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Dynamics of an acoustically levitated particle using the lattice Boltzmann method

  • G. BARRIOS (a1) and R. RECHTMAN (a1)


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.



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Aidun, C., Lu, Y. & Ding, E. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287311.
Alexander, F., Chen, H. & Doolen, G. 1992 Lattice Boltzmann model for compressible fluids. Phys. Rev. A 46, 19671970.
Awatani, J. 1955 Study on acoustic radiation pressure (iv) (radiation pressure on a cylinder). Mem. Inst. Sci. Osaka University 12, 95102.
Barmatz, M. 1982 Overview of containerless processing technologies. In Materials Processing in the Reduced Gravity Environment of Space (ed. Ridone, G. E.). Elsevier.
Benzi, R., Succi, S. & Vergassola, M. 1992 The lattice Boltzmann equation: Theory and applications. Physi. Rep. 222, 145197.
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.
Brandt, E. 2001 Suspended by sound. Nature 413, 474475.
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.
Buick, J., Greated, C. & Campbell, D. 1998 Lattice BGK simulation of sound waves. Europhys. Lett. 43, 235240.
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329364.
Chung, S. & Trinh, E. 1998 Containerless protein crystal growth in rotating levitated drops. J. Cryst. Growth 194, 384397.
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.
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.
Filippova, O. & Hanel, D. 1997 Lattice-Boltzmann simulation of gas-particle flow in filters. Computers Fluids 26, 697712.
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.
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.
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.
Hegger, R., Kantz, H. & Schreiber, T. 1999 Practical implementation of nonlinear time series methods: The TISEAN package. Chaos 9, 413435.
Hertz, H. 1995 Standing-wave acoustic trap for nonintrusive positioning of microparticles. J. App. Phys. 78, 48454849.
Higuera, F. J., Succi, S. & Benzi, R. 1989 Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345349.
Kantz, H. & Schreiber, T. 2004 Nonlinear Time Series Analysis. Cambridge.
King, L. V. 1934 On the acoustic radiation pressure on spheres. Proc. R. Soc. Lond. A 147, 212240.
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.
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.
McNamara, G. & Zanetti, G. 1988 Use of the Boltzmann equation to simulate lattice gas automata. Phys. Rev. Lett. 61.
Poe, G. G. & Acrivos, A. 1975 Closed streamline flows past rotating single cylinder and spheres: intertia effect. J. Fluid Mech. 72, 605.
Qian, Y. H., D'Humières, D. & Lallemand, P. 1992 Lattice BGK models for Navier-Stokes equations. Europhys. Lett. 17, 479484.
Rudnick, J. & Barmatz, M. 1990 Oscillational instabilities in single-mode acoustic levitators. J. Acoust. Soc. Am. 87, 8192.
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering. Perseus Books.
Strutt, J. W. & Rayleigh, Lord 1945 The Theory of Sound. Dover.
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.
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.
Xie, W. & Wei, B. 2001 Parametric study of single-axis acoustic levitation. App. Phys. Lett. 79, 881883.
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Dynamics of an acoustically levitated particle using the lattice Boltzmann method

  • G. BARRIOS (a1) and R. RECHTMAN (a1)


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