Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-20T06:42:42.697Z Has data issue: false hasContentIssue false

Dynamics of an acoustically levitated particle using the lattice Boltzmann method

Published online by Cambridge University Press:  17 January 2008

G. BARRIOS
Affiliation:
Centro de Investigación en Energía, Universidad Nacional Autónomade México, Apdo. Postal 34, Temixco, Morelos, 62580 [email protected]
R. RECHTMAN
Affiliation:
Centro de Investigación en Energía, Universidad Nacional Autónomade México, Apdo. Postal 34, Temixco, Morelos, 62580 [email protected]

Abstract

When the acoustic force inside a cavity balances the gravitational force on a particle the result is known as acoustic levitation. Using the lattice Boltzmann equation method we find the acoustic force acting on a rounded particle for two different single-axis acoustic levitators in two dimensions, the first with plane waves, the second with a rounded reflector that enhances the acoustic force. With no gravitational force, a particle oscillates around a pressure node; in the presence of gravity the oscillation is shifted a small vertical distance below the pressure node. This distance increases linearly as the density ratio between the solid particle and fluid grows. For both cavities, the particle oscillates with the frequency of the sound source and its harmonics and in some cases there is a much smaller second dominant frequency. When the momentum of the acoustic source changes, the oscillation around the average vertical position can have both frequencies mentioned above. However, if this quantity is large enough, the oscillations of the particle are aperiodic in the cavity with a rounded reflector.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aidun, C., Lu, Y. & Ding, E. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287311.CrossRefGoogle Scholar
Alexander, F., Chen, H. & Doolen, G. 1992 Lattice Boltzmann model for compressible fluids. Phys. Rev. A 46, 19671970.CrossRefGoogle ScholarPubMed
Awatani, J. 1955 Study on acoustic radiation pressure (iv) (radiation pressure on a cylinder). Mem. Inst. Sci. Osaka University 12, 95102.Google Scholar
Barmatz, M. 1982 Overview of containerless processing technologies. In Materials Processing in the Reduced Gravity Environment of Space (ed. Ridone, G. E.). Elsevier.Google Scholar
Benzi, R., Succi, S. & Vergassola, M. 1992 The lattice Boltzmann equation: Theory and applications. Physi. Rep. 222, 145197.CrossRefGoogle Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511525.CrossRefGoogle Scholar
Brandt, E. 2001 Suspended by sound. Nature 413, 474475.CrossRefGoogle ScholarPubMed
Buick, J., Buckley, C., Greated, C. & Gilbert, J. 2000 Lattice Boltzmann BGK simulations of nonlinear sound waves: the development of a shock front. J. Phys. A: Math. Gen. 33, 39173928.CrossRefGoogle Scholar
Buick, J., Greated, C. & Campbell, D. 1998 Lattice BGK simulation of sound waves. Europhys. Lett. 43, 235240.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329364.CrossRefGoogle Scholar
Chung, S. & Trinh, E. 1998 Containerless protein crystal growth in rotating levitated drops. J. Cryst. Growth 194, 384397.Google Scholar
Cosgrove, J., Buick, J., Campbell, D. & Greated, C. 2004 Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model. Ultrasonics 43, 2125.Google Scholar
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation. J. Fluid Mech. 261, 95134.CrossRefGoogle Scholar
Filippova, O. & Hanel, D. 1997 Lattice-Boltzmann simulation of gas-particle flow in filters. Computers Fluids 26, 697712.Google Scholar
Gor'kov, L. P. 1962 On the forces acting on a small particle in an acoustical field in an ideal fluid. Sov. Phys. 6 (9), 773775.Google Scholar
Haydock, D. 2005 a Calculation of the radiation force on a cylinder in a standing wave acoustic field. J. Phys. A: Math. Gen. 38, 32793285.Google Scholar
Haydock, D. 2005 b Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field. J. Phys. A: Math. Gen. 38, 32653277.CrossRefGoogle Scholar
Hegger, R., Kantz, H. & Schreiber, T. 1999 Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9, 413435.Google Scholar
Hertz, H. 1995 Standing-wave acoustic trap for nonintrusive positioning of microparticles. J. App. Phys. 78, 48454849.Google Scholar
Higuera, F. J., Succi, S. & Benzi, R. 1989 Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345349.CrossRefGoogle Scholar
Kantz, H. & Schreiber, T. 2004 Nonlinear Time Series Analysis. Cambridge.Google Scholar
King, L. V. 1934 On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. A 147, 212240.Google Scholar
Ladd, A. J. C. 1994 a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.CrossRefGoogle Scholar
Ladd, A. J. C. 1994 b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311339.Google Scholar
McNamara, G. & Zanetti, G. 1988 Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett. 61.Google Scholar
Poe, G. G. & Acrivos, A. 1975 Closed streamline flows past rotating single cylinder and spheres: intertia effect. J. Fluid Mech. 72, 605.Google Scholar
Qian, Y. H., D'Humières, D. & Lallemand, P. 1992 Lattice BGK models for Navier-Stokes equations. Europhys. Lett. 17, 479484.Google Scholar
Rudnick, J. & Barmatz, M. 1990 Oscillational instabilities in single-mode acoustic levitators. J. Acoust. Soc. Am. 87, 8192.CrossRefGoogle Scholar
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering. Perseus Books.Google Scholar
Strutt, J. W. & Rayleigh, Lord 1945 The Theory of Sound. Dover.Google Scholar
Trinh, E. H. 1985 Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity. Rev. Sci. Instrum. 56, 20592065.CrossRefGoogle Scholar
Wu, J., Du, G., Work, S. & Warshaw, D. 1990 Acoustic radiation pressure on a rigid cylinder: An analytical theory and experiments. J. Acoust. Soc. Am. 87, 581586.CrossRefGoogle Scholar
Xie, W. & Wei, B. 2001 Parametric study of single-axis acoustic levitation. App. Phys. Lett. 79, 881883.Google Scholar