声悬浮过程的格子Boltzmann方法研究

解文军; 滕鹏飞

doi:10.7498/aps.63.164301

摘要

采用轴对称多弛豫时间格子Boltzmann （LB）方法，研究了圆柱形封闭谐振腔中圆盘形样品的声悬浮过程. 模拟结果表明，（001）模式下谐振腔的共振长度L=0.499λ，在谐振腔中心引入样品后共振漂移量δL≈-0.9，这与线性声学理论计算结果基本相符. 声悬浮力的LB模拟过程包含了黏滞性效应和共振漂移效应，所获得的模拟结果与理论公式计算值在量值上一致，而且其在细节上更符合实验现象. 此外，LB模拟还揭示出了声悬浮过程中的声压波形畸变、声流和声辐射压等非线性声学效应.

关键词:

Abstract

The axisymmetric multiple-relaxation-time lattice Boltzmann (LB) method is used to study the acoustic levitation of a rigid disk sample in a closed cylindrical resonant chamber. The simulation results show that the resonant cavity length L is equal to 0.499λ for (001) mode, and the resonance shift δL is approximately equal to-0.9 with a disk sample located in the chamber center, which accord with the analytical results derived from linear acoustics. The LB method naturally includes the viscosity and resonance shift during the simulation of acoustic levitation force on the disk sample, which gives the results not only consistent with the theory in magnitude, but also coherent with the experiments in more details. Some of the nonlinear effects associated with acoustic levitation, such as waveform distortion, acoustic streaming, and radiation pressure, are also revealed by the LB simulation.

Keywords:

作者及机构信息

1.
西北工业大学空间应用物理与化学教育部重点实验室, 西安 710072

基金项目: 国家自然科学基金（批准号：51071126，51371148）资助的课题.

Authors and contacts

1.
Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, Northwestern Polytechnical University, Xi'an 710072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51071126, 51371148).

参考文献

[1]	Brandt E H 2001 Nature 413 474
[2]	Xie W J, Cao C D, L Y J, Hong Z Y, Wei B 2006 Appl. Phys. Lett. 89 214102
[3]	Weber J K R, Benmore C J, Tailor A N, Tumber S K, Neuefeind J, Cherry B, Yarger J L, Mou Q, Weber W, Byrn S R 2013 Chem. Phys. 424 89
[4]	Radnik J, Bentrup U, Leiterer J, Brckner A, Emmerling F 2011 Chem. Mater. 23 5425
[5]	Wolf S E, Leiterer J, Kappl M, Emmerling F, Tremel W 2008 J. Am. Chem. Soc. 130 12342
[6]	Lee S, Ohsaka K, Rednikov A, Sadhal S S 2006 Ann. N. Y. Acad. Sci. 1077 75
[7]	Tuckermann R, Bauerecker S, Cammenga H K 2005 Int. J. Thermophys. 26 1583
[8]	Saha A, Basu S, Suryanarayana C, Kumar R 2010 Int. J. Heat Mass Transfer 53 5663
[9]	Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302 (in Chinese) [邵学鹏, 解文军 2012 61 134302]
[10]	Brotton S J, Kaiser R I 2013 Rev. Sci. Instrum. 84 055114
[11]	Chainani E T, Ngo K T, Scheeline A 2013 Anal. Chem. 85 2500
[12]	Benmore C J, Weber J K R 2011 Phys. Rev. X 1 011004
[13]	Benmore C J, Weber J K R, Tailor A N, Cherry B R, Yarger J L, Mou Q S, Weber W, Neuefeind J, Byrn S R 2013 J. Pharm. Sci. 102 1290
[14]	Trinh E H, Robeyal J L 1994 Phys. Fluids 6 3567
[15]	Du R J, Xie W J 2011 Acta Phys. Sin. 60 114302 (in Chinese) [杜人君, 解文军 2011 60 114302]
[16]	Qian Z W 2009 Nonlinear Acoustics (Beijing: Science Press) p1 (in Chinese) [钱祖文 2009 非线性声学 (北京: 科学出版社) 第1页]
[17]	Aidun C K, Clausen J R 2010 Annu. Rev. Fluid Mech. 42 439
[18]	Chen S, Doolen G 1998 Annu. Rev. Fluid Mech. 30 329
[19]	Benzi R, Succi S, Vergassola M 1992 Phys. Rep. 222 145
[20]	Guo Z L, Zheng C G, Shi B C 2002 Chin. Phys. 11 366
[21]	Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
[22]	Wu W, Sun D K, Dai T, Zhu M F 2012 Acta Phys. Sin. 61 150501 (in Chinese) [吴伟, 孙东科, 戴挺, 朱鸣芳 2012 61 150501]
[23]	Buick J M, Buckley C L, Greated C A, Gilbert J 2000 J. Phys. A: Math. Gen. 33 3917
[24]	Haydock D, Yeomans J M 2001 J. Phys. A: Math. Gen. 34 5201
[25]	Haydock D 2005 J. Phys. A: Math. Gen. 38 3265
[26]	Barrios G, Rechtman R 2008 J. Fluid Mech. 596 191
[27]	Halliday I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208
[28]	Mukherjee S, Abraham J 2007 Phys. Rev. E 75 026701
[29]	Li Q, He Y L, Tang G H, Tao W Q 2010 Phys. Rev. E 81 056707
[30]	Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546
[31]	Landau L D, Lifshitz E M 1999 Fluid Mechanics (2nd Ed.) (Beijing: World Publishing Corporation) p45
[32]	Saenger R A, Hudson G E 1960 J. Acoust. Soc. Am. 32 961
[33]	Leung E, Lee C P, Jacobi N, Wang T G 1982 J. Acoust. Soc. Am. 72 615
[34]	Xie W J, Wei B 2004 Phys. Rev. E 70 046611
[35]	Xie W J, Wei B 2007 Chin. Phys. Lett. 24 135

