[1] Oh, C. and Sorensen, C. M. (1997). The effect of overlap between monomers on the determination of fractal cluster morphology. J. Colloid Interface Sci., 193, 17-25.

[2] Brasil, A. M., Farias, T. L., Carvalho, M. G. and Koylu, U. O. (2001). Numerical characterization of the morphology of aggregated particles. Aerosol Sci., 32, 489-508.

[3] Bushell, G. (1998). PhD thesis, The University of New South Wales.

[4] Lips, A. and Duckworth, R. M. (1988). Combined study of coagulation kinetics and close-range aggregate structure. J. Chem. Soc. Faraday Trans. I, 84, 1223-1242.

[5] Thouy, R., and Jullien, R. (1996). Structure factors for fractal aggregates built off-lattice with tunable fractal dimension. J. Phys. I France, 6, 1365-1376.

[6] Meakin, P. (1988). Fractal aggregates. Adv. Colloid Interface Sci., 28, 249-331.

[7] Gregory, J. (1997). The density of particle aggregates. Water Sci. Technol., 36, 1-13.

[8] Bushell, G., Yan, Y.-D., Woodfield, D., Raper, J. and Amal, R. (2002). On techniques for the measurement of the mass fractal dimension of aggregates. Adv. Colloid Interface Sci., 95, 1-50.

[9] Dimon, P. Sinha, S. K., Weitz, D. A., Safinya, C. R., Smith, G. S., Varady, W. A. and Lindsay, H. M. (1986). Structure of aggregated gold colloids. Phys. Rev. Lett., 57, 595-598.

[10] Lattuada, M., Wu, H. and Morbidelli, M. (2003). Hydrodynamic radius of fractal clusters. J. Colloid Interface Sci., 268, 96-105.

[11] Meakin, P., Donn, B., and Mulholland, G. W. (1989). Collisions between point masses and fractal aggregates. Langmuir, 5, 510-518.

[12] Hermawan, M., Bushell, G., Bickert, G. and Amal, R. (2004). Characterisation of short range structure of silica aggregates - implication to sediment compaction. International Journal of Mineral Processing, 73, 65-81.

[13] Lin, M. Y., Klein, R., Lindsay, H. M., Weitz, D. A., Ball, R. C., and Meakin, P. (1990). The structure of fractal colloidal aggregates of finite extent. J. Colloid Interface Sci., 137, 263-280.

[14] Bushell, G. C., and Amal, R. (1998). Fractal aggregates of polydisperse particles. J. Colloid Interface Sci., 205, 459-469.

[15] Bower, C., Washington, C., and Purewal, T. S. (1995). A combined rheometer and image analyser for the characterization of suspensions and aggregates in a shear field. Measure. Sci. Technol., 6, 196-201.

[16] Chakraborti, R. K., Atkinson, J. F., and Van Benschoten, J. E. (2000). Characterization of alum floc by image analysis. Environ. Sci. Technol., 34, 3969-3976.

[17] Boukari, H., Long, G. G. and Harris, M. T. (2000). Polydispersity during the formation and growth of the Stober silica particles from small-angle X-ray scattering measurements. J. Colloid Interface Sci., 229, 129-139.

[18] Koylu, U. O., Xing, Y. and Rosner, D. E. (1995). Fractal morphology of combustion-generated aggregates using angular light scattering and electron microscope images. Langmuir, 11, 4848-4854.

[19] Sorensen, C. M., Kim, W., Fry, D., Shi, D. and Chakraborti, A. (2003). Observation of soot superaggregates with a fractal dimension of 2.6 in laminar acetylene/air diffusion flames. Langmuir, 19, 7560-7563.

[20] Oles, V. (1992). Shear-induced aggregation and breakup of polystyrene latex particles. J. Colloid Interface Sci., 154, 351-358.

[21] Spicer, P. T., Pratsinis, S. E., Raper, J., Amal, R., Bushell, G. and Meesters, G. (1998). Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol., 97, 26-34.

