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Applied Scientific Research

, Volume 59, Issue 2–3, pp 255–268 | Cite as

Modelling the Aggregation and Break-up of Fractal Aggregates in a Shear Flow

  • Teresa Serra
  • Xavier Casamitjana
Article

Abstract

A population balance model has been proposed to describe simultaneous coagulation and fragmentation of fractal aggregates during shear-flocculation induced by means of a Couette-flow system. Given enough time, a floc-size distribution achieves the steady state, which reflects the balance between coagulation and fragmentation forces. Experimental results obtained recently show that higher shear rate values shift the steady state to smaller aggregate sizes. Also, for a fixed value of the shear rate, when the volume fraction of the particles increases, the steady state size increases if the flow is laminar, and decreases if the flow is turbulent. In order to model the fragmentation of the aggregates, a power dependence between the breakage rate coefficient and the shear rate has been proposed. The model is adjusted by using two different parameters: the effective probability of success for collisions αeff, and the break up coefficient for shear fragmentation, B′. The dependence of these two parameters on the shear rate and the volume fraction of the particles is discussed.

coagulation fragmentation shear rate concentration Couette latex 

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References

  1. 1.
    Boadway, J.D., Dynamics of growth and breakage of alum floc in presence of fluid shear. J. Env. Engrg. Div. Proc. ASCE 104(EE5) (1978) 901–915.Google Scholar
  2. 2.
    Burban, P.Y., Lick, W. and Lick, J., The flocculation of fine-grained sediments in estuarine waters. J. Geophys. Res. 94(C6) (1989) 8323–8330.Google Scholar
  3. 3.
    Burban, P.Y., Xu, Y.J., McNeil, J. and Lick, W., Settling speeds of flocs in freshwater and seawater. J. Geophysical Res. 95(C10) (1990) 18213–18220.Google Scholar
  4. 4.
    Casamitjana, X. and Schladow, G., Vertical distribution of particles in stratified lake. J. Environ. Engrg. 119(3) (1993) 443–462.Google Scholar
  5. 5.
    Jiang, Q. and Logan, B.E., Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 25(12) (1991) 2031–2037.Google Scholar
  6. 6.
    Kapur, P.C., Self-preserving size spectra of comminuted particles. Chem. Engrg. Sci. 27 (1972) 425–436.Google Scholar
  7. 7.
    Krishnappan, B.G., Madsen, N., Stephens, R. and Ongley, E.D., A field instrument for size distribution of flocculated sediment. Report of the National Water Research Institute, Canada, Berlington, Ontario L7R 4A6 (1996).Google Scholar
  8. 8.
    Lick, W. and Lick, J., Aggregation and disaggregation of fine-grained lake sediments. J. Great. Lakes Res. 14(4) (1988) 514–523.Google Scholar
  9. 9.
    Kiorboe, T., Andersen, K.P. and Dam, H.G., Coagulation efficiency and aggregate formation in marine phytoplankton. Marine Biology 107 (1990) 235–245.Google Scholar
  10. 10.
    Oles, V., Shear-induced aggregation and break up of polystyrene latex particles. J. Colloid Interface Sci. 154 (1992) 351–358.Google Scholar
  11. 11.
    Pandya, J.D. and Spielman, L.A., Floc breakage in agitated suspensions: Effect of agitation rate. Chem. Engrg. Sci. 38(12) (1983) 1893–1992.Google Scholar
  12. 12.
    Serra, T. and Casamitjana, X., Structure of the aggregates during the process of aggregation and break-up under a shear flow. J. Colloid Interface Sci. (in revision).Google Scholar
  13. 13.
    Serra, T., Colomer, J. and Casamitjana, X., Aggregation and break up of particles in a shear flow. J. Colloid Interface Sci. 187 (1997) 466–473.Google Scholar
  14. 14.
    Smoluchowski, M., Versuch einer mathematischen Theorie der Koagulations Kinetis kolloider Lösungen. Z. Physik. Chem. 92 (1917) 129–168.Google Scholar
  15. 15.
    Spicer, P.T. and Pratsinis, S.T., Coagulation and fragmentation: Universal steady-state particlesize distribution. AIChE 42(6) (1996) 1612–1620.Google Scholar
  16. 16.
    Tsai, C.H., Iacobellis, S. and Lick, W., Flocculation of fine-grained lake sediments due to a uniform shear stress. J. Great Lakes Res. 13(2) (1987) 135–146.Google Scholar
  17. 17.
    van Duurens, F.A., Defined velocity gradient model flocculator. J. Sanitary Engry. Div. 94(SA4) (1968) 671–682.Google Scholar
  18. 18.
    Wiesner, M.G., Wang, Y. and Zheng, L., Fallout of volcanic ash to the deep South China Sea induced by the 1991 eruption of Mount Pinatubo (Philippines). Geology 23(10) (1995) 885–888.Google Scholar
  19. 19.
    Williams, M.M.R., An exact solution of the fragmentation equation. Aerosol Sci. Tech. 12 (1990), 538–550.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Teresa Serra
    • 1
  • Xavier Casamitjana
    • 1
  1. 1.Department of Environmental SciencesUniversity of Girona, Campus MontiliviGironaSpain

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