Part V: Dynamic evolution of the multivariate particle size distribution undergoing combined particle growth and aggregation

Chemical Engineering Science

Volumn 64, Issue 14, 2009, Pages 3260-3269

  Alexopoulos, A H ^b   Roussos, A ^b   Kiparissides, C ^a,b  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^b Centre for Research Technology Hellas   (Greece)

Author keywords

Aggregation; Finite elements; Growth; Moving grid; Multivariate population balances; Particle size distribution

Indexed keywords

AGGREGATION; FINITE ELEMENTS; GROWTH; MOVING GRID; MULTIVARIATE POPULATION BALANCES;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; GALERKIN METHODS; PARTICLE SIZE; PARTICLE SIZE ANALYSIS; SIZE DISTRIBUTION;

AGGLOMERATION;

EID: 67349165599     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2009.04.012     Document Type: Article

References (40)

1. Alexopoulos A.H., Roussos A.I., and Kiparissides C. Part I: dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation. Chemical Engineering Science 59 (2004) 5751-5769
2. Alexopoulos A.H., and Kiparissides C. Part II: dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation. Chemical Engineering Science 60 15 (2005) 4157-4169
3. Alexopoulos, A.H., Kiparissides, C., 2005b. Solution of the bi-variate dynamic population balance equation in batch particulate systems, ESCAPE-15, Barcelona, Spain, May 29-June 1.
4. Annapragada A., and Neily J. On the modelling of granulation processes: a short note. Powder Technology 89 (1996) 83-84
5. Attarakih M.M., Bart H.-J., and Faqir N.M. The bivariate spatially distributed population balance equation: an accurate reduction technique. Computer Aided Chemical Engineering 20 1 (2005) 163-168
6. Attarakih M.M., Bart H.-J., and Faqir N.M. Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid-liquid extraction columns. Chemical Engineering Science 61 (2006) 113-123
7. Finlayson B.A. The Method of Weighted Residuals and Variational Principles (1972), Academic Press, New York
8. Friedlander S.K. Smoke, Dust, and Haze. Fundamentals of Aerosol Dynamics (2000), Oxford University Press, New York, NY
9. Gelbard F., and Seinfeld J.H. Coagulation and growth of a multicomponent aerosol. Journal of Colloid and Interface Science 63 3 (1978) 472-479
10. Gelbard F., and Seinfeld J.H. Simulation of multicomponent aerosol dynamics. Journal of Colloid and Interface Science 78 (1980) 485-501
11. Gillespie D.T. An exact method for numerically simulating the stochastic coalescence process in a cloud. Journal of the Atmospheric Sciences 32 (1975) 1977-1989
12. Heintzenberg J., and Covert D.S. On the distribution of physical and chemical particle properties in the atmospheric aerosol. Journal of Atmospheric Chemistry 10 (1990) 383-397
13. Iveson S.M. Limitations of one-dimensional population balance models of wet granulation processes. Powder Technology 124 (2002) 219-229
14. Kim Y.P., and Seinfeld J.H. Simulation of multicomponent aerosol dynamics. Journal of Colloid and Interface Science 149 2 (1992) 425-449
15. Kronberger T., Ortner A., Zulehner W., and Bart H.-J. Numerical simulation of extraction columns using a drop population model. Computers and Chemical Engineering 19 (1995) 639-644
16. Laurenzi I.J., Bartels J.D., and Diamond S.L. A general algorithm for exact simulation of multicomponent aggregation processes. Journal of Computational Physics 177 (2002) 418-449
17. Lushnikov A. Evolution of coagulating systems III. Coagulating mixtures. Journal of Colloid and Interface Science 54 1 (1976) 94-101
18. Mantzaris N.V., Daoutidis P., and Srienc F. Numerical solution of multi-variable cell population balance models: I. Finite difference methods. Computers and Chemical Engineering 25 (2001) 1411-1440
19. Mantzaris N.V., Daoutidis P., and Srienc F. Numerical solution of multi-variable cell population balance models: II. Spectral methods. Computers and Chemical Engineering 25 (2001) 1441-1462
