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Sedimentation of Particulate Systems

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Solid-Liquid Separation in the Mining Industry

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 105))

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Abstract

This chapter deals with sedimentation of particulate systems considered as discrete media. Sedimentation is the settling of a particle or suspension of particles in a fluid due to the effect of an external force such as gravity, centrifugal force or any other body force. Discrete sedimentation has been successful in establishing constitutive equations for continuous sedimentation processes. The foundation of the motion of particles in fluids is discussed in different flow regimes, Euler’s flow, Stokes flow and flows with a boundary layer. Starting from the sedimentation of a sphere in an unbounded fluid, a complete analysis is made of the settling of individual spherical particles and suspensions. The results are extended to isometric particles and to arbitrarily shaped particles. Sphericity as a shape factor is used to describe the form of isometric particles. A hydrodynamic sphericity must be defined for particles with arbitrary shapes by performing sedimentation or fluidization experiments, calculating the drag coefficient for the particles using the volume equivalent diameter and obtaining a sphericity defined for isometric particles that fits experimental values. A modified drag coefficient and sedimentation velocities permits grouping all sedimentation results in one single equation for particles of any shape.

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References

  • Abraham, F. F. (1970). Functional dependence of the drag coefficient of a sphere on Reynolds number. Physics of Fluids, 13, 2194–2195.

    Article  Google Scholar 

  • Barker, H. (1951). The effect of shape and density on the free settling rates of particles at high Reynolds Numbers, Ph.D. Thesis, University of Utah, Table 7, pp. 124–132; Table 9, pp. 148–153.

    Google Scholar 

  • Barnea, E., & Mitzrahi, J. (1973). A generalized approach to the fluid dynamics of particulate systems, 1. General correlation for fluidization and sedimentation in solid multiparticle systems. Chemical Engineering Journal, 5, 171–189.

    Article  Google Scholar 

  • Barnea, E., & Mednick, R. L. (1975). Correlation for minimum fluidization velocity. Transactions on Institute of Chemical Engineers, 53, 278–281.

    Google Scholar 

  • Batchelor, G. K. (1967). An introduction for fluid dynamics (p. 262). Cambridge: Cambridge University Press.

    Google Scholar 

  • Brauer, H., & Sucker, D. (1976). Umströmung von Platten, Zylindern un Kugeln. Chemie Ingenieur Technik, 48, 665–671.

    Article  Google Scholar 

  • Cabtree, L. F. (1963). Three dimensional boundary layers. In L. Rosenhead (Ed.), Laminar boundary layers, Oxford: Oxford Univesity press, p. 423.

    Google Scholar 

  • Chabra, R. P., Agarwal, L., & Sinha, N. K. (1999). Drag on non-spherical particles: An evaluation of available methods. Powder Technology, 101, 288–295.

    Article  Google Scholar 

  • Concha, F., & Almendra, E. R. (1979a). Settling velocities of particulate systems, 1. Settling velocities of individual spherical particles. International Journal of Mineral Processing, 5, 349–367.

    Article  Google Scholar 

  • Concha, F., & Almendra, E. R. (1979b). Settling velocities of particulate systems, 2. Settling velocities of suspensions of spherical particles. International Journal of Mineral Processing, 6, 31–41.

    Article  Google Scholar 

  • Concha, F., & Barrientos, A. (1986). Settling velocities of particulate systems, 4. settling of no spherical isometric particles. International Journal of Mineral Processing, 18, 297–308.

    Article  Google Scholar 

  • Concha, F., & Christiansen, A. (1986). Settling velocities of particulate systems, 5. Settling velocities of suspensiones of particles of arbitrary shape. International Journal of Mineral Processing, 18, 309–322.

    Article  Google Scholar 

  • Christiansen, E. B., & Barker, D. H. (1965). The effect of shape and density on the free settling rate of particles at high Reynolds numbers. AIChE Journal, 11(1), 145–151.

    Article  Google Scholar 

  • Darby, R. (1996). Determining settling rates of particles, Chemical Engineering, 109–112.

    Google Scholar 

  • Fage, A. (1937). Experiments on a sphere at critical Reynolds number (pp. 108, 423). London: Aeronautical Research Council, Reports and Memoranda, N°1766.

    Google Scholar 

  • Flemmer, R. L., Pickett, J., & Clark, N. N. (1993). An experimental study on the effect of particle shape on fluidization behavior. Powder Technology, 77, 123–133.

    Article  Google Scholar 

  • Ganguly, U. P. (1990). On the prediction of terminal settling velocity in solids-liquid systems. International Journal of Mineral Processing, 29, 235–247.

    Article  MathSciNet  Google Scholar 

  • Ganser, G. H. (1993). A rational approach to drag prediction of spherical and non-spherical particles, 1993. Powder Technology, 77, 143–152.

    Article  Google Scholar 

  • Goldstein, S. (Ed.). (1965). Modern development in fluid dynamics (Vols. 1, 2, p. 702). New York: Dover.

