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On shear layers in mixture separation in rotating containers with inclined walls

Published online by Cambridge University Press:  21 April 2006

M. Ungarish
M. Ungarish
Affiliation:
Computer Science Department, Technion, Haifa 32000. Israel
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Abstract

The rotating flow of a separating mixture within an axisymmetric container is considered with emphasis on the pure fluid layer adjacent to the inclined ‘bottom’ boundary from which particles are removed by centrifugal buoyancy. Within the framework of ‘mixture’ (‘diffusion’) model and when the relative density difference, the Ekman number E and particle Taylor number β are small, it is shown that the behaviour of that layer is governed by Ξ = E½αI|cotγB|/β (where αI is the volume fraction of the dispersed particles and γB is the elevation angle of the bottom wall with respect to the centrifugal force). If Ξ is small the layer thickens quickly into an inviscid core, in accordance with previous studies. However, novel features show up for Ξ large or O(1), when the viscosity-induced Ekman suction is able to counteract the separation velocity. In the former case the pure fluid layer is thin and quasi-steady, and the remaining part of the interface is essentially perpendicular to the force field, in close apparent resemblance to the analog gravitational process. In the latter case, a thin quasi-steady layer and a continuously thickening core of pure fluid coexist in the same vessel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 27 - 51
Copyright
© 1988 Cambridge University Press

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