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Enhanced sedimentation in narrow tilted channels

Published online by Cambridge University Press:  20 April 2006

Eric Herbolzheimer  and
Andreas Acrivos
Eric Herbolzheimer
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305 Present address: Chemical Engineering, California Institute of Technology, Pasadena, CA 91125.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305
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Abstract

The analysis of Acrivos & Herbolzheimer (1979) is extended to describe the sedimentation of dilute suspensions in tilted two-dimensional channels in which the spacing between the plates is small compared with their length. The theory assumes that the flow is laminar and that the suspension consists of monodisperse spherical beads having small particle Reynolds number. Expressions for the flow fields in the clearfluid region and in the suspension, as well as for the location of the interface separating these two regions, are obtained asymptotically in the limit of Λ [Gt ] 1 with $R\Lambda^{-\frac{1}{3}}\ll 1$, where R and A are as defined in the previous work. The present analysis differs from that given earlier in that the aspect ratio, i.e. the ratio of the height of the suspension to the channel width, is now taken to be O(A1/3) rather than O(1) as was the case before. Under these conditions, the solution of the time-dependent equations leads to the surprising prediction that the clear-fluid layer which forms beneath the downward-facing plate attains a steady shape only along the lower portion of the channel while, in contrast, its thickness increases with time for locations along the channel that are above some critical point. Because of this transient behaviour, the well-known Ponder-Nakamura-Kuroda (PNK) formula overestimates the rate at which the top of the suspension region falls with time; however, the PNK results for the volumetric settling rate still hold under the conditions considered in this paper. It is shown that this discontinuity in the interface shape can be suppressed in continuous settling systems but only if the feed and withdrawal locations are chosen properly.

Batch sedimentation experiments were conducted in a channel with parallel flat walls under the following sets of conditions: H0/b ≈ 90, 5° ≤ θ ≤ 45°, 0·01 ≤ c0 ≤ 0·025, 1·7 × 107 < Λ < 3·5 × 107, and 1·8 < R < 2·1, where θ is the angle of inclination of the vessel from the vertical, and c0 is the initial volume fraction of solids in the suspension. The experimental observations were found to be in excellent agreement with the theoretical predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 485 - 499
Copyright
© 1981 Cambridge University Press

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References

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