1 |
Timin T, Esmail MN. A comparative study of central and upwind difference schemes using the primitive variables. Int. J. Numer. Methods Fluids 1983;3:295-305.
DOI
ScienceOn
|
2 |
LeVeque RJ. High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 1996;33:627-665.
DOI
ScienceOn
|
3 |
Bushell GC, Yan YD, Woodfield D, Raper J, Amal R. On techniques for the measurement of the mass fractal dimension of aggregates. Adv. Colloid Interface Sci. 2002;95:1-50.
DOI
ScienceOn
|
4 |
Turchiuli C, Fargues C. Influence of structural properties of alum and ferric flocs on sludge dewaterability. Chem. Eng. J. 2004;103:123-131.
DOI
ScienceOn
|
5 |
Hinds WC. Aerosol technology: properties, behavior, and measurement of airborne particles, 2nd ed. New York: John Wiley & Sons Inc. 1999.
|
6 |
Strogatz SH. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Reading: Perseus Books Publishing. 1994.
|
7 |
Bungartz H, Wanner SC. Significance of particle interaction to the modelling of cohesive sediment transport in rivers. Hydrol. Process. 2004;18:1685-1702.
DOI
ScienceOn
|
8 |
Winterwerp JC. On the flocculation and settling velocity of estuarine mud. Cont.Shelf Res. 2002;22:1339-1360.
DOI
ScienceOn
|
9 |
Maggi F, Mietta F, Winterwerp JC. Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment. J. Hydrol. 2007;343:43-55.
DOI
ScienceOn
|
10 |
Adachi Y. Dynamic aspects of coagulation and flocculation. Adv. Colloid Interface Sci. 1995;56:1-31.
DOI
ScienceOn
|
11 |
Miyahara K, Adachi Y, Nakaishi K, Ohtsubo M. Settling velocity of a sodium montmorillonite floc under high ionic strength. Colloids Surf. A Physicochem. Eng. Asp. 2002;196:87-91.
DOI
ScienceOn
|
12 |
Ding A, Hounslow MJ, Biggs CA. Population balance modelling of activated sludge flocculation: investigating the size dependence of aggregation, breakage and collision efficiency. Chem. Eng. Sci. 2006;61:63-74.
DOI
ScienceOn
|
13 |
Parker DS, Kaufman WJ, Jenkins D. Floc breakup in turbulent flocculation processes. J. Sanit. Eng. Div. 1972;98:79-99.
|
14 |
Langseth JO, Tveito A, Winther R. On the convergence of operator splitting applied to conservation laws with source terms. SIAM J. Numer. Anal. 1996;33:843-863.
DOI
ScienceOn
|
15 |
Rogers SE, Kwak D. An upwind differencing scheme for the incompressible Navier-Strokes equations. Washington, DC: National Aeronautics and Space Administration; 1988.
|
16 |
Aro CJ, Rodrigue GH, Rotman DA. A high performance chemical kinetics algorithm for 3-D atmospheric models. Int. J. High Perform. Comput. Appl. 1999;13:3-15.
DOI
ScienceOn
|
17 |
Badrot-Nico F, Brissaud F, Guinot V. A finite volume upwind scheme for the solution of the linear advection-diffusion equation with sharp gradients in multiple dimensions. Adv. Water Resour. 2007;30:2002-2025.
DOI
ScienceOn
|
18 |
Durran DR. Numerical methods for wave equations in geophysical fluid dynamics. New York: Springer; 1999.
|
19 |
Alhumaizi K. Comparison of finite difference methods for the numerical simulation of reacting flow. Comput. Chem. Eng. 2004;28:1759-1769.
DOI
ScienceOn
|
20 |
White FM. Viscous fluid flow. 2nd ed. New York: McGraw-Hill; 1991.
|
21 |
Lian G, Moore S, Heeney L. Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer. Chem. Eng. Sci. 2006;61:7819-7826.
DOI
ScienceOn
|
22 |
Schwarzer HC, Schwertfirm F, Manhart M, Schmid HJ, Peukert W. Predictive simulation of nanoparticle precipitation based on the population balance equation. Chem. Eng. Sci. 2006;61:167-181.
DOI
ScienceOn
|
23 |
Stokes GG. Mathematical and physical papers (Vol. 1). Cambridge: Cambridge University Press; 1880.
|
24 |
Brown PP, Lawler DF. Sphere drag and settling velocity revisited. J. Environ. Eng. 2003;129:222-231.
DOI
ScienceOn
|
25 |
Chakraborti RK, Atkinson JF, Van Benschoten JE. Characterization of alum floc by image analysis. Environ. Sci. Technol. 2000;34:3969-3976.
DOI
ScienceOn
|
26 |
Jiang Q, Logan BE. Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 1991;25:2031-2038.