[22] Kusters, K. A., Wijers, J. G. andThoenes, D. (1997). Aggregation kinetics of small particles in agitated vessels. Chem. Eng. Sci., 52, 107-121.

[23] Johnson, C. P., Li, X. Y. and Logan, B. E. (1996). Settling velocities of fractal aggregates. Environ. Sci. Technol., 30, 1911-1918.

[24] Thill, A., Veerapaneni, S., Simon, B., Wiesner, M., Bottero, J. Y. and Snidaro, D. (1998). Determination of structure of aggregates by confocal scanning laser microscopy. J. Colloid Interface Sci., 204, 357-362.

[25] Guinier, A. and Fournet, G. (1955). Small Angle Scattering ofX-Rays, John Wiley & Sons, Ltd, New York.

[26] Sorensen, C. M. (2001). Light scattering by fractal aggregates: a review. Aerosol Sci. Technol., 35, 648-687.

[27] Hasmy, A., Vacher, R. and Jullien, R. (1994). Small-angle scattering by fractal aggregates -a numerical investigation of the crossover between the fractal regime and the Porod regime. Phys. Rev. B, 50, 1305-1308.

[28] Cai, J., Lu, N. and Sorensen, C. M. (1995). Analysis of fractal cluster morphology parameters: structural coefficient and density autocorrelation function cutoff. J. Colloid Interface Sci., 171, 470-473.

[29] Freltoft, T., Kjems, J. K. and Sinha, S. K. (1986). Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering. Phys. Rev. B, 33, 269-275.

[30] Jullien, R. (1992). From Guinier to fractals. J. Phys. I, 2, 759-770.

[31] Mountain, R. D. and Mulholland, G. W. (1988). Light-scattering from simulated smoke agglomerates. Langmuir, 4, 1321-1326.

[32] Hurd, A. J. and Flower, W. L. (1988). In situ growth and structure of fractal silica aggregates in a flame. J. Colloid Interface Sci., 122, 178-192.

[33] Zeng, Y. W. and Meriani, S. (1994). Scaling functions for the finite-size effect in fractal aggregates. J. Appl. Crystallogr., 27, 782-790.

[34] Sorensen, C. M., Lu, N. and Cai, J. (1995). Fractal cluster size distribution measurement using static light scattering. J. Colloid Interface Sci., 174, 456-460.

[35] Sorensen, C. M., Cai, J. and Lu, N. (1992). Test of static structure factors for describing light scattering from fractal soot aggregates. Langmuir, 8, 2064-2069.

[36] Van de Hulst, H. C. (1981). Light Scattering by Small Particles. Dover, New York.

[37] Farias, T. L., Koylu, U. O. and Carvalho, M.G. (1996). Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates. Appl. Optics, 35, 6560-6567.

[38] Nelson, J. (1989). Test of a mean field theory for the optics of fractal clusters. J. Mod. Optics, 36, 1031-1057.

[39] Botet, R., Rannou, P. and Cabane, M. (1997). Mean-field approximation of Mie scattering by fractal aggregates of identical spheres. Appl. Optics, 36, 8791-8797.

[40] Ortiz, G. P. and Mocan, W.L. (2003). Scaling condition for multiple scattering in fractal aggregates. Pysica B, 338, 103-106.

[41] Nelson, J. A., Crookes, R. J. and Simons, S. (1990). On obtaining the fractal dimension of a 3D cluster from its projection on a plane - application to smoke agglomerates. J. Phys. D: Appl. Phys., 23, 465-468.

[42] Koylu, U. O., Faeth, G. M., Farias, T. L. and Carvalho, M. G. (1995). Fractal and projected structure properties of soot aggregates. Combust. Flame, 100, 621-633.

[43] Lambert, S., Moustier, S., Dussouillez, P., Barakat, M., Bottero, J. Y., Le Petit, J. and Ginestet, P. (2003). Analysis of the structure of very large baterial aggregates by small angle multiple light scattering and confocal image analysis. J. Colloid Interface Sci., 262, 384-390.