    Google Scholar 

  • Haider, A., & Levenspiel, O. (1998). Drag coefficient and terminal velocity of spherical and non-spherical particles. Powder Technology, 58, 63–70.

    Article  Google Scholar 

  • Happel, J., & Brenner, H. (1965). Low Reynolds hydrodynamics (p. 220). NJ: Prentice-Hall Inc.

    Google Scholar 

  • Heywood, H. (1962). Uniform and non-uniform motion of particles in fluids: Proceeding of the Symposium on the Interaction between Fluid and Particles, Institute of Chemical Engineering, London, pp. 1–8.

    Google Scholar 

  • Lapple, C. E., & Shepherd, C. B. (1940). Calculation of particle trajectories. Industrial and Engineering Chemistry, 32, 605.

    Article  Google Scholar 

  • Lee, K., & Barrow, H. (1968). Transport process in flow around a sphere with particular reference to the transfer of mass. International Journal of Heat and Mass Transfer, 11, 1020.

    Google Scholar 

  • Lighthill, M. J. (1963). Boundary layer theory. In L. Rosenhead (Ed.), Laminar boundary layers, Oxford: Oxford University, p. 87.

    Google Scholar 

  • Massarani, G. (1984). Problemas em Sistemas Particulados, Blücher Ltda., Río de Janeiro, Brazil, pp. 102–109.

    Google Scholar 

  • McDonal, J. E. (1954). Journal of Applied Meteorology, 11, p. 478.

    Google Scholar 

  • Meksyn, D. (1961). New methods in boundary layer theory, New York.

    Google Scholar 

  • Newton, I. (1687). Filosofiae naturalis principia mathematica, London.

    Google Scholar 

  • Nguyen, A. V., Stechemesser, H., Zobel, G., & Schulze, H. J. (1997). An improved formula for terminal velocity of rigid spheres. International Journal of Mineral Processing, 50, 53–61.

    Article  Google Scholar 

  • Richardson, J. F., & Zaki, W. N. (1954). Sedimentation and fluidization: Part I. Transactions on Institute of Chemical Engineers, 32, 35–53.

    Google Scholar 

  • Perry 1963, p. 5.61.

    Google Scholar 

  • Pettyjohn, E. S., & Christiansen, E. B. (1948). Effect of particle shape on free-settling of isometric particles. Chemical Engineering Progress, 44(2), 157–172.

    Google Scholar 

  • Rosenhead, L. (ed) (1963). Laminar boundary layers (pp. 87, 423, 687). Oxford: Oxford University Press.

    Google Scholar 

  • Schlichting, H. (1968). Boundary layer theory. New York: McGraw-Hill. 747.

    Google Scholar 

  • Stokes, G. G. (1844). On the theories of internal friction of fluids in motion and of the equilibrium and motion of elastic solids. Transactions on Cambridge Philosophical Society, 8(9), 287–319.

    Google Scholar 

  • Taneda, S. (1956). Rep. Res. Inst. Appl. Mech., 4, 99.

    Google Scholar 

  • Thomson, T., & Clark, N. N. (1991). A holistic approach to particle drag prediction. Powder Technology, 67, 57–66.

    Article  Google Scholar 

  • Tomotika, A.R.A. (1936). Reports and memoranda N°1678, See also Goldstein 1965, p. 498.

    Google Scholar 

  • Tory, E. M. (1996). Sedimentation of small particles in a viscous fluid. UK: Computational Mechanics Publications Inc.

    Google Scholar 

  • Tsakalis, K. G., & Stamboltzis, G. A. (2001). Prediction of the settling velocity of irregularly shaped particles. Minerals Engineering, 14(3), 349–357.

    Article  Google Scholar 

  • Tourton, R., & Clark, N. N. (1987). An explicit relationship to predict spherical termninal velocity. Powder Technology, 53, 127–129.

    Article  Google Scholar 

  • Tourton, R., & Levenspiel, O. (1986). A short Note on the drag correlation for spheres. Powder Technology, 47, 83–86.

    Article  Google Scholar 

  • Wadell, J. (1932). Volume shape and roundness of rock particles, Journal of Geology, 15, 43–451.

    Google Scholar 

  • Wadell, J. (1934). The coefficient of resistance s a function of the Reynolds number for solids of various shapes, Journal of the Franklin Institute 217, 459–490.

    Google Scholar 

  • Zens, F. A., & Othme, D. F. (1966). Fluidization and fluid-particle systems. New York: McGraw-Hill.

    Google Scholar 

  • Zigrang, D. J., & Sylvester, N. D. (1981). An explicit equation for particle settling velocities in solid-liquid systems. AIChE Journal, 27, 1043–1044.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Metallurgical Engineering, University of Concepcion, Concepcion, Chile

    Fernando Concha A.

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  1. Fernando Concha A.
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Concha A., F. (2014). Sedimentation of Particulate Systems. In: Solid-Liquid Separation in the Mining Industry. Fluid Mechanics and Its Applications, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-02484-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-02484-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02483-7

  • Online ISBN: 978-3-319-02484-4

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