20. Mantzaris N.V., Daoutidis P., and Srienc F. Numerical solution of multi-variable cell population balance models: III. Finite elements methods. Computers and Chemical Engineering 25 (2001) 1463-1481
21. Marchisio D.L., and Fox R.O. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science 36 (2005) 43-73
22. Noble C.A., and Prather K.A. Real-time measurement of correlated size and composition profiles of individual atmospheric aerosol particles. Environmental Science and Technology 30 (1996) 2667-2680
23. Obrigkeit D.D., and McRae G.J. Integrated framework for the numerical solution of multicomponent population balances. 1. Formulation, representation, and growth mechanisms. Industrial & Engineering Chemistry Research 43 (2004) 4380-4393
24. Obrigkeit D.D., Resch T.J., and McRae G.J. Integrated framework for the numerical solution of multicomponent population balances. 2. The split composition distribution method. Industrial & Engineering Chemistry Research 43 (2004) 4394-4404
25. Pilinis C. Derivation and numerical-solution of the species mass-distribution equations for multicomponent particulate systems. Atmospheric Environment Part A: General 24 (1990) 1923-1928
26. Qamar S., and Warnecke G. Solving population balance equations for two-component aggregation by a finite volume scheme. Chemical Engineering Science 62 (2007) 679-693
27. Qamar S., Ashfaq A., Elsner M.P., Angelov I., Warnecke G., and Seidel-Morgenstern A. Adaptive high resolution schemes for multidimensional population balances in crystallization processes. Computers and Chemical Engineering 31 (2007) 1296-1311
28. Ramabhadran T.E., Peterson T.W., and Seinfeld J.H. Dynamics of aerosol coagulation and condensation. A.I.Ch.E. J. 22 5 (1976) 840-851
29. Ramkrishna D., and Mahoney A.W. Population balance modelling. Promise for the future. Chemical Engineering Science 57 (2002) 595-606
30. Ramkrishna D. Population Balances. Theory and Applications to Particulate Systems in Engineering (2000), Academic Press, SanDiego, CA
31. Ramkrishna D. The status of population balances. Review in Chemical Engineering 3 1 (1985) 49-95
32. Rosner D.E., McGraw R., and Tandon P. Multivariate population balances via moment and Monte-Carlo simulation methods: an important sol reaction engineering bivariate example and "mixed" moments for the estimation of deposition, scavenging, and optical properties for populations of nonspherical suspended particles. Industrial & Engineering Chemistry Research 42 (2003) 2699-2711
33. Roussos A.I., Alexopoulos A.H., and Kiparissides C. Part III: dynamic evolution of the particle size distribution in batch and continuous particulate processes: a Galerkin on finite elements approach. Chemical Engineering Science 61 (2005) 124-134
34. Spiegel M.R., and Liu J. Schaum's Mathematical Handbook of Formulas and Tables (1998), McGraw-Hill, New York
35. Toon O.B., Turco R.P., Westphal D., Malone R., and Liu M.S. A multidimensional model for aerosols-description of computational analogs. Journal of the Atmospheric Sciences 45 (1988) 2123
36. Tsang T.H., and Rao A. A moving finite element method for the population balance equation. International Journal for Numerical Methods in Fluids 10 (1990) 753-769
37. Vale H.G., and McKenna T.F. Solution of the population balance equation for two-component aggregation by an extended fixed pivot technique. Industrial & Engineering Chemistry Research 44 20 (2005) 7885-7891
38. Vemury S., Janzen C., and Pratsinis S.E. Coagulation of symmetric and asymmetric bipolar aerosols. Journal of Aerosol Science 28 4 (1997) 599-611
39. Verkoijen D., Pouw G.A.P., Meesters G.M.H., and Scarlett B. Population balances for particulate processes-a volume approach. Chemical Engineering Science 57 (2002) 2287-2303
40. Xiong Y., and Pratsinis S. Formation of agglomerate particles by coagulation and sintering-part 1. A two-dimensional solution of the population balance equation. Journal of Aerosol Science 24 (1993) 283-300