Simulation of sedimentation of polydisperse suspensions: A particle-based approach

AIChE Journal

Volumn 51, Issue 9, 2005, Pages 2457-2468

  Bargieł, Monika ^a   Ford, Robert A ^b   Tory, Elmer M ^c  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

^b Spielo Gaming International   (Canada)

^c MOUNT ALLISON UNIVERSITY   (Canada)

Author keywords

Polydisperse suspensions; Sedimentation; Settling; Simulation

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA ACQUISITION; MATHEMATICAL MODELS; PARTICLES (PARTICULATE MATTER); RANDOM PROCESSES;

CONCENTRATION GRADIENT; DENSITY INVERSIONS; POLYDISPERSE SUSPENSIONS; STOCHASTIC SIMULATIONS;

SEDIMENTATION;

SEDIMENTATION; SETTLING; SUSPENSION;

EID: 26944440481     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.10517     Document Type: Conference Paper

References (55)

1. Happel J, Brenner H. Low Reynolds Number Hydrodynamics. Dordrecht: Martinas Nijhoff; 1986.
2. Kim S, Karrila SJ. Microhydrodynamics: Principles and Selected Examples. Boston: Butterworth-Heineman; 1991.
3. Bustos MC, Concha F, Bürger R, Tory EM. Sedimentation and Thickening. Phenomenological Foundation and Mathematical Theory. Dordrecht: Kluwer Academic; 1999.
4. Zeidan A, Rohani S, Bassi A, Whiting P. Review and comparison of solids settling velocity models. Reviews in Chem Eng. 2003; 19:473-530.
5. Tory EM, Pickard DK. A three-parameter Markov model for sedimentation. Can J Chem Eng. 1977;55:655-665.
6. Al-Naafa MA, Selim MS. Sedimentation of monodisperse and bidisperse hard-sphere colloidal suspensions. AIChE J. 1992;38:1618-1630.
7. Tory EM, Kamel MT. Mean velocities in polydisperse suspensions. Powder Technol. 1997;93:199-207.
8. Shannon PT, Stroupe E, Tory EM. Batch and continuous thickening. Basic theory. Solids flux for rigid spheres. Ind Eng Chem Fundam. 1963;2:203-211. Correction, ibid. 1964;3;184.
9. Davis RH, Hassen MA. Spreading of the interface at the top of a slightly polydisperse sedimenting suspension. J Fluid Mech. 1988; 196: 107-134.
10. Davis RH, Birdsell KH. Hindered settling of semidilute monodisperse and polydisperse suspensions. AIChE J. 1988;34:123-129.
11. Xue B, Sun Y. Modeling of sedimentation of polydisperse spherical beads with a broad size distribution. Chem Eng Sci. 2003;58:1531-1543.
12. Bürger R, Karlsen KH, Tory EM, Wendland WL. Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres. Z Angew Math Mech. 2002;82:699-722.
13. Bürger R, Concha F, Fjelde K-K, Karlsen KH. Numerical simulation of the settling of polydisperse suspensions of spheres. Powder Technol. 2000; 113:30-54.
14. Shannon PT, DeHaas RD, Stroupe EP, Tory EM. Batch and continuous thickening. Prediction of batch settling behavior with results for rigid spheres. Ind Eng Chem Fundam. 1964;3:250-260.
15. Kynch GJ. A theory of sedimentation. Trans Faraday Soc. 1952;48: 166-176.
16. Bürger R, Tory EM. On upper rarefaction waves in batch setting. Powder Technol. 2000;108:74-87.
17. Tory EM, Bargiel M, Honeycutt RL. A three-parameter Markov model for sedimentation III. A stochastic Runge-Kutta method for computing first-passage times. Powder Technol. 1994;80:133-146.
18. Tory EM, Pickard DK. Extensions and refinements of a Markov model for sedimentation. J Math Anal Appl. 1982;86:442-470.
19. Pickard DK, Tory EM. A Markov model for sedimentation: Fundamental issues and insights. In: MacNeill IB, Umphrey GJ. Advances in the statistical sciences, Vol. IV, Stochastic hydrology. Dordrecht: D. Reidell, 1987:1-25.
20. Hesse CH, Ramos E. Dynamic simulation of a stochastic model for particle sedimentation in fluids. Appl. Math. Modelling. 1994;18:437-445.
21. Tory EM, Ford RA. Stochastic Simulation of Sedimentation. In: Rahman M, Brebbia CA. Advances in Fluid Mechanics III. Southampton: WIT Press; 2000:663-672.
22. Tory EM, Ford RA. Simulation of sedimentation of bidisperse suspensions. Int J Mineral Processing. 2004;73:119-130.
23. Steinour HH. Rate of sedimentation. Non-flocculated suspensions of uniform spheres. Ind Eng Chem. 1944;36:618-624.
