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Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers

Published online by Cambridge University Press:  26 April 2006

Alexander Goldshtein ,
Michael Shapiro ,
Leonid Moldavsky  and
Mati Fichman
Alexander Goldshtein
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Michael Shapiro
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Leonid Moldavsky
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Mati Fichman
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed.

A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = (Aω)/(hmg)1/2, with g, hm being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = (Aω2)/g. The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data.

Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 349 - 382
Copyright
© 1995 Cambridge University Press

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