Nonlinear Behavior of a Suspended Particle in  Single-Axis Acoustic Levitators

Celso Abud; Mirosmar  Rodrigues; Tiago Ramos

doi:10.31686/ijier.vol7.iss12.2016

Authors

Celso Abud

Federal University of Goiás - UFG, Goiás, Brazil.
Mirosmar Rodrigues

Federal University of Goiás - UFG, Goiás, Brazil
Tiago Ramos

University of São Paulo - USP, São Paulo, Brazil

DOI:

https://doi.org/10.31686/ijier.vol7.iss12.2016

Keywords:

Nonlinear Phenomena, Acoustic Levitation, Lyapunov Exponents

Abstract

The nonlinear behavior of a suspended sphere in a single-axis acoustic levitator was studied. Spontaneous oscillations of the sphere in this levitator were experimentally analyzed recording its positions using a high speed camera. A mathematical model based on acoustic radiation forces and real parameters is proposed to describe the dynamics of the sphere movement and its stability. The stability of the motion was investigated via a Lyapunov exponent diagram. We observed that the axial and radial movements of small spheres under levitation may present regular stability and chaotic ones. The Lyapunov exponent diagram for the model shows a complexity structure sharing different regions of stability according to the model parameters.

Author Biographies

Celso Abud, Federal University of Goiás - UFG, Goiás, Brazil.

Institute of Mathematics and Technology.
Mirosmar Rodrigues, Federal University of Goiás - UFG, Goiás, Brazil

Department of Mining Engineering,
Tiago Ramos, University of São Paulo - USP, São Paulo, Brazil

Department of Mechatronics and Mechanical Systems Engineering,

References

[1] R. J. K. Weber, C. J. Benmore, S. K. Tumber, A. N. Tailor, L. S. T. C. A. Rey, S. R. Byrn, Acoustic levitation: recent developments and emerging opportunities in biomaterials research, Eur. Biophys. J. 41 (2012) 379.

[2] A. Scheeline, R. L. Behrens, Potential of levitated drops to serve as microreactors for biophysical measurements, Biophys. Chem. 165-166 (2012) 1.

[3] C. R. P. Courtney, C. E. M. Demore, A. G. H. Wu, P. D. W. S. Cochran, B. W. Drinkwater, Independent trapping and manipulation of microparticles using dexterous acoustic tweezers, Appl. Phys. Lett. 104 (2014) 154103.

[4] F. Petersson, A. Nilsson, C. Holm, H. J ̈onsson, T. Laurell, Separation of lipids from blood utilizing ultrasonic standing waves in microfluidic channels, Analyst 129 (2004) 938.

[5] S. Santesson, S. Nilsson, Airborne chemistry: Acoustic levitation in chemical analysis, Anal. Bioanal. Chem. 378 (2004) 1704.

[6] L. Puskar, R. Tuckermann, T. Frosch, J. Popp, V. Ly, D. McNaughton, B. R. Wood, Raman acoustic levitation spectroscopy of red blood cells and plasmodium falciparum trophozoites, Lab Chip 7 (2007) 11251131.

[7] J. Schenk, L. TrObs, F. Emmerling, J. Kneipp, U. Panne, M. Albrecht, Simultaneous uv/vis spectroscopy and surface enhanced raman scattering of nanoparticle formation and aggregation in levitated droplets, Anal. Methods 4 (2012) 12521258.

[8] W. J. Xie, B. Wei, Parametric study of single-axis acoustic levitation, Appl.Phys. Lett. 79 (2001) 881883.

[9] M. A. B. Andrade, N. Péres, J. C. Adamowski, Experimental study of the oscillation of spheres in an acoustic levitator, J. Acoust. Soc. Am 136 (2014)
1518.

[10] N. Péres, M. A. B. Andrade, R. Canetti, J. C. Adamowski, Experimental determination of the dynamics of an acoustically levitated sphere, Journal of Applied Physics 116 (2014) 184903.

[11] G. Whitworth, M. A. Grundy, W. T. Coakley, Transport and harvesting of suspended particles using modulated ultrasound, Ultrasonics 29 (1991) 439.

[12] G. Whitworth, W. T. Coakley, Particle column formation in a stationary ultrasonic field, J. Acoust. Soc. Am. 91(1) (1992) 79.

[13] L. P. Gor’kov, On the forces acting on a small particle in an acoustic field in an ideal fluid, Sov. Phys. Doklady 6 (1962) 773.

[14] K. Yosioka, Y. Kawasima, Acoustic radiation pressure on a compressible sphere, Acoustics 5 (1955) 167.

[15] M. A. B. Andrade, T. S. Ramos, F. T. A. Okina, J. C. Adamowski, Nonlinear characterization of a single-axis acoustic levitator, Rev. Sci. Instrum. 85 (2014) 045125.

[16] F. Takens, Detecting strange atractors in turbulence, Lecture Notes in Mathematics 898 (1981) 366.

[17] J. Gallas, Structure of the parameter space of the hnon map, Phys. Rev. Lett. 70 (1993) 271.

[18] E. Medeiros, S. de Souza, R. Medrano, I. Caldas, Replicate periodic windows in the parameter space of driven oscillators, Chaos, Solitons & Fractals 44 (2011) 982 – 989.

[19] C. V. Abud, R. E. de Carvalho, Robust attractor of non-twist systems, Physica A 440 (2015) 42.

[20] J. C. Sprott, Chaos and time-series analysis, Oxford University Press 91(1) (2003) 116–117.