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Streaming motions in a bed of vibrationally fluidized dry granular material

Published online by Cambridge University Press:  21 April 2006

Stuart B. Savage
Stuart B. Savage
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada.
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Abstract

Experimental and theoretical studies of vibration-induced flow and mixing of dry granular materials are described. Tests were performed on rounded polystyrene beads contained in a rectangular box having transparent front and back walls and a flexible, nominally horizontal bottom which could be driven at various frequencies and amplitudes. The amplitude of the bottom vibrations was a maximum at the centre and decreased towards the vertical sidewalls. Slow recirculating flows were observed; they had the form of two vortices in which the velocity was upwards at the vertical centreline and downwards along the vertical sidewalls. The streaming velocities were measured as a function of bed vibration frequency and displacement amplitude. An explanation proposed for the recirculating flows is that the vibrating base sends ‘acoustic’ waves upwards through the bed. These waves ‘fluidize’ the granular material but are in turn attenuated because of the dissipative nature of the collisions between the ‘fluidized’ particles. Thus the slow recirculating flows in the granular material are analogous to the more familiar ‘acoustic streaming’ in air. An approximate analysis of these streaming motions is developed by making use of a modification of the constitutive theory of Jenkins & Savage (1983). A number of simplifying assumptions are introduced to make the analysis tractable. The general flow patterns of the streaming motions are predicted, but the velocities are overestimated as a result of the simplifying assumptions. The analysis is restricted to a rather narrow range of conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 457 - 478
Copyright
© 1988 Cambridge University Press

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