Zhongfan Zhu
College of Water Sciences, Beijing Normal University, Beijing, China.
DOI: 10.4236/gep.2014.25003   PDF    HTML     7,260 Downloads   9,330 Views   Citations

Abstract

Investigation on flocculation phenomenon of cohesive fine-grained sediment has been a important part of sediment dynamics. During all of three dynamical factors (i.e., Brownian motion, flow shear and differential settling) that have been verified to play important roles in promoting flocculation of cohesive sediment, the influence of flow shear on sediment flocculation has been paid great attention by many researchers (this flocculation pattern has been termed as “orthokinetic flocculation” in most of published literatures). Among many researches regarding orthokinetic flocculation, the dynamical equation developed by Smoluchowski in 1917 (we called it as Smoluchowski equation hereafter) has been widely adopted as an origin and basement for theoretically analyzing sediment flocculation under a shear flow. Meanwhile, many researchers have also pointed out the deficiencies of Smoluchowski equation (this is because the derivation of Smoluchowski equation was based on six different assumptions), and correspondingly have amended this equation from different aspects. In this paper, we attempt to summarize these results, hopefully providing the theoretical research of sediment orthokinetic flocculation with some references.

Keywords

Sediment, Orthokinetic Flocculation, Review

Share and Cite:

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bache, D. H. (2004). Floc Rupture and Turbulence: A Framework for Analysis. Chemical Engineering Science, 59, 2521- 2534. http://dx.doi.org/10.1016/j.ces.2004.01.055 [Google Scholar] [CrossRef]
[2]	Bouyer, D., & Line, A. (2004). Experimental Analysis of Floc Size Distribution under Different Hydrodynamics in a Mixing Tank. AIChE Journal, 50, 2064-2081. http://dx.doi.org/10.1002/aic.10242 [Google Scholar] [CrossRef]
[3]	Burban, P. Y., Lick, W, & Lick, J. (1989). The Flocculation of Fine-Grained Sediments in Estuarine Waters. Journal of Geophysical Research, 94, 8323-8330. http://dx.doi.org/10.1029/JC094iC06p08323 [Google Scholar] [CrossRef]
[4]	Camp, T. R., & Stein, P. C. (1943). Velocity Gradients and Internal Work in Fluid Motion. Journal of Boston Society of Civil Engineering, 30, 219-237.
[5]	Chang, Q., Fu, J., & Li, Z.(1992). The Principal of Flocculation. Lanzhou: Lanzhou University Press. (In Chinese)
[6]	Chen, H., Shao, M., & Li, Z. (2001). Preliminary Study on the Effect of NaCl on Fine Sediment Flocculation and Settling in Still Water. Acta Pedologica Sinica, 1, 131-134. (In Chinese)
[7]	Coufort, C., Bouyer, D., & Line, A. (2005). Flocculation Related to Local Hydrodynamics in a Taylor-Couette Reactor and in a Jar. Chemical Engineering Science, 60, 2179-2192. http://dx.doi.org/10.1016/j.ces.2004.10.038 [Google Scholar] [CrossRef]
[8]	Coufort, C., Bouyer, D., Line, A., & Haut, B. (2007). Modelling of Flocculation Using a Population Balance Equation. Chemical Engineering and Processing, 46, 1264-1273. http://dx.doi.org/10.1016/j.cep.2006.10.012 [Google Scholar] [CrossRef]
