Adjustable discretized population balance equations: Numerical simulation and parameter estimation for fractal aggregation and break-up

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Volumn 292, Issue 2-3, 2007, Pages 173-188

  Kim, Jinwook ^a   Kramer, Timothy A ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Agglomeration; Aggregation; Break up; Breakage; Coagulation; Collision efficiency; Flocculation; Fractal; Parameter estimation; Particle size distribution

Indexed keywords

COAGULATION; COMPUTER SIMULATION; FLOCCULATION; FRACTALS; PARAMETER ESTIMATION; PARTICLE SIZE ANALYSIS;

COLLISION EFFICIENCY; FRACTAL AGGREGATION; MASS CONSERVATION; POPULATION BALANCE EQUATIONS (PBE);

AGGLOMERATION;

ARTICLE; CALCULATION; DYNAMICS; FRACTAL ANALYSIS; GEOMETRY; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; POPULATION BALANCE EQUATION; PRIORITY JOURNAL; SIMULATION;

EID: 33845507832     PISSN: 09277757     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.colsurfa.2006.06.020     Document Type: Article

References (52)

1. Li X., and Zhang J. Numerical simulation and experimental verification of particle coagulation dynamics for a pulsed input. J. Coll. Interf. Sci. 262 (2003) 149-161
2. Drake R.L. In: Hidy G.M., and Brock J.R. (Eds). Topics in Current Aerosel Research (1972), Pergamon, New York
3. Ramkrishna D. The status of population balance. Rev. Chem. Eng. 3 1 (1985) 49-95
4. Smoluchowski M.V. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Losungen. Z. Physk. Chem. 92 (1917) 129-168
5. Gelbard F., and Seinfeld J.H. Numerical solution of the dynamic equation for particulate systems. J. Comput. Phys. 28 (1978) 357-375
6. Gelbard F., Tambour Y., and Seinfeld J.H. Sectional representation of simulating aerosol dynamics. J. Coll. Interf. Sci. 76 (1980) 541-556
7. Batterham R.J., Hall J.S., and Barton G. Pelletizing kinetics and simulation of full scale balling circuits. International Symposium on Agglomeration (3rd). Nurnberg (1981) A136-A150
8. Hounslow M.J., Ryall R.L., and Marshall V.R. A discretized population balance for nucleation, growth, and aggregation. AIChE J. 34 11 (1988) 1821-1832
9. Marchal P., David R., Klein J.P., and Villermaux J. Crystallization and precipitation engineering: I. An efficient method for solving population balance in crystallization with agglomeration. Chem. Eng. Sci. 43 (1988) 59-67
10. Litster J.D., Smit D.J., and Hounslow M.J. Adjustable discretized population balance for growth and aggregation. AIChE J. 41 3 (1995) 591-603
11. Hill P.J., and Ng K.M. New discretization procedure for the agglomeration equation. AIChE J. 42 3 (1996) 727-741
12. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization - I. A fixed pivot technique. Chem. Eng. Sci. 51 8 (1996) 1311-1332
13. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization - II. A moving pivot technique. Chem. Eng. Sci. 51 8 (1996) 1333-1342
14. Vanni M. Approximate population balance equations for aggregation-breakage processes. J. Coll. Interf. Sci. 221 (2000) 143-160
15. J. Kim, The modeling of arsenic removal from contaminated water using coagulation and sorption, PhD Dissertation, Texas A&M University, College Station, Texas, 2005.
16. Hill P.J., and Ng K.M. New discretization procedure for the breakage equation. AIChE J. 41 5 (1995) 1204-1216
17. Meakin P. Fractal aggregates. Adv. Coll. Interf. Sci. 28 (1988) 249-331
18. Kim J., and Kramer T.A. Improved models for fractal colloidal agglomeration: computationally efficient algorithms. Coll. Surf. A 253 (2005) 33-49
19. Kim J., and Kramer T.A. Improved orthokinetic coagulation models for fractal colloids: aggregation and break-up. Chem. Eng. Sci. 61 1 (2006) 45-53
20. Vanni M. Discretization procedure for the breakage equation. AIChE J. 45 4 (1999) 916-919
21. Patil D.P., Andrews J.R.G., and Uhlherr P.H.T. Shear flocculation - kinetics of floc coalescence and breakage. Int. J. Miner Process. 61 (2001) 171-188
