Optimal low order methods of moments for solving the fragmentation equation

Powder Technology

Volumn 143-144, Issue , 2004, Pages 280-290

  Kostoglou, M ^a   Karabelas, A J ^a,b  

^a Centre for Research Technology Hellas   (Greece)

^b ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

Fragmentation equation; Method of moments; Particle size distribution

Indexed keywords

COMPUTATIONAL METHODS; FUNCTIONS; MATHEMATICAL MODELS;

DISCRETIZATION; FRAGMENTATIONS;

PROBLEM SOLVING;

POWDER;

ARTICLE; FRAGMENTATION REACTION; MATHEMATICAL COMPUTING; MODULATION; PARTICLE SIZE; TECHNIQUE;

EID: 4143062491     PISSN: 00325910     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.powtec.2004.04.020     Document Type: Article

References (39)

1. Ziff R.M., McGrady E.D. Kinetics of polymer degradation. Macromolecules. 19:1986;2513-2519
2. Valentas K.J., Amudson N.R. Breakage and coalescence in dispersed phase systems. Ind. Eng. Chem. Fundam. 5:1966;533-542
3. K. Wohletz, W. Brown, Particulate size distributions and sequential fragmentation/transport theory. Manuscript presented in NSF/JSPS AMIGO-IMI Seminar, Santa Barbara, CA, June 8-13, (1995).
4. Nielsen J., Villadsen J. Bioreaction Engineering Principles. 1994;Plenum, New York
5. Sato K., Meguri N., Shoji K., Kanemoto H., Hasegawa T., Maruyama T. Breakage of coals in ring-roller mills: Part I. The breakage properties of various coals and simulation model to predict steady-state mill performance. Powder Technol. 86:1996;275-283
6. Shinohara K., Golman B., Uchiyama T., Otani M. Fine-grinding characteristics of hard materials by attrition mill. Powder Technol. 103:1999;292-296
7. Frances C., Laguerie C. Fine wet grinding of an alumina hydrate in a ball mill. Powder Technol. 99:1998;147-153
8. Ramkrishna D. Population Balances. Theory and Application to Particulate Systems in Engineering. 2000;Academic Press, San Diego
9. Ziff R.M. New solutions to the fragmentation equation. J. Phys., A, Math. Gen. 24:1991;2821-2828
10. Lee K., Matsoukas T. Simultaneous coagulation and break-up using constant-N Monte Carlo. Powder Technol. 110:2000;82-89
11. Mishra B.K. Monte Carlo simulation of particle breakage process during grinding. Powder Technol. 110:2000;246-252
12. Ramkrishna D., Sathyagal A., Narsimhan G. Analysis of dispersed phase systems - fresh perspective. AIChE J. 41:1995;35-44
13. Everson R.C., Eyre D., Campbell Q.P. Spline method for solving continuous batch grinding and similarity equations. Comput. Chem. Eng. 21:1997;1433-1440
14. Kumar S., Ramkrishna D. On the solution of population balance equations by discretizations - I. A fixed pivot technique. Chem. Eng. Sci. 51:1996;1311-1332
15. Kumar S., Ramkrishna D. On the solution of population balance equations by discretization - II. A moving pivot technique. Chem. Eng. Sci. 51:1996;1333-1342
16. Attarakih M.M., Bart H.J., Faqir N.M. Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: droplet breakage. Chem. Eng. Sci. 58:2003;1311-1332
17. Kostoglou M., Karabelas A.J. An assessment of low order methods for solving the breakage equation. Powder Technol. 127:2002;116-127
18. Mihalyko C., Blickle T., Lacatos B.G. A simulation model for analysis and design of continuous grinding mills. Powder Technol. 97:1998;51-58
19. Lacatos B.G., Auer R. Two level model based design of solids processing systems. Comput. Chem. Eng. 22(Supp. 1):1998;S785-S788
20. Treat R.P. On the similarity solution of the fragmentation equation. J. Phys., A, Math. Gen. 30:1997;2519-2543
21. McGrady E.D., Ziff R.M. Shattering transition in fragmentation. Phys. Rev. Lett. 58:1987;892-895
22. Ernst M.H., Szamel G. Fragmentation kinetics. J. Phys., A, Math. Gen. 26:1993;6085-6091
23. Lee K.W. Conservation of particle size distribution parameters during Brownian coagulation. J. Colloid Interface Sci. 108:1985;199-206
24. Tsang T.H., Rao A. Comparison of different numerical schemes for condensational growth of aerosols. Aerosol Sci. Technol. 9:1990;271-277
25. Hamilton R.A., Curtis J.S., Ramkrishna D. Beyond log-normal distributions: Hermite spectra for solving population balances. AIChE J. 49:2003;2328-2343
26. McGraw R. Description of atmospheric aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27:1997;255-265
27. Marchisio D.L., Pikturna J.T., Fox R.O., Vigil R.D., Barresi A.A. Quadrature method of moments for population balance equations. AIChE J. 49:2003;1266-1276
28. Marchisio D.L., Vigil R.D., Fox R.O. Quadrature method of moments for aggregation breakage processes. J. Colloid Interface Sci. 258:2003;322-334
29. Piskunov V.N., Golubev A.I. Generalized approximation to the solution of the kinetic coagulation equation. J. Aerosol Sci. 30(Suppl. 1):1999;S451-S452
30. Piskunov V.N., Golubev A.I. The generalized approximation method for modeling coagulation kinetics - Part 1. Justification and implementation of the method. J. Aerosol Sci. 33:2002;51-63
31. Piskunov V.N., Golubev A.I., Barret J.C., Ismailova N.A. The generalized approximation method for modeling coagulation kinetics - Part 2. Comparison with other methods. J. Aerosol Sci. 33:2002;65-75
32. Liou J., Srienc F., Fredrikson A.G. Solutions of population balance models based on successive generations approach. Chem. Eng. Sci. 52:1997;1529-1540
33. Luo H., Svendsen H.F. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 42:1996;1225-1233
34. Ramkrishna D. Drop-breakage in agitated liquid-liquid dispersions. Chem. Eng. Sci. 29:1974;987-992
35. Eyre D., Everson R.C., Campbell Q.P. New parameterization for a discrete batch grinding equation. Powder Technol. 98:1998;265-272
36. Landgrebe J.D., Pratsinis S.E. A discrete-sectional model for particulate production by gas phase chemical reaction and aerosol coagulation in the free molecular regime. J. Colloid Interface Sci. 139:1990;63-86
37. Varinot C., Hiltgun S., Pons M.-N., Dodds J. Identification of the fragmentation mechanisms in wet-phase fine grinding in a stirred bead mill. Chem. Eng. Sci. 52:1997;3605-3612
38. Varinot C., Berthiaux H., Dodds J. Prediction of the product size distribution in associations of stirred bead mills. Powder Technol. 105:1999;228-236
39. Hill P.J., Ng K.M. New discretization procedure for the breakage equation. AIChE J. 42:1995;1600-1611