[9]	Coufort, C., Dumas, C., Bouyer, D., & Line, A. (2008). Analysis of Floc Size Distribution in a Mixing Tank. Chemical Engineering and Processing: Process Intensification, 47, 287-294. http://dx.doi.org/10.1016/j.cep.2007.01.009 [Google Scholar] [CrossRef]
[10]	Delichatsios, M. A., & Probstein, R. F. (1974). Coagulation in Turbulent Flow: Theory and Experiment. Journal of Colloid and Interface Science, 51, 394-405. http://dx.doi.org/10.1016/0021-9797(75)90135-6 [Google Scholar] [CrossRef]
[11]	Elimelech, M., & O’Melia, C. R. (1990). Effect of Partilce Size on Collision Efficiency in the Deposition of Brownian Particles with Electrostaic Energy Barriers. Langmuir, 6, 1153-1163. http://dx.doi.org/10.1021/la00096a023 [Google Scholar] [CrossRef]
[12]	Feder, J. (1988). Fractals. New York: Plenum. http://dx.doi.org/10.1007/978-1-4899-2124-6 [Google Scholar] [CrossRef]
[13]	Guan, X., & Chen, Y. (1995). Experimental Study on Dynamic Formula of Sand Coagulation Sinking in Stationary Water in Yangtze Estuary. Ocean Engineering, 1, 46-50. (In Chinese)
[14]	Guan, X., Chen, Y., & Du, X. (1996). Experimental Study on Mechanism of Flocculation in Yangtze Estuary. Journal of Hydraulic Engineering, 6, 70-80. (In Chinese)
[15]	Han, B., Akeprathumchai, S., Wickramasinghe, S. R., & Qian, S. (2003). Flocculation of Piological Cells: Experiment vs Theory. AIChE Journal, 49, 1687-1701. http://dx.doi.org/10.1002/aic.690490709 [Google Scholar] [CrossRef]
[16]	Han, M. Y., & Lawler, D. F. (1992). The Relative Insignificance of G in Flocculation. American Water Works Association Journal, 84, 79-91.
[17]	Higashitani, K., & Iimura, K. (1998). Two-Dimensional Simulation of Breakup Process of Aggregates in Shear and Elongational Flows. Journal of Colloid and Interface Science, 204, 320-327. http://dx.doi.org/10.1006/jcis.1998.5561 [Google Scholar] [CrossRef] [PubMed]
[18]	Jiang, G., & Zhang, Z. (1995). Flocculation Deposition of Fin-Grained Sediment and the Concentration of Cation in Yangtze Estuary. Acta Oceanologica Sinica, 17, 76-82. (In Chinese)
[19]	Jiang, G., Yao, Y., & Tang, Z. (2002). The Analysis of Factors of Flocculation of Fine-Grained Sediment in Yangtze Estuary. Acta Oceanologica Sinica, 24, 51-56. (In Chinese)
[20]	Jin, D., Wu, H., & Shi, F. (1998). Analysis of Sediment Flocculation. Water Conservancy and Hydropower in Northeast China, 11, 25-37. (in Chinese)
[21]	Jin, Y., Wang, Y., & Li, Y. (2002). Experimental Study on Flocculation of Cohesive Fine Grain Sediment in Yangtze River Estuary. Journal of Hohai University (Natural Sciences), 30, 61-63. (In Chinese)
[22]	Kim, J., & Kramer, T. A. (2007). Adjustable Discretized Population Balance Equations: Numerical Simulation and Parameters Estimation for Fractal Aggregation and Breakup. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 27, 173-188. http://dx.doi.org/10.1016/j.colsurfa.2006.06.020 [Google Scholar] [CrossRef]
[23]	Kramer, T. A. (1997). The Modeling of Coagulation Kinetics in Complex Laminar Flow. Ph.D. Thesis, Illinois: University of Illinois at Urbana-Champaign.
