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Sedimentation and sediment flow on inclined surfaces

Published online by Cambridge University Press:  26 April 2006

A. Nir  and
A. Acrivos
A. Nir
Affiliation:
Department of Chemical Engineering. Technion. Haifa. Israel 32000
A. Acrivos
Affiliation:
The Levich Institute, T202 The City College of the City University of New York, New York, NY 10031, USA
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Abstract

The steady sedimentation of a suspension over an inclined surface is analysed by considering the combined effects of settling hindrance, bulk motion and particle resuspension. The coupled momentum and mass balances suggest that a thin high-density sediment layer will form over the inclined surface, reminiscent of the thin thermal boundary layers in the classical problem of natural convection. It is shown that for a given value of the particle volume fraction in the unsettled suspension, a steady flow of the sediment can be maintained only if the angle of inclination exceeds a minimum value. The analysis further predicts the existence of a sharp discontinuity in the particle volume fraction across the suspension–sediment interface along which the bulk velocity has a local maximum. High particle volume fractions within the sediment are predicted when the unsettled suspension is either very dilute or very concentrated. This leads to the formation of relatively large sediment-layer thicknesses which reflect the fact that a large body force is required in these two limiting cases to overcome the viscous resistance to flow near the inclined boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 139 - 153
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K.: 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.Google Scholar
Borhan, A. & Acrivos, A., 1988 The sedimentation of nondilute suspensions in inclined settlers. Phys. Fluids 31, 3488–3501.Google Scholar
Boycott, A. E.: 1920 Sedimentation of blood corpuscles. Nature 104, 532.Google Scholar
Brady, J. F. & Bossis, G., 1988 Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157.Google Scholar
Davis, R. H. & Acrivos, A., 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Ann. Rev. Fluid Mech. 17, 91–118.Google Scholar
Durlofsky, L. J. & Brady, J. F., 1989 Dynamic simulation of bounded suspensions of hydrodynamically interacting particles. J. Fluid Mech. 200, 39–67.Google Scholar
Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799–814.Google Scholar
Leighton, D.: 1985 The shear-induced migration of particulates in concentrated suspensions. Ph.D. thesis, Stanford University.
Leighton, D. & Acrivos, A., 1986 Viscous resuspension. Chem. Engng Sci. 41, 1377–1384.Google Scholar
Leighton, D. & Acrivos, A., 1987a Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109–131.Google Scholar
Leighton, D. & Acrivos, A., 1987b The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Leung, W.-F. & Probstein, R. F. 1983 Lamella and tube settlers. 1. Model and operation. Ind. Engng Chem. Proc. Des. Dev. 22, 58–73.Google Scholar
Nakamura, H. & Kuroda, K., 1937 La cause de l'acceleration de la vitesse de sedimentation des suspensions dans les recipients inclines. Keijo J. Med. 8, 256–296.Google Scholar
Ponder, E.: 1925 On sedimentation and rouleaux formation. Q. J. Exp. Physiol. 15, 235–252.Google Scholar
Probstein, R. F., Yung, R. & Hicks, R., 1981 A model for lamella settlers. In Physical Separations (ed. M. P. Freeman & J. A. Fitzpatrick), pp. 53–92. New York: Engineering Foundation.
Schalflinger, U., Acrivos, A. & Zhang, K., 1989 Viscous resuspension of a sediment within a laminar and stratified flow. Intl J. Multiphase Flow (submitted).Google Scholar
Schlichting, H.: 1968 Boundary Layer Theory, sixth edn, p. 192 ff. McGraw-Hill.