24. Richardson JF, Zaki WN. Sedimentation and fluidization: Part 1. Trans Instn Chem. Engrs (London). 1954;32:35-53.
25. Barnea E, Mizrahi JA. A generalized approach to the fluid dynamics of paniculate systems, Part 1. General correlation for fluidization and sedimentation in solid multi-particle systems. Chem Eng J. 1973;5:171-189.
26. Tory EM, Kamel MT, Chan Man Fong CF. Sedimentation is container-size dependent. Powder Technol. 1992;73:219-238.
27. Koglin B. Zum. mechanismus der Sinkgeschwindigkeitserhönhung in niedrig konzentrierten Suspension. In: 27 Vorträge des 1st Europäischen Symposiums 'Partikelmesstechnik' Nürnberg, 17-19 Sept. 1975, Dechema Monographien 1589-1615, 1976: vol. 79B:235-250.
28. Pickard DK, Tory EM. A Markov model for sedimentation. J Math Anal Appl. 1977;60:349-369.
29. Tory EM. Stochastic sedimentation and hydrodynamic diffusion. Chem Eng J. 2000;80:81-89.
30. Beenakker CWJ, Mazur P. On the Smoluchowski paradox in a sedimenting suspension. Phys Fluids. 1985;28:767-769.
31. MacKay GDM, Mason SG. Approach of a solid sphere to a rigid plane interface. J Colloid Sci. 1961; 16:632-635.
32. MacKay GDM, Suzuki M, Mason SG. Approach of a solid sphere to a rigid plane interface. Part 2. J Colloid Sci. 1963;18:103-104.
33. Brenner, H. The slow motion of a sphere through a viscous fluid towards a plane surface. Chem Eng Sci. 1962;17:242-251.
34. Ham JM, Homsy GM. Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions. Int J Multiphase Flow. 1988;14: 533-546.
35. Masliyah JH. Hindered settling in a multiple-species particle system. Chem Eng Sci. 1979;34:1166-1168.
36. Lockert MJ, Bassoon KS. Sedimentation theory of binary particle mixtures. Powder Technol. 1979;24:1-7.
37. Berres S, Bürger R, Karlsen KH, Tory EM. Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. SIAM J Appl Math. 2003;64:41-80.
38. Drew DA. Theory of multicomponent fluids. New York: Springer-Verlag; 1999.
39. Chung KL. A Course in Probability Theory. 2nd ed. New York: Academic Press; 1974.
40. Davis RH, Gecol H. Hindered settling function with no empirical parameters for polydisperse suspensions. AIChE J. 1994;40:570-575.
41. Patwardhan VS, Tien C, Sedimentation and fluidization in solid-liquid systems: A simple approach. AIChE J. 1985;31:146-149.
42. Smith TN. The sedimentation of particles having a dispersion of sizes. Trans Instn Chem Engrs. 1966;44:T143-T157.
43. Scott KJ, Mandersloot WGB. The mean particle size in hindered settling of multisized particles. Powder Technol. 1979;24:99-101.
44. Stroupe EP. Batch Sedimentation of Rigid Spheres in a Newtonian Fluid. Purdue University; 1962. MS Thesis.
45. Pfaffenberger RC, Patterson JH. Statistical methods for business and economics. Homewood: Richard D. Irwin; 1977.
46. Been K, Sills GC. Self-weight consolidation of soft soils: an experimental and theoretical study. Géotechnique. 1981;31:519-535.
47. Laso M. Stochastic dynamic approach to transport phenomena. AIChE J. 1994;40:1297-1311.
48. Bargił M, Tory EM. Stochastic dynamic solution of nonlinear differential equations for transport phenomena. AIChE J. 1996;42:889-891.
49. Nicolai H, Herzhaft B, Hinch EJ, Oger L, Guazzelli E. Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres. Phys Fluids. 1995;7:12-23.
50. Kamel MT, Tory EM, Jodrey WS. The distribution of kth nearest neighbours and its application to cluster settling in dispersions of equal spheres. Powder Technol. 1979;24:19-34.
51. Mucha PJ, Tee S-Y, Weitz DA, Shraiman BI. Brenner, MP. A model for velocity fluctuations in sedimentation. J Fluid Mech. 2004;501:71-104.
52. Verhoeven J. Prediction of batch settling behaviour. B. Chem. Eng. McMaster University, April 1963. Thesis.
53. Nicolai H, Peysson Y, Guazzelli E. Velocity fluctuations of a heavy sphere falling through a sedimenting suspension. Phys Fluids. 1996;8: 855-862.
54. Berres S, Bürger R, Tory EM. Applications of polydisperse sedimentation models. Chem Eng J; to appear.
55. Berres S, Bürger R, Tory EM. On mathematical models and numerical simulation of the fluidization of polydisperse suspensions. Appl Math Modelling. 2005;29:159-193.