Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-10-06T08:16:25.517Z Has data issue: false hasContentIssue false

Particle size segregation in inclined chute flow of dry cohesionless granular solids

Published online by Cambridge University Press:  21 April 2006

S. B. Savage
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6
C. K. K. Lun
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada H3A 2K6

Abstract

If granular materials comprising particles of identical material but different sizes are sheared in the presence of a gravitational field, the particles are segregated according to size. The small particles fall to the bottom and the larger ones drift to the top of the sheared layer. In an attempt to isolate and study some of the essential segregation mechanisms, the paper considers a simplified problem involving the steady two-dimensional flow of a binary mixture of small and large spherical particles flowing down a roughened inclined chute. The flow is assumed to take place in layers that are in motion relative to one another as a result of the mean shear. For relatively slow flows, it is proposed that there are two main mechanisms responsible for the transfer of particles between layers. The first mechanism, termed the ‘random fluctuating sieve’, is a gravity-induced, size-dependent, void-filling mechanism. The probability of capture of a particle in one layer by a randomly generated void space in the underlying layer is calculated as a function of the relative motion of the two layers. The second, termed the ‘squeeze expulsion’ mechanism, is due to imbalances in contact forces on an individual particle which squeeze it out of its own layer into an adjacent one. It is assumed that this mechanism is not size preferential and that there is no inherent preferential direction for the layer transfer. This second physical mechanism in particular was proposed on the basis of observations of video recordings that were played back at slow speed. Since the magnitude of its contribution is determined by the satisfaction of overall mass conservation, the exact physical nature of the mechanism is of less importance. By combining these two proposed mechanisms the net percolation velocity of each species is obtained. The mass conservation equation for fines is solved by the method of characteristics to obtain the development of concentration profiles with downstream distance. Although the theory involves a number of empirical constants, their magnitude can be estimated with a fair degree of accuracy. A solution for the limiting case of dilute concentration of fine particles and a more general solution for arbitrary concentrations are presented. The analyses are compared with experiments which measured the development of concentration profiles during the flow of a binary mixture of coarse and fine particles down a roughened inclined chute. Reasonable agreement is found between the measured and predicted concentration profiles and the distance required for the complete separation of fine from coarse particles.

Type
Research Article
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solids spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.Google Scholar
Bridgwater, J. 1971 Rate of spontaneous interparticle percolation. Trans. Instn Chem. Engrs 49, 163169.Google Scholar
Bridgwater, J. 1976 Fundamental powder mixing mechanisms. Powder Technol. 15, 215236.Google Scholar
Bridgwater, J., Cook, H. H. & Drahun, J. A. 1985a Strain induced percolation. In Instn Chem. Engrs Symposium Series No. 69, pp. 171191.
Bridgwater, J., Cooke, M. H. & Scott, A. M. 1978 Inter-particle percolation: Equipment development and mean percolation velocities. Trans. Instn Chem. Engrs. 56, 157167.Google Scholar
Bridgwater, J., Foo, W. S. & Stephens, D. J. 1985b Particle mixing and segregation in failure zones — theory and experiment. Powder Technol. 41, 147158.Google Scholar
Brown, C. B. 1978 The use of maximum entropy in the characterization of granular media. In Proc. US—Japan Seminar on Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials (ed. S. C. Cowin & M. Satake), pp. 98108. Tokyo: Gakujutsu Bunken Fukyukai.
Campbell, A. P. & Bridgwater, J. 1973 The mixing of dry solids by percolation. Trans. Instn Chem. Engrs 51, 7274.Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-uniform Gases, 3rd edn. Cambridge University Press.
Cooke, M. H. & Bridgwater, J. 1979 Interparticle percolation: A statistical mechanical interpretation. Ind. Engng Chem. Fundam. 18, 2527.Google Scholar
Cooke, M. H., Bridgwater, J. & Scott, A. M. 1978 Interparticle percolation: lateral and axial diffusion coefficients. Powder Technol. 21, 183193.Google Scholar
Drahun, J. A. & Bridgwater, J. 1981 Free surface segregation. In Insin Chem. Engrs Symposium Series No. 65, pp. S4/Q/1S4/q/14.
Drahun, J. A. & Bridgwater, J. 1983 The mechanism of free surface segregation. Powder Technol. 36, 3953.Google Scholar
Farrell, M., Lun, C. K. K. & Savage, S. B. 1986 A simple kinetic theory for granular flow of binary mixtures of smooth, inelastic, spherical particles. Acta Mech. 63, 4560.Google Scholar
Foo, W. S. & Bridgwater, J. 1983 Particle migration. Powder Technol. 36, 271273.Google Scholar
Jaynes, E. T. 1963 Information theory and statistical mechanics. Statistical Physics III (ed. K. W. Ford), pp. 181218.
Johanson, J. R. 1978 Particle segregation and what to do about it. Chem. Engng 85, 183188.Google Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepuniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223256.Google Scholar
Masliyah, J. & Bridgwater, J. 1974 Particle percolation: a numerical study. Trans. Instn Chem. Engrs 52, 3142.Google Scholar
Middleton, G. V. 1970 Experimental studies related to problems of flysch sedimentation. In Flysch Sedimentology in North America (ed. J. Lajoie), pp. 253272. Toronto: Business and Economics Science Ltd.
Middleton, G. V. & Hampton, M. A. 1976 Subaqueous sediment transport and deposition by sediment gravity flows. In Marine Sediment Transport and Environmental Management (ed. D. J. Stanley & D. J. P. Swift), pp. 197218. Wiley.
Naylor, M. A. 1980 The origin of inverse grading in muddy debris flow deposits — A review. J. Sedimentary Petr. 50, 11111116.Google Scholar
Sallenger, A. H. 1979 Inverse grading and hydraulic equivalence in grain-flow deposits. J. Sedimentary Petr. 49, 553562.Google Scholar
Savage, S. B. 1984 The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 289366.Google Scholar
Scott, A. M. & Bridgwater, J. 1975 Interparticle percolation: a fundamental solids mixing mechanism. Ind. Engng Chem. Fundam. 14, 2227.Google Scholar
Walker, R. G. 1973 Mopping up the turbidite mess. In Evolving Concepts in Sedimentology (ed. R. N. Ginsberg), pp. 137. Johns Hopkins Press.
Walton, O. R. 1983 Particle dynamics calculations of shear flow. Mechanics of Granular Materials: New Models & Constitutive Relations. (ed. J. T. Jenkins & M. Satake), pp. 327338. Amsterdam. Elsevier.
Williams, J. C. 1976 The segregation of particulate materials. A review. Powder Technol. 15, 245251.Google Scholar
Wills, B. A. 1979 Mineral Processing Technology. Pergamon.
Zallen, R. 1983 The Physics of Amorphous Solids. Wiley.