[24]	Kramer, T. A., & Clark, M. A. (1997). Influence of Strain Rate on Coagulation Kinetics. Journal of Environmental Engineering, 123, 444-452. http://dx.doi.org/10.1061/(ASCE)0733-9372(1997)123:5(444) [Google Scholar] [CrossRef]
[25]	Kramer, T. A., & Clark, M. M. (1999). Incorporation of Aggregate Breakup in the Simulation of Orthokinetic Coagulation. Journal of Colloid and Interface Science, 216, 116-126. http://dx.doi.org/10.1006/jcis.1999.6305 [Google Scholar] [CrossRef] [PubMed]
[26]	Kusters, K. A., Wijers, J. G., & Thoenes, D. (1997). Aggregation Kinetics of Small Particles in Agitated Vessels. Chemical Engineering Science, 5, 107-121. http://dx.doi.org/10.1016/S0009-2509(96)00375-2 [Google Scholar] [CrossRef]
[27]	Lartiges, B. S., Deneux-Mustin, S., Villemin, G., Mustin, C., Barrès, O., Chamerois, M., et al. (2001). Composition Structure and Size Distribution of Suspended Particulates from Rhine River. Water Research, 135, 808-816. http://dx.doi.org/10.1016/S0043-1354(00)00293-1 [Google Scholar] [CrossRef]
[28]	Li, D., Tan, W., & Huang, M. (2004). Study on Fractal Properties of Flocs. Water and Wastewater Engineering, 30, 5-9. (In Chinese)
[29]	Li, X. Y., Passow, U., & Logan, B. E. (1998). Fractal Dimensions of Small (15-200 ?m) Particles in Eastern Pacific Coastal Waters. Deep-Sea Research, 45, 115-131. http://dx.doi.org/10.1016/S0967-0637(97)00058-7 [Google Scholar] [CrossRef]
[30]	Li, X., & Logan, B. (1997). Collision Frequencies between Fractal Aggregates and Small Particles in a Turbulently Sheared Fluid. Environmental Science and Technology, 31, 1237-1242. http://dx.doi.org/10.1021/es960772o [Google Scholar] [CrossRef]
[31]	Li, X., Zhang, J., & Joseph Lee, H. W. (2004). Modelling Particle Size Distribution Dynamics in Marine Waters. Water Research, 38, 1305-1317. http://dx.doi.org/10.1016/j.watres.2003.11.010 [Google Scholar] [CrossRef] [PubMed]
[32]	Liu, Y. (1994). The Influence of Temperature on Setting Velocity and Siltation of Cohesive Sediment. Express Water Resources & Hydropower Information, 13, 21-24. (In Chinese)
[33]	Lu, S., Ding, Y., & Guo, J. (1998). Kinetics of Fine Particle Aggregation in Turbulence. Advances in Colloid and Interface Science, 78, 197-235. http://dx.doi.org/10.1016/S0001-8686(98)00062-1 [Google Scholar] [CrossRef]
[34]	Ma, K. S., & Pierre, A. C. (1995). Colloidal Behavior of Montmorillonite in the Presence of Fe3+ Ions. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 155, 359-372. http://dx.doi.org/10.1016/S0927-7757(99)00032-1 [Google Scholar] [CrossRef]
[35]	Maggi, F., Mietta, F., & Winterwerp, J. C. (2007). Effect of Variable Fractal Dimension on the Floc Size Distribution of Suspended Cohesive Sediment. Journal of Hydrology, 343, 43-55. http://dx.doi.org/10.1016/j.jhydrol.2007.05.035 [Google Scholar] [CrossRef]
[36]	Meakin, P. (1988). Fractal Aggregation. Advances in the Colloid Interface, 28, 249-331. http://dx.doi.org/10.1016/0001-8686(87)80016-7 [Google Scholar] [CrossRef] [PubMed]
[37]	Muhle, E. K. (1993). Floc Stability in Laminar and Turbulent Floc. In B. Dobias (Ed.), Coagulation and Flocculation (pp. 355-390). New York: Marcel Dekker.
[38]	Muhle, E. K., & Domasch, K. (1990). Floc Strength in Bridging Flocculation. In H. H. Hahn, & R. Klute (Eds.), Chemical water and Wastewater Treatment (pp.106-115). Heidelberg: Springer-Verlag Berlin Heidelberg. http://dx.doi.org/10.1007/978-3-642-76093-8_8 [Google Scholar] [CrossRef]
[39]	Pedocchi, F., & Piedra-Cueva, I. (2005). Camp and Stein’s Velocity Gradient Formalization. Journal of Environmental Engineering, 131, 1369-1376. http://dx.doi.org/10.1061/(ASCE)0733-9372(2005)131:10(1369) [Google Scholar] [CrossRef]
[40]	Prat, O. P., & Ducoste, J. J. (2006). Modeling Spa-tial Distribution of Floc Size in Turbulent Processes Using the Quadrature Method of Moment and Computational Fluid Dynamics. Chemical Engineering Science, 61, 75-86. http://dx.doi.org/10.1016/j.ces.2004.11.070 [Google Scholar] [CrossRef]
[41]	Runkana, V. (2003). Mathematical modeling of flocculation and dispersion of colloidal suspensions. Ph.D. Thesis, New York: Columbia University.