[44] Gregory, J. and Chung, H. (1995). Continuous monitoring of floc properties in stirred suspensions. J. Water Supply Res. Technol. -Aqua, 44, 125-1313.

[45] Berthon, S., Barbieri, O., Ehrburger-Dolle, F., Geissler, E., Achard, P., Bley, F., Hecht, A-M., Livet, F., Pajonk, G. M., Pinto, N., Rigacci, A. and Rochas, C. (2001). DLS and SAXS investigations of organic gels and aerogels. J. Non-Cryst. Solids, 285, 154-161.

[46] Schmidt, P. W. (1991). Small-angle scattering studies of disordered, porous and fractal systems. J. Appl. Crystallogr., 24, 414-435.

[47] Kaye, B. H. (1994). A Random Walk Through Fractal Dimensions. Weinheim, New York.

[48] Jullien, R., Thouy, R. and Ehrburger-Dolle, F. (1994). Numerical investigation of two-dimensional projections of random fractal aggregates. Phys. Rev. E, 50, 3878-3885.

[49] Tence, M., Chevalier, J. P. and Jullien, R. (1986). On the measurement of the fractal dimension of aggregated particles by electron-microscopy - experimental-method, corrections and comparison with numerical-models. J. Phys., 47, 1989-1998.

[50] Cross, S. S. (1994). The application of fractal geometric analysis to microscopic images. Micron, 25, 101-113.

[51] Gonzales, R. C. and Woods, R. E. (2002). Digital Image Processin , second edition. Prentice Hall, New York.

[52] Allen, M., Brown, G. J. and Miles, N. J. (1995). Measurement of boundary fractal dimensions: review of current techniques. Powder Technol., 84, 1-14.

[53] Adler, J. and Hancock, D. (1994). Advantages of using a discrete distance transform function in the measurement of fractal dimensions by the dilation method. Powder Technol., 78, 191-196.

[54] Forrest, S. R. and Witten, T. A. (1979). Long-range correlations in smoke-particle aggregates, J. Phys. A, 12, L109-L117.

[55] Park, K., Kittelson, D. B. and McMurry, P. H. (2004). Structural properties of diesel exhaust particles measured by transmission electron microscopy (TEM): relationships to particle mass and mobility, Aerosol Sci. Technol., 38, 881-889.

[56] Bower, C., Washington, C. and Purewal, T. S. (1997). The use of image analysis to characterize aggregates in a shear field. Colloids Surf. A: Physicochem. Eng. Aspects, 127, 105-112.

[57] Bremer, L. G. B., Bijsterbosch, B. H., Walstra, P. and van Vliet, T. (1993). Formation, properties and fractal structure of particle gels. Adv. Colloid Interface Sci., 46, 117-128.

[58] Thill, A., Wagner, M. and Bottero, J. Y. (1999). Confocal scanning laser microscopy as a tool for the determination of 3D floc structure. J. Colloid Interface Sci., 220, 465-467.

[59] Snidaro, D., Zartarian, F., Jorand, F., Bottero, J. Y., Block, J. C. and Manem, J. (1997). Characterization of activated sludge flocs structure. Water Sci. Technol., 36, 313-320.

[60] Dinsmore, A. D. and Weitz, D. A. (2002). Direct imaging of three-dimensional structure and topology of colloidal gels. J. Phys.: Condens. Matter, 14, 7581-7597.

[61] Mellema, M., Heesakkers, J. W. M., van Opheusden, J. H. J. and van Vliet, T. (2000). Structure and scaling behaviour of aging rennet-induced casein gels examined by confocal microscopy and permeametry. Langmuir, 16, 6847-3854.

[62] Schmid, M., Thill, A., Purkhold, U., Walcher, M., Bottero, J. Y., Ginestet, P., Nielsen, P. J., Wertz, S. and Wagner, M.(2003). Characterisation of activated sludge flocs by confocal scanning microscopy and image analysis. Water Res., 17, 2043-2052.