施引文献

[1]	Brandt E H 2001 Nature 413 474
[2]	Xie W J, Cao C D, L Y J, Hong Z Y, Wei B 2006 Appl. Phys. Lett. 89 214102
[3]	Weber J K R, Benmore C J, Tailor A N, Tumber S K, Neuefeind J, Cherry B, Yarger J L, Mou Q, Weber W, Byrn S R 2013 Chem. Phys. 424 89
[4]	Radnik J, Bentrup U, Leiterer J, Brckner A, Emmerling F 2011 Chem. Mater. 23 5425
[5]	Wolf S E, Leiterer J, Kappl M, Emmerling F, Tremel W 2008 J. Am. Chem. Soc. 130 12342
[6]	Lee S, Ohsaka K, Rednikov A, Sadhal S S 2006 Ann. N. Y. Acad. Sci. 1077 75
[7]	Tuckermann R, Bauerecker S, Cammenga H K 2005 Int. J. Thermophys. 26 1583
[8]	Saha A, Basu S, Suryanarayana C, Kumar R 2010 Int. J. Heat Mass Transfer 53 5663
[9]	Shao X P, Xie W J 2012 Acta Phys. Sin. 61 134302 (in Chinese) [邵学鹏, 解文军 2012 61 134302]
[10]	Brotton S J, Kaiser R I 2013 Rev. Sci. Instrum. 84 055114
[11]	Chainani E T, Ngo K T, Scheeline A 2013 Anal. Chem. 85 2500
[12]	Benmore C J, Weber J K R 2011 Phys. Rev. X 1 011004
[13]	Benmore C J, Weber J K R, Tailor A N, Cherry B R, Yarger J L, Mou Q S, Weber W, Neuefeind J, Byrn S R 2013 J. Pharm. Sci. 102 1290
[14]	Trinh E H, Robeyal J L 1994 Phys. Fluids 6 3567
[15]	Du R J, Xie W J 2011 Acta Phys. Sin. 60 114302 (in Chinese) [杜人君, 解文军 2011 60 114302]
[16]	Qian Z W 2009 Nonlinear Acoustics (Beijing: Science Press) p1 (in Chinese) [钱祖文 2009 非线性声学 (北京: 科学出版社) 第1页]
[17]	Aidun C K, Clausen J R 2010 Annu. Rev. Fluid Mech. 42 439
[18]	Chen S, Doolen G 1998 Annu. Rev. Fluid Mech. 30 329
[19]	Benzi R, Succi S, Vergassola M 1992 Phys. Rep. 222 145
[20]	Guo Z L, Zheng C G, Shi B C 2002 Chin. Phys. 11 366
[21]	Shi Z Y, Hu G H, Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 59 2595]
[22]	Wu W, Sun D K, Dai T, Zhu M F 2012 Acta Phys. Sin. 61 150501 (in Chinese) [吴伟, 孙东科, 戴挺, 朱鸣芳 2012 61 150501]
[23]	Buick J M, Buckley C L, Greated C A, Gilbert J 2000 J. Phys. A: Math. Gen. 33 3917
[24]	Haydock D, Yeomans J M 2001 J. Phys. A: Math. Gen. 34 5201
[25]	Haydock D 2005 J. Phys. A: Math. Gen. 38 3265
[26]	Barrios G, Rechtman R 2008 J. Fluid Mech. 596 191
[27]	Halliday I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208
[28]	Mukherjee S, Abraham J 2007 Phys. Rev. E 75 026701
[29]	Li Q, He Y L, Tang G H, Tao W Q 2010 Phys. Rev. E 81 056707
[30]	Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546
[31]	Landau L D, Lifshitz E M 1999 Fluid Mechanics (2nd Ed.) (Beijing: World Publishing Corporation) p45
[32]	Saenger R A, Hudson G E 1960 J. Acoust. Soc. Am. 32 961
[33]	Leung E, Lee C P, Jacobi N, Wang T G 1982 J. Acoust. Soc. Am. 72 615
[34]	Xie W J, Wei B 2004 Phys. Rev. E 70 046611
[35]	Xie W J, Wei B 2007 Chin. Phys. Lett. 24 135

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