[42]	Saffman, P. G., & Turner, J. S. (1956). On the Collisions of Drops in Turbulent Clouds. Journal of Fluid Mechanics, 1, 16- 30. http://dx.doi.org/10.1017/S0022112056000020 [Google Scholar] [CrossRef]
[43]	Selomulya, C., Bushell, G., Amal, R., & Waite, T. D. (2003). Under-standing the Role of Restructuring in Flocculation: The Application of a Population Balance Model. Chemical Engineering Science, 58, 327-338. http://dx.doi.org/10.1016/S0009-2509(02)00523-7 [Google Scholar] [CrossRef]
[44]	Shi, Z. (2000). Fine Sediment Processes in Yangtze River Estuary. Journal of Sediment Research, 6, 72-80. (in Chinese)
[45]	Smoluchowski, M. V. (1917). Versuch Einer Mathematischen Theorie der Koagulationskinetik kolloider Losungen. Zeitschrift f. Physik. Chemie. XCII, 92, 129-168.
[46]	Son, M., & Hsu, T. J. (2009). The Effect of Variable Yield Strength and Variable Fractal Dimension on Flocculation of Cohesive Sediment. Water Research, 43, 3582-3592. http://dx.doi.org/10.1016/j.watres.2009.05.016 [Google Scholar] [CrossRef] [PubMed]
[47]	Thill, A., Moustier, S., Aziz, J., Wiesner, M. R., & Bottero, J. Y. (2001). Flocs Restructuring during Aggregation: Experimental Evidence and Numerical Simulation. Journal of Colloid and Interface Science, 243, 171-182. http://dx.doi.org/10.1006/jcis.2001.7801 [Google Scholar] [CrossRef]
[48]	Thomas, D. N., Judd, S. J., & Fawcett, N. (1999). Flocculation Modeling: A Review. Water Research, 33, 1579-1592. http://dx.doi.org/10.1016/S0043-1354(98)00392-3 [Google Scholar] [CrossRef]
[49]	van de Ven, T. G. M., & Maso, S. G. (1977). The Microrheology of Colloidal Dispersions. VII. Orthokinetic Doublet Formation of Spheres. Colloid and Polymer Science, 255, 468-479. http://dx.doi.org/10.1007/BF01536463 [Google Scholar] [CrossRef]
[50]	Veerapaneni, S., & Wiesner, M. R. (1996). Hydrodynamics of Fractal Aggregates with Radially Varying Permeability. Journal of Colloid and Interface Science, 177, 45-57. http://dx.doi.org/10.1006/jcis.1996.0005 [Google Scholar] [CrossRef] [PubMed]
[51]	Wang, L., Wexler, A. S., & Zhou, Y. (1998). Statistical Mechanical Descriptions of Turbulent Coagulation. Physic of Fluids, 10, 2647-2651. http://dx.doi.org/10.1063/1.869777 [Google Scholar] [CrossRef]
[52]	Xia, Z. (1992). Modern Hydraulics (Volume 3). Beijing: High Education Press. (In Chinese)
[53]	Yang, M., & Qian, N. (1986). The Effect of Turbulence on the Flocculation Structure of the Slurry of Fine-Grained Sediment. Journal of Hydraulic Engineering, 8, 21-30. (In Chinese)
[54]	Yang, T., Xiong X., Zhan X., & Yang, M. (2003). On Flocculation of Cohesive Fine Sediment. Hydro-Science and Engineering, 2, 65-77. (In Chinese)
[55]	Zhang, J., & Li, X. (2003). Modelling Particle-Size Distribution Dynamics in a Flooculation System. AIChE Journal, 49, 1870-1882. http://dx.doi.org/10.1002/aic.690490723 [Google Scholar] [CrossRef]
[56]	Zhang, Z. (1996). Studies on Basic Characteristics of Fine Sediment in Yangtze Estuary. Journal of Sediment Research, 1, 67-73. (In Chinese)