22. Chen W., Fisher R.R., and Berg J.C. Simulation of particle size distribution in an aggregation-breakup process. Chem. Eng. Sci. 45 9 (1990) 3003-3006
23. Spicer P.T., and Pratsinis S.E. Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 42 6 (1996) 1612-1620
24. Flesch J.C., Spicer P.T., and Pratsinis S.E. Laminar and Turbulent shear-induced flocculation of fractal aggregates. AIChE J. 45 5 (1999) 1114-1124
25. Serra T., and Casamitjana X. Effect of the shear and volume fraction on the aggregation and breakup of particles. AIChE J. 44 8 (1998) 1724-1730
26. Kramer T.A., and Clark M.M. Incorporation of aggregate breakup in the simulation of orthokinetic coagulation. J. Coll. Interf. Sci. 216 (1999) 116-126
27. Delichatsios M.A., and Probstein R.F. Coagulation in Turbulent flow: theory and experiment. J. Coll. Interf. Sci. 51 (1975) 394-405
28. K.A. Kusters, The Influence of turbulence on aggregate of small particles in agitated vessels, PhD Dissertation, 1991.
29. Zhang J., and Li X. Modeling particle-size distribution dynamics in a flocculation systems. AIChE J. 49 7 (2003) 1870-1882
30. Pandya J.D., and Spielman L.A. Floc breakage in agitated suspensions: effect of agitation rate. Chem. Eng. Sci. 38 12 (1982) 1983-1992
31. Lu C.F., and Spielman L.A. Kinetics of Floc breakage and agglomeration in agitated liquid suspensions. J. Coll. Interf. Sci. 103 1 (1985) 95-105
32. Coulaloglou C.A., and Tavlarides L.L. Description of interaction processes in agitated liquid-liquid dispersions. Chem. Eng. Sci. 32 (1977) 1289-1297
33. Ziff R.M. New solutions to the fragmentation equation. J. Phys. A: Math. Gen. 24 (1991) 2821-2828
34. Thomas D.G. Turbulent disruption of flocs in small particle suspensions. AIChE J. 10 (1964) 517-523
35. Argaman Y., and Kaufman W.J. Turbulent and flocculation. J. Sanit. Eng. Div. ASCE 96 (1970) 223-241
36. Parker D.S., Kaufman W.J., and Jenkins D. Floc breakup in turbulent flocculation process. J. Sanit. Eng. Div. ASCE 98 SA1 (1972) 79-99
37. Kao S.V., and Mason S.G. Dispersion of particles by shear. Nature 253 (1975) 619-621
38. Tambo N., and Watanabe Y. Physical aspect of flocculation process - I. Fundemental treatise. Water Res. 13 (1979) 429-439
39. Ray D.T., and Hogg R. Agglomerate breakage in polymer-flocculated suspensions. J. Coll. Interf. Sci. 116 1 (1986) 256-268
40. Sonntag R.C., and Russel W.B. Structure and breakup of floc subjected to fluid stresses: II. Theory. J. Coll. Interf. Sci. 115 (1987) 378-389
41. Serra T., and Casamitjana X. Effect of the shear and volume fraction on the aggregation and breakup of particles. AIChE J. 44 8 (1999) 1724-1730
42. Kramer T.A., and Clark M.M. Influence of strain-rate on coagulation kinetics. J. Environ. Eng., ASCE 123 5 (1997) 444-452
43. Scott W.T. Analytical Studies of cloud droplet coalescence I. J. Atmos. Sci. 25 (1968) 54-65
44. Friedlander S.K. Smoke, Dust, and Haze (1977), Wiley-Interscience Publication, New York
45. Vemury S., and Pratsinis S.E. Self-preserving size distributions of agglomerates. J. Aerosol Sci. 26 2 (1995) 175-185
46. Liu Y., and Cameron I.T. A new wavelet-based adaptive method for solving population balance equations. Powder Technol. 130 (2003) 181-188
47. Elimelch M., Gregory J., Jia X., and Williams R.A. Particle Deposition and Aggregation (1995), Butterworth Heinemann
48. Friedlander S.K. Smoke, Dust, and Haze (2000), Wiley-Interscience Publication
49. Constantinides A., and Mostoufi N. Numerical Methods for Chemical Engineers with MATLAB Applications (1999), Prentice Hall, New Jersey
50. Ernest A.N., Bonner J.S., and Autenrieth R.L. Model parameter estimation for particle transport. J. Environ. Eng., ASCE 117 5 (1991) 573-594
51. Elimelch M. Predicting collision efficiencies of colloidal particles in porous media. Water Res. 26 1 (1992) 1-8
52. Han M.Y., and Lawler D.F. The (relative) insignificance of g in flocculation. J. AWWA 84 (1992) 79-91