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To identify the correlation between sound propagation and molecular multimode vibrational relaxation in polyatomic gas mixture, an analytical model that constructs acoustic multi-relaxation spectrum is presented. The frequency-dependent effective specific heat of gas is formulated from the micro view of vibrational mode energy transfer as well as the macro view of relaxation process due to vibrational-vibrational mode energy coupling. With the aid of the general relaxation equations of multimode vibrational energy transfer, the analytical expressions to calculate acoustic relaxation absorption and dispersion, which reflect both primary and secondary relaxation processes, are developed from the effective specific heat. The constructed absorption spectra of various gas mixtures, consisting of carbon dioxide, methane, nitrogen, and oxygen, accord with the experimental data very well. Especially, the peak errors of those results are less than 1%. Moreover, the simulation results illustrate that less than two single processes with higher strength appear generally in a multi-relaxation absorption spectrum. Compared with the existing models, the analytical model can directly obtain the analytical expressions of characteristic points in the relaxation spectrum of gas mixtures, which makes it advantageous to analyze the spectral characteristics qualitatively and quantitatively. Consequently, the model provides an effective approach to analyzing the relationship between sound propagation and molecular vibrational relaxation of gas mixtures.
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Keywords:
- gas relaxation /
- acoustic spectrum /
- acoustic attenuation /
- effective heat capacity
[1] Petculescu A G, Lueptow R M 2007 Icarus 186 413
[2] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[3] Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[4] Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phys. Sin. 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[5] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) p55-216
[6] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p1-114
[7] Lueptow R M, Phillips S 1994 Meas. Sci. Technol. 5 1375
[8] Herzfeld K F, Rice F O 1928 phys. rev. 31 691
[9] Knudsen V O 1931 J. Acoust. Soc. Am. 3 126
[10] Bauer H J, Shields F D, Bass H E 1972 J. Chem. Phys. 57 4624
[11] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[12] Tanczos F I 1956 J. Chem. Phys. 25 439
[13] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[14] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[15] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[16] Bass H E, Sutherland L C, Piercy J, Evans L 1984 Absorption of Sound by the Atmosphere in Physical Acoustics edited by Mason W P, Thurston R N (Vol. XVII) (Orlando: Academic) p145-232
[17] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[18] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[19] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[20] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[21] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[22] Zhang H L 2007 Theoretical acoustics (Beijing: Higher Education Press) p221 (in Chinese) [张海澜 2007 理论声学(北京:高等教育出版社) 第221页]
[23] Zhang J C, Yuan P, Ouyang Y H 2010 Acta Phys. Sin. 59 8287 (in Chinese) [张景川, 袁萍, 欧阳玉花 2010 59 8287]
[24] Morse P M, Ingard K U 1968 Theoretical acoustics (New York: McGraw-Hill) p294-300
[25] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324-332
[26] Gravitt J C, Whetstone C N, Lagemann R T 1966 J. Chem. Phys. 44 70
[27] Yardley J T, Moore C B 1968 J. Chem. Phys. 49 1111
[28] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[29] Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
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[1] Petculescu A G, Lueptow R M 2007 Icarus 186 413
[2] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[3] Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[4] Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phys. Sin. 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[5] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) p55-216
[6] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p1-114
[7] Lueptow R M, Phillips S 1994 Meas. Sci. Technol. 5 1375
[8] Herzfeld K F, Rice F O 1928 phys. rev. 31 691
[9] Knudsen V O 1931 J. Acoust. Soc. Am. 3 126
[10] Bauer H J, Shields F D, Bass H E 1972 J. Chem. Phys. 57 4624
[11] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[12] Tanczos F I 1956 J. Chem. Phys. 25 439
[13] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[14] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[15] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[16] Bass H E, Sutherland L C, Piercy J, Evans L 1984 Absorption of Sound by the Atmosphere in Physical Acoustics edited by Mason W P, Thurston R N (Vol. XVII) (Orlando: Academic) p145-232
[17] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[18] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[19] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[20] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[21] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[22] Zhang H L 2007 Theoretical acoustics (Beijing: Higher Education Press) p221 (in Chinese) [张海澜 2007 理论声学(北京:高等教育出版社) 第221页]
[23] Zhang J C, Yuan P, Ouyang Y H 2010 Acta Phys. Sin. 59 8287 (in Chinese) [张景川, 袁萍, 欧阳玉花 2010 59 8287]
[24] Morse P M, Ingard K U 1968 Theoretical acoustics (New York: McGraw-Hill) p294-300
[25] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324-332
[26] Gravitt J C, Whetstone C N, Lagemann R T 1966 J. Chem. Phys. 44 70
[27] Yardley J T, Moore C B 1968 J. Chem. Phys. 49 1111
[28] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[29] Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
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