najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-260-265najo-671Research ArticlePHYSICSФИЗИКАAsymptotic solution of ultrasonic near-field levitation problemMelikhovI. F.

Kronverkskiy, 49, St. Petersburg, 197101

ivan.melikhov@gmail.comITMO UniversityRussian Federation20171208202582260265Copyright © Melikhov I.F., 20252025Melikhov I.F.Melikhov I.F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/671

Ultrasonic near-field levitation allows suspension of a moderately large object at a height of tens of microns above sound actuator. We developed an asymptotic approach to describe the air dynamics in the gap between an acoustic source and the levitating object. The suggested method allows computation of the lifting force. Due to resolving of both viscous and inertial effects, it remains applicable across a wide range of levitation distances. The paper explains theoretical background of the model and presents a numerical solution of the obtained equations. The results are compared to published numerical and experimental data showing very good agreement.

ultrasonic levitationacoustic streamingasymptotic analysisThis work was partially financially supported by the Government of the Russian Federation (grant 074-U01), by grant MK-5161.2016.1 of the President of the Russian Federation, by grant 16-11-10330 of Russian Science Foundation.ReferencesSalbu E.O.J. Compressible Squeeze Films and Squeeze Bearings. Journal of Basic Engineering, ASME, 1964, 86, P. 355–364.Salbu E.O.J. Compressible Squeeze Films and Squeeze Bearings. Journal of Basic Engineering, ASME, 1964, 86, P. 355–364.Hashimoto Y., Koike Y., Ueha S. Near-field acoustic levitation of planar specimens using flexural vibration. The Journal of the Acoustical Society of America, 1996, 100, P. 2057–2061.Hashimoto Y., Koike Y., Ueha S. Near-field acoustic levitation of planar specimens using flexural vibration. The Journal of the Acoustical Society of America, 1996, 100, P. 2057–2061.Hashimoto Y., Koike Y., Ueha S. Transporting objects without contact using flexural traveling waves. The Journal of the Acoustical Society of America, 1998, 103, P. 3230–3233.Hashimoto Y., Koike Y., Ueha S. Transporting objects without contact using flexural traveling waves. The Journal of the Acoustical Society of America, 1998, 103, P. 3230–3233.Yoshimoto S., Anno Y., Sato Y., Hamanaka K. Float Characteristics of Squeeze-Film Gas Bearing with Elastic Hinges for Linear Motion Guide. JSME International Journal Series C, 1997, 40, P. 353–359.Yoshimoto S., Anno Y., Sato Y., Hamanaka K. Float Characteristics of Squeeze-Film Gas Bearing with Elastic Hinges for Linear Motion Guide. JSME International Journal Series C, 1997, 40, P. 353–359.Yoshimoto S., Kobayashi H., Miyatake M. Float characteristics of a squeeze-film air bearing for a linear motion guide using ultrasonic vibration. Tribology International, 2007, 40, P. 503–511.Yoshimoto S., Kobayashi H., Miyatake M. Float characteristics of a squeeze-film air bearing for a linear motion guide using ultrasonic vibration. Tribology International, 2007, 40, P. 503–511.Lord Rayleigh. On the pressure of vibrations Philosophical. Magazine Series 6, 1902, 3, P. 338–346.Lord Rayleigh. On the pressure of vibrations Philosophical. Magazine Series 6, 1902, 3, P. 338–346.Lord Rayleigh. On the momentum and pressure of gaseous vibrations, and on the connexion with the virial theorem. Magazine Series 6, 1905, 10, P. 364–374.Lord Rayleigh. On the momentum and pressure of gaseous vibrations, and on the connexion with the virial theorem. Magazine Series 6, 1905, 10, P. 364–374.Chu B.-T., Apfel R.E. Acoustic radiation pressure produced by a beam of sound. The Journal of the Acoustical Society of America, 1982, 72, P. 1673–1687.Chu B.-T., Apfel R.E. Acoustic radiation pressure produced by a beam of sound. The Journal of the Acoustical Society of America, 1982, 72, P. 1673–1687.Lee C.P., Wang T.G. Acoustic radiation pressure. The Journal of the Acoustical Society of America, 1993, 94, P. 1099–1109.Lee C.P., Wang T.G. Acoustic radiation pressure. The Journal of the Acoustical Society of America, 1993, 94, P. 1099–1109.Makeev I.V, Popov I.Yu. Steady Stokes flow between confocal semi-ellipses. Nanosystems: Phys. Chem. Math., 2016, 7 (2), P. 324–331.Makeev I.V, Popov I.Yu. Steady Stokes flow between confocal semi-ellipses. Nanosystems: Phys. Chem. Math., 2016, 7 (2), P. 324–331.Yamazaki Y, Ohmori S. Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation. Nanosystems: Phys. Chem. Math., 2017, 8 (1), P. 38–41.Yamazaki Y, Ohmori S. Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation. Nanosystems: Phys. Chem. Math., 2017, 8 (1), P. 38–41.Minikes A., Bucher I. Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: numerical analysis and experimental study. Journal of Sound and Vibration, 2003, 263, P. 241–268.Minikes A., Bucher I. Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: numerical analysis and experimental study. Journal of Sound and Vibration, 2003, 263, P. 241–268.Minikes A., Bucher I., Haber S. Levitation force induced by pressure radiation in gas squeeze films. The Journal of the Acoustical Society of America, 2004, 116, P. 217–226.Minikes A., Bucher I., Haber S. Levitation force induced by pressure radiation in gas squeeze films. The Journal of the Acoustical Society of America, 2004, 116, P. 217–226.Ilssar D., Bucher I. On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies. Journal of Sound and Vibration, 2015, 354, P. 154–166.Ilssar D., Bucher I. On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies. Journal of Sound and Vibration, 2015, 354, P. 154–166.Nomura H., Kamakura T., Matsuda K. Theoretical and experimental examination of near-field acoustic levitation. The Journal of the Acoustical Society of America, 2002, 111, P. 1578–1583.Nomura H., Kamakura T., Matsuda K. Theoretical and experimental examination of near-field acoustic levitation. The Journal of the Acoustical Society of America, 2002, 111, P. 1578–1583.Minikes A., Bucher I. Comparing numerical and analytical solutions for squeeze-film levitation force. Journal of Fluids and Structures, 2006, 22, P. 713–719.Minikes A., Bucher I. Comparing numerical and analytical solutions for squeeze-film levitation force. Journal of Fluids and Structures, 2006, 22, P. 713–719.Landau L.D., Lifshitz E.M. Fluid Mechanics, 2nd ed., Vol. 6, Pergamon Press, Oxford, 1987, 532 p.Landau L.D., Lifshitz E.M. Fluid Mechanics, 2nd ed., Vol. 6, Pergamon Press, Oxford, 1987, 532 p.Sutherland W. The viscosity of gases and molecular force. Philosophical Magazine Series 5, 1893, 36, P. 507–531.Sutherland W. The viscosity of gases and molecular force. Philosophical Magazine Series 5, 1893, 36, P. 507–531.

The authors declare that there are no conflicts of interest present.