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TECHNICAL PAPERS

Motion of a Sphere Suspended in a Vibrating Liquid-Filled Container

[+] Author and Article Information
Samer Hassan

Department of Chemical Engineering and Applied Chemistry,  University of Toronto, Toronto, Ont. M5S 3E5, Canada

Tatyana P. Lyubimova

 Institute of Continuous Media Mechanics UB, RAS, Perm, Russia

Dmitry V. Lyubimov

Theoretical Physics Department,  Perm State University, Perm, Russia

Masahiro Kawaji1

Department of Chemical Engineering and Applied Chemistry,  University of Toronto, Toronto, Ont. M5S 3E5, Canadakawaji@ecf.utoronto.ca

1

To whom correspondence should be addressed.

J. Appl. Mech 73(1), 72-78 (May 19, 2005) (7 pages) doi:10.1115/1.1992516 History: Received August 06, 2004; Revised May 19, 2005

The effects of small vibrations on the motion of a solid particle suspended in a fluid cell were investigated theoretically and experimentally. An inviscid model was developed to predict the amplitude of a solid particle suspended by a thin wire in the fluid cell which was vibrated horizontally. Both the model and experimental data showed that the particle amplitude is linearly proportional to the cell amplitude, and the existence of a resonance frequency. At higher cell vibration frequencies well above the resonance frequency, both the model and experiments showed that the particle amplitude becomes constant and independent of the wire length.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 8

Variation of particle amplitude with cell amplitude for different frequencies (water, wire length: 70mm)

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Figure 9

Particle Amplitude versus frequency for different cell amplitude, L=70mm

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Figure 10

Particle amplitude variation with wire length for different frequencies (steel ball, liquid: Water, cell amplitude: 1.0mm)

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Figure 7

Effect of wire diameter on the particle amplitude for wire length=7cm and different cell vibration conditions

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Figure 6

Variation of particle amplitude with wire length (L−R0) for cell vibration frequency of 1Hz at different cell vibration amplitudes

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Figure 5

Variation of particle amplitude with wire length (L−R0) for cell vibration amplitude of 4.0mm at different frequencies

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Figure 4

Instantaneous particle displacement from the mean position, (a) f=0.25Hz, a=8mm; (b) f=0.5Hz, a=4mm; (c) f=0.75Hz, a=2mm; (d) f=1Hz, a=1mm

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Figure 3

Particle displacement from the mean position, (a) instantaneous data, (b) first-smoothed data, (c) second-smoothed data, and (d) third-smoothed data

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Figure 2

Balance of forces acting on a particle of a mass m suspended by a wire of length L

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Figure 1

Experimental setup

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