[63] Gibson, J. R., Lin, H. and Bruns, M. A. (2006). A comparison of fractal analytical methods on 2- and 3-dimensional computed tomographic scans of soil aggregates. Geoderma, 134, 335-348.

[64] Li, D. H. and Ganczarczyk, J. J. (1988). Flow through activated sludge flocs. Water Res., 22, 789-792.

[65] Serra, T. and Logan, B. E. (1999). Collision frequencies of fractal bacterial aggregates with small particles in a sheared fluid. Environ. Sci. Technol., 33, 2247-2251.

[66] Hess, W., Frisch, H. L. and Klein, R. (1986). On the hydrodynamic behaviour of colloidal aggregates. Z. Phys. B - Condens. Matter, 64, 65-67.

[67] Li, X. Y. and Logan, B. E. (2001). Permeability of fractal aggregates. Water Res., 35, 3373-3380.

[68] Woodfield, D. and Bickert, G. (2001). An improved permeability model for fractal aggregates settling in creeping flow. Water Res., 35, 3807-3806.

[69] Farrow, J. B. and Warren, L. J. (1993). Measurement of the size of aggregates in suspension. In Coagulation and Flocculation - Theory and Applications, Dobias B. (ed.). Marcel Dekker, New York.

[70] Nobbs, D.,Tang, P. andRaper, J. A. (2002). The design, construction and commissioning of a low-cost optical particle size analyser specifically for measurement of settling velocities and size of flocs. Meas. Sci. Technol., 13, 297-302.

[71] Glover, S. M., Yan, Y. -D., Jameson, G. J. and Biggs, S. (2000). Bridging flocculation studies by light scattering and settling. Chem. Eng. J., 80, 3-12.

[72] Alfano, J. C., Carter, P. W., Dunham, A. J., Nowak, M. J. and Tubergen, K. R. (2000). Polyelectrolyte-induced aggregation of microcrystalline cellulose: reversibility and shear effects. J. Colloid Interface Sci., 223, 244-254.

[73] Owen, A. T., Fawell, P. D., Swift, J. D. and Farrow, J. B. (2002). The impact of polyacrylamide flocculant solution age on flocculation performance. Int. J. Miner. Process., 67, 123-144.

[74] Kovalsky, P. and Bushell, G. (2005). In situ measurement of fractal dimension using focussed beam reflectance measurement. Chem. Eng. J., 111, 181-188.

[75] Logan, B. E. and Wilkerson, D. B. (1991). Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates. Biotechnol. Bioeng., 23, 389-396.

[76] Stoll, S., Elaissari, A. and Pefferkorn, E. (1990). Fractal dimensions of latex aggregates: correlation between hydrodynamic radius and cluster size. J. Colloid Interface Sci., 140, 98-104.

[77] Jackson, G. A., Logan, B. E., Alldredge, A. L. and Dam, H. G. (1995). Combining particle size spectra from a mesocosm experiment measured using photographic and aperture impedance (Coulter and Elzone) techniques. Deep-Sea Res. II, 42, 139-157.

[78] Sterling, M. C. Jr, Bonner, J. S., Ernest, A. N. S., Page, C. A. and Autenrieth, R.L. (2004). Characterizing aquatic sediment-oil aggregates using in situ measurements. Mar. Pollut. Bull., 48, 533-542.

4 Fractal Structures and Mechanisms in Coagulation/Flocculation Processes in Environmental Systems: Theoretical Aspects

Serge Stoll1 and Silvia Diez2

1 Department of Inorganic, Analytical and Applied Chemistry CABE, University of Geneva, Sciences II, 30 Quai Ernest Ansermet, CH-1211 Geneva 4/Switzerland

2 CIEMAT, Avda. Complutense 22, 28040, Madrid, Spain

0 0

Post a comment