Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Analytical model for acoustic multi-relaxation spectrum in gas mixtures

Zhang Ke-Sheng Wang Shu Zhu Ming Hu Yi Jia Ya-Qiong

Citation:

Analytical model for acoustic multi-relaxation spectrum in gas mixtures

Zhang Ke-Sheng, Wang Shu, Zhu Ming, Hu Yi, Jia Ya-Qiong
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • 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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 60971009, 61001011), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090142110019), the Natural Science Foundation of Hubei Province, China(Grant No. 2010CDB02701), and the Fundamental Research Funds For Center Universities (Grant No. 2012QN083).
    [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 物理学报 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 物理学报 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 物理学报 57 4282]

  • [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 物理学报 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 物理学报 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 物理学报 57 4282]

  • [1] Song Tong-Tong, Luo Jie, Lai Yun. Pseudo-local effect medium theory. Acta Physica Sinica, 2020, 69(15): 154203. doi: 10.7498/aps.69.20200196
    [2] Zhai Han-Yu, Shen Jia-Yin, Xue Xun. Effective quintessence from string landscape. Acta Physica Sinica, 2019, 68(13): 139501. doi: 10.7498/aps.68.20190282
    [3] Zhang Xiang-Qun, Wang Shu, Zhu Ming. Acoustic rotational relaxation of hydrogen around normal temperture. Acta Physica Sinica, 2018, 67(9): 094301. doi: 10.7498/aps.67.20172665
    [4] Chen Yan-Hong, Cheng Rui, Zhang Min, Zhou Xian-Ming, Zhao Yong-Tao, Wang Yu-Yu, Lei Yu, Ma Peng-Peng, Wang Zhao, Ren Jie-Ru, Ma Xin-Wen, Xiao Guo-Qing. Experimental investigation on diagnosing effective atomic density in gas-type target by using proton energy loss. Acta Physica Sinica, 2018, 67(4): 044101. doi: 10.7498/aps.67.20172028
    [5] Xu Yan, Fan Wei, Ji Yan-Jun, Song Ren-Gang, Chen Bing, Zhao Zhen-Hua, Chen Da. Effective field theory approach to the weakly interacting bose gas. Acta Physica Sinica, 2014, 63(4): 040501. doi: 10.7498/aps.63.040501
    [6] Ouyang Yu-Hua, Yuan Ping, Jia Xiang-Dong, Wang Xiao-Yun, Xue Si-Min. Thunder acoustic spectrum obtained by using digital signal processing and propagation effects. Acta Physica Sinica, 2013, 62(8): 084303. doi: 10.7498/aps.62.084303
    [7] Jia Ya-Qiong, Wang Shu, Zhu Ming, Zhang Ke-Sheng, Yuan Fei-Ge. The analytic model between effective heat capacity and relaxation time in gas acoustic relaxation process. Acta Physica Sinica, 2012, 61(9): 095101. doi: 10.7498/aps.61.095101
    [8] Dai Yu-Rong, Ding De-Sheng. Second-harmonic generation of the Bessel sound beam of several lobes. Acta Physica Sinica, 2011, 60(12): 124302. doi: 10.7498/aps.60.124302
    [9] Chen Xiao-Xue, Teng Li-Hua, Liu Xiao-Dong, Huang Qi-Wen, Wen Jin-Hui, Lin Wei-Zhu, Lai Tian-Shu. Study of injection and relaxation of electron spins in InGaN film by time-resolved absorption spectroscopy. Acta Physica Sinica, 2008, 57(6): 3853-3856. doi: 10.7498/aps.57.3853
    [10] Wu Bing-Guo, Zhao Zhi-Gang, You Yu-Xin, Liu Mei. Phase transition and vortex noise spectrum in two-dimensional Josephson-junction array. Acta Physica Sinica, 2007, 56(3): 1680-1685. doi: 10.7498/aps.56.1680
    [11] Cheng Tai-Min, Xianyu Ze. Transverse acoustic phonon excitation of two-dimensional Heisenberg ferromagnetic system. Acta Physica Sinica, 2006, 55(9): 4828-4836. doi: 10.7498/aps.55.4828
    [12] Yu Xue-Cai, Ye Yu-Tang, Cheng Lin. Criterion for validity of potential and limiting atom number in a potential well for Bose-Einstein condensation gas. Acta Physica Sinica, 2006, 55(2): 551-554. doi: 10.7498/aps.55.551
    [13] Xu Hai-Ying, Zhao Zhi-Gang, Liu Mei. Spectrum analysis of voltage noise of moving vortex lattice and dynamic phase transition. Acta Physica Sinica, 2005, 54(6): 2924-2928. doi: 10.7498/aps.54.2924
    [14] ZHANG BAO-ZHENG, LI YU-XING, LIN MEI-RONG, CHEN WEN-JU. THEORETICAL STUDY OF MULTIPHONON RADIATIONLESS RELAXATION RATE. Acta Physica Sinica, 1990, 39(2): 261-269. doi: 10.7498/aps.39.261
    [15] LIN ZI-JING, WANG KE-LIN. INVESTIGATION OF SURFACE PHONONS AT IDEAL, RELAXED AND 2×1 RECONSTRUCTED Si(lll) SURFACE. Acta Physica Sinica, 1989, 38(6): 891-899. doi: 10.7498/aps.38.891
    [16] WENG ZHENG-YU, WU HANG-SHENG. RELATION BETWEEN THE FORM OF THE NORMALIZED EFFECTIVE PHONON SPECTRUM AND THE SUPERCONDUCTING Tc. Acta Physica Sinica, 1988, 37(2): 239-247. doi: 10.7498/aps.37.239
    [17] XU JI-REN, HUANG NAN-TANG, JIANG YI-FENG, FU GUANG-SHENG, WU ZHEN-QIU. INFRARED ABSORPTION INVESTIGATION OF VIBRATIONAL EXCITED RELAXATIONS IN BCl3. Acta Physica Sinica, 1981, 30(11): 1456-1463. doi: 10.7498/aps.30.1456
    [18] LI HONG-CHENG. INFLUENCE OF EFFECTIVE PHONON SPECTRUM α2F(ω) ON Tc OF SUPERCONDUCTORS. Acta Physica Sinica, 1979, 28(1): 104-116. doi: 10.7498/aps.28.104
    [19] WEI YUNG-CHIO, CHANG SHU-I. ABSORPTION OF ULTRASONIC WAVES IN ETHYL AND METHYL ACETATES. Acta Physica Sinica, 1962, 18(6): 298-304. doi: 10.7498/aps.18.298
    [20] CHIEN TSU-WEN. THEORY OF SOUND ABSORPTION AND THE RELAXATION MECHANISM OF MgSO4 IN WATER SOLUTION. Acta Physica Sinica, 1962, 18(10): 501-508. doi: 10.7498/aps.18.501
Metrics
  • Abstract views:  6023
  • PDF Downloads:  447
  • Cited By: 0
Publishing process
  • Received Date:  22 December 2011
  • Accepted Date:  20 February 2012
  • Published Online:  05 September 2012

/

返回文章
返回