On the solution of population balance equations by discretization - I. A fixed pivot technique

Chemical Engineering Science

Volumn 51, Issue 8, 1996, Pages 1311-1332

  Kumar, Sanjeev ^a   Ramkrishna, D ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; CALCULATIONS; ERRORS; ESTIMATION; MATHEMATICAL TECHNIQUES; NUMERICAL METHODS; PARTICLES (PARTICULATE MATTER);

BREAKAGE; DISCRETIZATION; FINEGRIDS; FIXED PIVOT TECHNIQUE; NUMBER DENSITY FUNCTION; POPULATION BALANCE EQUATIONS;

PARTICLE SIZE ANALYSIS;

EID: 0030128282     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/0009-2509(96)88489-2     Document Type: Article

References (21)

1. Batterham, R. J., Hall, J. S. and Barton, G., 1981, Pelletizing kinetics and simulation of full scale balling circuits, in Proceedings of the 3rd International Symposium on Agglomeration, Nurnberg, W. Germany, p. A136.
2. Blatz, P. J. and Tobolsky, A. V., 1945, Note on the kinetics of systems manifesting simultaneous polymerization-depolymerization phenomena. J. phys. Chem. 49, 77-80.
3. Bleck, R., 1970, A fast, approximate method for integrating the stochastic coalescence equation. J. Geophys. Res. 75, 5165-5171.
4. Chen, A. W., Fisher, R. R. and Berg, J. C., 1990, Simulation of particle size distribution in an aggregation-breakup process. Chem. Engng Sci. 45, 3003-3006.
5. Gelbard F. and Seinfeld, J. H., 1979, The general dynamic equation for aerosols. J. Colloid Interface Sci. 68, 363-382.
6. Gelbard, F., Tambour, Y. and Seinfeld, J. H., 1980, Sectional representation of simulating aerosol dynamics. J. Colloid Interface Sci. 76, 541-556.
7. Hidy, G. M., 1965, On the theory of the coagulation of noninteracting particles in Brownian motion. J. Colloid Interface Sci. 20, 123-144.
8. Hounslow, M. J., Ryall, R. L. and Marshall, V. R., 1988, A discretized population balance for nucleation, growth and aggregation. A.I.Ch.E. J. 34, 1821-1832.
9. Koh, P. T. L., Andrews, J. R. G. and Uhlherr, P. H. T., 1987, Modeling shear flocculation by population balances. Chem. Engng Sci. 42, 353-362.
10. Kostoglou M. and Karabelas, A. J., 1994, Evaluation of zero order methods for simulating particle coagulation. J. Colloid Interface Sci. 163, 420-431.
11. Kumar, S. and Ramkrishna, D., 1996, On the solution of population balance equations by discretization-II. A moving pivot technique. Chem. Engng Sci. 51, 1333-1342.
12. Landgrebe, J. D. and Pratsinis, S. E., 1990, 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, 63-86.
13. Marchal, P., David, R., Klein, J. P. and Villermaux, J., 1988, Crystallization and precipitation engineering - I. An efficient method for solving population balances in crystallization with agglomeration. Chem. Engng Sci. 43, 63-86.
14. Nambiar, D. K. R., Kumar, R. and Gandhi, K. S., 1992, A new model for the breakage frequency of drops in turbulent stirred dispersions, Chem. Engng Sci. 47, 2989-3002.
15. Narsimhan, G., Ramkrishna, D. and Gupta, J. P., 1980, Analysis of drop size distributions in lean liquid-liquid dispersions, A.I.Ch.E. J. 26, 991-1000.
16. Ramkrishna, D., 1985, The status of population balances. Rev. Chem. Engng 3, 49-95.
17. Sastry, K. V. S. and Gaschignard, P., 1981, Discretization procedure for the coalescence equation of particulate processes. Ind. Engng Chem. Fundam. 20, 355-361.
18. Scott, W. T., 1968, Analytical studies in cloud droplet coalescence I. J. Atmos. Sci. 25, 54-65.
19. van Dongen, P. G. J. and Ernst, M. H., 1988, Scaling solutions of Smoluchowski's coagulation equation. J. Statist. Phys. 50, 295-329.
20. Ziff, R. M. and Mcgrady, E. D., 1985, The kinetics of cluster fragmentation and depolymerization. J. Phys. A: Math. Gen. 18, 3027-3037.
21. Ziff, R. M., 1991, New solutions to the fragmentation equation. J. Phys. A: Math. Gen. 24, 2821-2828.