Flocculation modelling: A review

Water Research

Volumn 33, Issue 7, 1999, Pages 1579-1592

  Thomas, D N ^a   Judd, S J ^a   Fawcett, N ^b  

^a CRANFIELD UNIVERSITY   (United Kingdom)

^b Yorkshire Water   (United Kingdom)

Author keywords

Coagulation; Flocculation; Fractal; Modelling; Particles

Indexed keywords

ELECTROSTATICS; LAMINAR FLOW; MATHEMATICAL MODELS; MIXING; PARTICLES (PARTICULATE MATTER); SHEAR FLOW; SURFACE CHEMISTRY; VAN DER WAALS FORCES;

CAMP NUMBER; PARTICLE DYNAMICS;

FLOCCULATION;

FLOCCULATION; MODELING;

FLOCCULATION; MATHEMATICAL MODEL; PARTICLE SIZE; PRIORITY JOURNAL; REVIEW; WASTE WATER MANAGEMENT;

EID: 0033059685     PISSN: 00431354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0043-1354(98)00392-3     Document Type: Review

References (63)

1. Adler P. M. (1981a) Streamlines in and around porous particles. J. Coll. Interface Sci. 81, 531-535.
2. Adler P. M. (1981b) Heterocoagulation in shear flow. J. Coll. Interface Sci 83, 106-115.
3. Argaman Y. and Kaufman W. J. (1970) Turbulence and flocculation. J. Sanit. Eng. Div. ASCE 96, 223.
4. Bhaskar G. V., Campenella O. H. and Munro P. A. (1993) Effect of agitation on the coagulation time of mineral acid casein curd: application of Smoluchowski's othokinetic aggregation theory. Chem. Eng. Sci. 48, 4075-4080.
5. Brinkman H. C. (1947) A calculation of the viscous forces extended by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27-34.
6. Calabrese R. V., Wang M. H., Zhang N. and Gentry J. W. (1992) Simulatio and analysis of particle breakage phenomena. Trans. IChemE. 70(A), 189-191.
7. Camp T. R. and Stein P. C. (1943) Velocity gradients and internal work in fluid motion. J. Boston Soc. Civ. Eng. 30, 219-237.
8. Casson L. W. and Lawler D. F. (1990) Flocculation in turbulent flow: measurement and modelling of particle size distributions. J. Am. Water Works Assoc. 63(8), 54-68.
9. Chellam S. and Wiesner M. R. (1993) Fluid mechanics and fractal aggregates. Water Res. 27, 1493-1496.
10. Costas M. E., Moreau M. and Vicente L. (1995) Some analytical and numerical solutions for colloidal aggregation with fragmentation. J. Phys. A Math. Gen. 28, 2981-2994.
11. Delichatsios M. A. and Probstein R. F. (1974) Coagulation in turbulent flow: theory and experiment. J. Colloid Interface Sci. 51, 394-405.
12. Deryaguin B. V. and Landau L. D. (1941) A theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. USSR 14, 633.
13. Dharmappa H. B., Vigneswaran S., Verink J. and Fujiwara O. (1994) Water-treatment-system design for turbidity removal. I. Simulation. J. Env. Eng. 120, 900-914.
14. Elminyawi I. M., Gangopadhyay S. and Sorensen C. M. (1991) Numerical solutions to the Smoluchowski aggregation-fragmentation equation. J. Coll. Interface Sci. 144, 315-323.
15. Fair G. M. and Gemmell R. S. (1964) A mathematical model of coagulation. J. Coll. Sci. 19, 360-372.
16. Family F., Meakin P. and Deutch J. M. (1986) Kinetics of coagulation with fragmentation: scaling behaviour and fluctuations. Phys. Rev. Lett. 57, 727-730.
17. Fuchs N. (1934) Über die Stabilität und Aufladung der Aerosole. Z. Phys. 89, 736-743.
18. Gregory J. (1981) Flocculation in laminar tube flow. Chem. Eng. Sci. 36, 1789-1794.
19. Han M. Y. and Lawler D. F. (1991) Interactions of two settling spheres: settling rates and collision efficiencies. J. Hydraul. Eng. ASCE. 117, 1269-1289.
20. Han M. Y. and Lawler D. F. (1992) The (relative) insignificance of G in flocculation. J. Am. Water Works Assoc. 84, 79-91.
21. Han M. Y. (1989) Mathematical Modelling of Heterogeneous Flocculant Sedimentation. Ph.D. thesis, University of Texas, Austin.
22. Harris H. S., Kaufman W. J. and Krone R. B. (1966) Orthokinetic flocculation in water treatment. J. Sanit. Eng. Div. Proc. ASCE 92(SA6), 95-111.
23. Hidy G. M. and Lilly D. K. (1965) Solutions of the equations for the kinetics of coagulation. J. Coll. Sci. 20, 867-874.
24. Hudson H. E. (1965) Physical aspects of flocculation. J. Am. Water Works Assoc. 57, 885-892.
25. Jiang Q. and Logan B. E. (1996) Fractal dimension of aggregates from shear devices. J. Am. Water Works Assoc. 60, 1040-1046.
26. Kihira H. and Matijevic E. (1992) An assessment of heterocoagulation theories. Adv. Coll.Interface Sci. 42, 1-31.
27. Koh P. L. T., Andrews J. R.G. and Uhlherr P. H. T. (1986) Floe-size distribution of Scheelite treated by shear-flocculation. Int. J. Miner. Process. 17, 45-65.
28. Kramer T. A. and Clark M. M. (1997) Influence of strain-rate on coagulation kinetics. J. Environ. Eng. ASCE 123, 444-452.
29. Kusters K. A., Wijers J. G. and Thoenes D. (1991) Numerical particle tracking in a turbine agitated vessel. In Proceedings of the 7th European Conference on Mixing, Vol. II, Brugge, Belgium, pp. 429-441.