DOI
|
27 |
Johnson CP, Li X, Logan BE. Settling velocities of fractal aggregates. Environ. Sci. Technol. 1996;30:1911-1918.
DOI
ScienceOn
|
28 |
Spicer PT, Pratsinis SE, Raper J, Amal R, Bushell G, Meesters G. Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol. 1998;97:26-34.
DOI
ScienceOn
|
29 |
Chakraborti RK, Gardner KH, Atkinson JF, Van Benschoten JE. Changes in fractal dimension during aggregation. Water Res. 2003;37:873-883.
DOI
ScienceOn
|
30 |
McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 1997;27:255-265.
DOI
ScienceOn
|
31 |
Somasundaran P, Runkana V. Modeling flocculation of colloidal mineral suspensions using population balances. Int. J. Miner. Process. 2003;72:33-55.
DOI
ScienceOn
|
32 |
Rahmani NH, Dabros T, Masliyah JH. Evolution of asphaltene floc size distribution in organic solvents under shear. Chem. Eng. Sci. 2004;59:685-697.
DOI
ScienceOn
|
33 |
Prat OP, Ducoste JJ. Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics. Chem. Eng. Sci. 2006;61:75-86.
DOI
ScienceOn
|
34 |
Marchisio DL, Vigil RD, Fox RO. Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems. Chem. Eng. Sci. 2003;58:3337-3351.
DOI
ScienceOn
|
35 |
Runkana V, Somasundaran P, Kapur PC. A population balance model for flocculation of colloidal suspensions by polymer bridging. Chem. Eng. Sci. 2006;61:182-191.
DOI
ScienceOn
|
36 |
Lee DG, Bonner JS, Garton LS, Ernest AN, Autenrieth RL. Modeling coagulation kinetics incorporating fractal theories: a fractal rectilinear approach. Water Res. 2000;34:1987-2000.
DOI
ScienceOn
|
37 |
Fox RO. Computational models for turbulent reacting flows. Cambridge: Cambridge University Press; 2003.
|
38 |
Kumar S, Ramkrishna D. On the solution of population balance equations by discretization: I. A fixed pivot technique. Chem. Eng. Sci. 1996;51:1311-1332.
DOI
ScienceOn
|
39 |
Ramkrishna D, Mahoney AW. Population balance modeling: promise for the future. Chem. Eng. Sci. 2002;57:595-606.
DOI
ScienceOn
|
40 |
Gowdy W, Iwinski SR, Woodstock G. Removal efficiencies of polymer enhanced dewatering systems. Proceedings of the 9th Biennial Conference on Stormwater Research & Watershed Management; 2007 May 2-3; Orlando, FL.
|
41 |
Kang JH, Li Y, Lau SL, Kayhanian M, Stenstrom MK. Particle destabilization in highway runoff to optimize pollutant removal. J. Environ. Eng. 2007;133:426-434.
DOI
ScienceOn
|
42 |
Akan AO, Houghtalen RJ. Urban hydrology, hydraulics, and stormwater quality. Hoboken: John Wiley & Sons; 2003.
|
43 |
Smoluchowski MV. Versuch einer mathematischen theorie der koagulationskinetik kolloider Losungen. Z. Phys. Chem. 1917;92:129-168.
|
44 |
Spicer PT, Pratsinis SE. Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 1996;42:1612-1620.
DOI
ScienceOn
|
45 |
Lawler DF, Wilkes DR. Flocculation model testing; particle sizes in a softening plant. J. Am. Water Works Assoc. 1984;76:90-97.
|
46 |
Hounslow MJ, Ryall RL, Marshall VR. A discretized population balance for nucleation, growth, and aggregation. AIChE J. 1988;34:1821-1832.
DOI
ScienceOn
|
47 |
Spicer PT, Pratsinis SE. Shear-induced flocculation: the evolution of floc structure and the shape of the size distribution at steady state. Water Res. 1996;30:1049-1056.
DOI
|
48 |
Flesch JC, Spicer PT, Pratsinis SE. Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 1999;45:1114-1124.
DOI
ScienceOn
|
49 |
Sterling MC Jr, Bonner JS, Ernest AN, Page CA, Autenrieth RL. Application of fractal flocculation and vertical transport model to aquatic sol-sediment systems. Water Res. 2005;39:1818-1830.
DOI
ScienceOn
|
50 |
Marchisio DL, Vigil RD, Fox RO. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 2003;258:322-334.
DOI
ScienceOn
|
51 |
Harper HH. Current research and trends in alum treatment of stormwater runoff. Proceedings of the 9th Biennial Conference on Stormwater Research & Watershed Management; 2007 May 2-3; Orlando, FL.
|
52 |
Heath AR, Koh PT. Combined population balance and CFD modelling of particle aggregation by polymeric flocculant. Proceedings of the 3rd International Conference on CFD in the Minerals and Process Industries; 2003 Dec 10-12; Melbourne, Australia.
|