaxation spectra. From this
decomposable characteristic, the contribution of each vibrational mode available in the gaseous medium
to the multi-relaxation absorption is obtained at room temperature. For various gas compositions includ-
ing carbon dioxide, methane, nitrogen etc., the calculated contributions of vibrational modes are verified
by the comparison with experiment data. We prove the following views with quantifiable outcomes that
the primary molecular relaxation process associated with the lowest mode plays the major role in acous-
tic relaxational absorption of gas mixtures; the mode with lower vibrational frequency provides higher
contribution to the primary relaxation process. This work could provide a deeper insight into the relation-
ship between the sound relaxational absorption spectroscopy and gas molecules.
Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Acoustic relaxational absorption spectroscopy of gas mixtures is
potentially applied for gas composition detection, such as practical
applications for real-time monitoring of natural gas [1–8]. The
propagation of acoustic waves in gases is fundamentally a molecu-
lar phenomenon [9]. The sound absorption in excitable gases (poly-
atomic or diatomic gases or their mixtures) is caused by two
mechanisms: the classical absorption associated with transport
phenomena (e.g., heat conduction and viscosity) and the non-
classical, or relaxational absorption associated with the lag in
adjustment between the internal states of the molecules and their
external energy [10]. In a thermal equilibrium, the energy distribu-
tion of a gas between the external (translational) molecular kinetic
energy and the internal (e.g., vibrational, rotational) states of
energy of the molecules only depends on the temperature of the
gas. When the equilibrium is disturbed by the propagation of an
acoustic wave through the gas, there is an instantaneous increase
(due to compression) in the external energy. By molecular colli-
sions, some of this energy increase enters into the internal states.
A certain relaxation time (or time lag) is required for this energy
to be transferred back to the external form to reestablish equilib-
rium. As a result of that, much of this energy released on
de-excitation will be released as heat to give rise to a net absorp-
tion of acoustic energy—the relaxational absorption. For most sim-
ple molecules at room temperature, the rapid equilibration
between rotation and translation makes Vibrational-Rotational
plus Rotational-Translational energy transfer process indistin-
guishable from the Vibrational-Translational (V-T) process. Thus,
rotation is usually classified as translation as ‘‘external” degrees
of freedom (DOF) to distinguish from vibration as the ‘‘internal”
DOF which takes a longer time to adjust [10]. Thus, the internal
DOF thermal relaxation is almost entirely attributed to the vibra-
tional modes, whose relaxation processes are the cause for the
sound relaxational absorption around room temperature [3].
http://dx.doi.org/10.1016/j.apacoust.2016.09.025
0003-682X/Ó 2016 Elsevier Ltd. All rights reserved.
⇑
Corresponding author.
E-mail address: zhuming@mail.hust.edu.cn (M. Zhu).
Applied Acoustics 116 (2017) 195–204
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Applied Acoustics
journal homepage: www.elsevier.com/locate/apacoust