30. Kusters K. A., Wijers J. G. and Thoenes D. (1997) Aggregation kinetics of small particles in agitated vessels. Chem. Eng. Sci. 52, 107-121.
31. Lai F. S., Friedlander S. K., Pich J. and Hidy G. M. (1972) The self-preserving particle size distribution for Brownian coagulation in the free-molecular regime. J. Coll. Interface Sci. 36, 395-405.
32. Lawler D. F. (1993) Physical aspects of flocculation: from microscale to macroscale. Water Res. 27, 164-180.
33. Li D.-H. and Ganczarczyk J. (1989) Fractal geometry of particle aggregates generated in water and wastewater treatment processes. Environ. Sci. Technol. 23, 1385-1389.
34. Li X. and Logan B. E. (1997a) Collision frequencies of fractal aggregates with small particles by differential sedimentation. Environ. Sci. Technol. 31, 1229-1236.
35. Li X. and Logan B. E. (1997b) Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid. Environ. Sci. Technol 31, 1237-1242.
36. Meakin P. and Ernst M. H. (1988) Scaling in aggregation with breakup simulations and mean-field theory. Phys. Rev. Lett. 60, 2503-2506.
37. Mühle K. and Domasch K. (1990) Floe Strength in Bridging Flocculation. In Chemical Water and Wastewater Treatment, ed. H. H. Hahn and R. Klute. Springer-Verley, Berlin.
38. Mühle K (1993) In Coagulation and Flocculation, ed. B. Dobias. Marcel Dekker, New York, pp. 355-390.
39. O'Melia C. R. (1972) Coagulation and flocculation. In Physicochemical Processes for Water Quality Control, ed. W. J., Weber Jr. Wiley Interscience, New York.
40. Parker D. S., Kaufman W. J. and Jenkins D. (1972) Floe break-up in turbulent flocculation processes.. J. Sanit. Eng. Pro. Div. Am. Soc. Civ. Eng. 98 (SA1), 79-99.
41. Pulvermacher B. and Ruckenstein E. (1974) Similarity solutions of population balances. J. Coll. Interface Sci. 46, 428-436.
42. Peng S. J. and Williams R. A. (1993) Control and optimisation of mineral flocculation and transport porcesses using on-line particle size analysis. Miner. Eng. 6, 133-153.
43. Rajagopalan R. (1993) Stability of colloidal dispersions: a thermodynamic approach. Water Sci. Tech. 27, 117-129.
44. Ritchie A. R. (1955) Certain aspects of flocculation as applied to sewage purification. Ph.D. thesis, University of London.
45. Rosen J. M. (1984) A statistical description of coagulation. J. Coll. Interface Sci. 99, 9-19.
46. Schumann T. E. W. (1940) Theoretical aspects of the size distribution of fog particles. Q. J. R. Meteorolog. Soc. 66, 195-207.
47. Smoczynski L. and Wardzynska R. (1996) Study on macroscopic aggregation of silica suspensions and sewage. J. Coll. Interface Sci. 183, 309-314.
48. Smoluchowski M. (1917) Versuch einer Mathematischen Theorie der Koagulationskinetik Kolloider Lösungen. Z. Phys. Chem. 92, 129-168.
49. Sorensen C. M., Zhang H. X. and Taylor T. W. (1987) Cluster-size evolution in a coagulation-fragmentation system. Phys. Rev. Lett. 59, 363-366.
50. Spicer P. T. and Pratsinis S. E. (1996a) Shear-induced flocculation: the evolution of floe structure and the shape of the size distribution at steady-state. Water Res. 30, 1049-1056.
51. Spicer P. T. and Pratsinis S. E. (1996b) Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 42, 1612-1620.
52. Stratton D. M., Gans J. and Williams E. (1994) Coagulation algorithms with size binning. J. Comput. Phys. 112, 364-369.
53. Swift D. L. and Friedlander S. K. (1964) The coagulation of hydosols by Brownian motion and laminar shear flow. J. Coll. Sci. 19, 621.
54. Tambo N. (1965) A fundamental investigation of floe growth (1). J. Jpn. Water Works Assoc. 372, 10-19.
55. Tambo N. (1991) Criteria of flocculator design. J. Water SRT Aqua. 40, 97-102.
56. Tambo N. and Hozumi H. (1979) Physical Characteristics of Flocs-II. Strength of Floe. Water Res. 13, 421.
57. Tambo N. and Ogasawara M. (1970) Pipe flocculator studies. J. Jpn. Water Works Assoc. 426, 29-39.
58. Tambo N. and Watanabe Y. (1979) Physical characteristics of floes. I. The density function and aluminium floe. Water Res. 13, 409-419.
59. Veerapaneni S. and Wiesner M. R. (1996) Hydrodynamics of fractal aggregates with radially varying permeability. J. Coll.Interface Sci. 177, 45-57.
60. Verwey E. J. W. and Overbeek J. Th. G. (1948) Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam.
61. Wiesner M. R. (1992) Kinetics of aggregate formation in rapid mix. Water Res. 26(3), 379-387.
62. Wu R. M. and Lee D. J. (1998) Hydrodynamic drag force exerted on a moving floe and its implication to free-settling tests. Water Res. 32, 760-7681.
63. Yeung A. K. C. and Pelton R. (1996) Micromechanics: a new approach to studying the strength and break-up of floes. J. Coll. Interface Sci. 184, 579-585.