Analytical treatment of fragmentation-diffusion population balance

AIChE Journal

Volumn 50, Issue 8, 2004, Pages 1746-1759

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

^a Centre for Research Technology Hellas   (Greece)

^b ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

DEPOSITION; MATHEMATICAL MODELS; MICROORGANISMS; PARTICLE SIZE ANALYSIS; POPULATION STATISTICS;

FRAGMENTATION; TEMPORAL MODES;

DIFFUSION;

MODEL;

ARTICLE; DECOMPOSITION; DIFFUSION; FRAGMENTATION REACTION; PARTICLE SIZE; PROCESS MODEL;

EID: 3242749802     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.10286     Document Type: Article

References (38)

1. Austin, L. G. "A review: Introduction to the Mathematical Description of Grinding as a Rate Process," Powder Technol., 5, 1 (1972).
2. Baker, R. C. "Computational Method to Assess Concentration of Water in Crude Oil Downstream of a Mixing Section," Proc. Inst. Mech. Eng., 202, 117 (1988).
3. Carrier, G. F., and C. E. Pearson, Partial Differential Equation. Theory and Techniques, Academic Press, London (1976).
4. Carslaw, H. S., and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London (1959).
5. Courant, R., and D. Hilbert, Methods of Mathematical Physics, Wiley Interscience Classics Edition, New York (1989).
6. Diemer, R. B., and J. H. Olson, "A Moment Methodology for Coagulation and Breakage Problems Part 2-Moment Models and Distribution Reconstruction," Chem. Eng. Sci., 57, 2211 (2002a).
7. Diemer, R. B. and J. H. Olson, "A Moment Methodology for Coagulation and Breakage Problems Part 3-Generalized Daughter Distribution Functions," Chem. Eng. Sci., 57, 4187 (2002b).
8. Elimelech, M., J. Gregory, X. Jia, and R. Williams, Particle Deposition & Aggregation: Measurement, Modelling and Simulation, Butterworth-Heinemann, Oxford (1995).
9. Friedlander, S. K., Smoke, Dust and Haze, Wiley Interscience, New York (1977).
10. Karabelas, A.J., "Vertical Distribution of Dilute Suspensions in Turbulent Pipe Flow," AIChE J., 23, 426 (1977).
11. Kiparissides, C., "Polymerization Reactor Modelling: A Review of Recent Developments and Future Directions," Chem. Eng. Sci., 51, 1637 (1996).
12. Kostoglou, M., and A. J. Karabelas, "On the Breakage Problem with a Homogeneous Erosion Type Kernel," J. of Physics A: Math. Gen., 34, 1 (2001).
13. Kostoglou, M., and A. J. Karabelas, "An Assesment of Low Order Methods for the Solution of the Breakage Equation," Powder Technol., 127, 116 (2002).
14. Kumar, S., and D. Ramkrishna, "On the Solution of Population Balance Equations by Discretizations-I. A Fixed Pivot Technique," Chem. Eng. Sci., 51, 1311 (1996).
15. Lee, K., and T. Matsoukas, "Simultaneous Coagulation and Break-Up Using Constant-N Monte Carlo," Powder Technol., 110, 82 (2000).
16. Lensu, M., "Distribution of the Number of Fragmentations in Continuous Fragmentation," J. Phys. A: Math. Gen., 31, 5707 (1998).
17. Liou, J., Srienc, F., and A. G. Fredrikson, "Solutions of Population Balance Models Based on Successive Generations Approach," Chem. Eng. Sci., 52, 1529 (1997).
18. Madras, G., and B. J., McCoy, "Time Evolution to Similarity Solutions for Polymer Degradation," AIChE J., 44, 647 (1998).
19. McGrady E. D., and R. M. Ziff, "Shattering Transition in Fragmentation," Phys. Rev. Lett., 58, 892 (1987).
20. Mantzaris, N.V., P Daoutidis, and F. Srienc, "Numerical Solution of Multivariable Cell Population Balance Models I. Finite Difference Methods," Computer & Chem. Eng., 25, 1411 (2001).
21. Mihalyko, C., Blickle, T. and B. G. Lacatos, "A Simulation Model for Analysis and Design of Continuous Grinding Mills," Powder Technol., 97, 51 (1998).
22. Mishra, B.K., "Monte Carlo Simulation of Particle Breakage Process During Grinding," Powder Technol., 110, 246 (2000).
23. Nielsen, J., and J. Villadsen, Bioreaction Engineering Principles, Plenum Press, New York (1994).
24. Press, W. H., S.A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed., Cambridge University Press, New York (1992).
25. Ramkrishna, D., "Drop-Breakage in Agitated Liquid-Liquid Dispersions," Chem. Eng. Sci., 29, 987 (1974).
26. Ramkrishna, D., "The Status of Population Balances," Rev. Chem. Eng., 3, 49 (1985)
27. Ramkrishna, D., Population Balances. Theory and Application to Particulate systems in engineering, Academic Press, San Diego (2000).
28. Randolph, A. D., and M. A. Larson, Theory of Particulate Processes, Academic Press, New York (1971).
29. Senckler, M. M., O. S. L. Bruinsma, and G. M. Van Rosmalen, "Influence of Hydrodynamics on Precipitation: A computational study," Chem. Eng. Comm,. 135, 113 (1995).
30. Söhnel, O., and G. Garside, Precipitation. Basic Principles and Industrial Applications, Butterworth-Heinemann, Oxford (1992).
31. Tandon, P., and D. E. Rosner, "Codeposition on Hot CVD Surfaces: Particles Dynamics and Deposit Roughness Interactions," AIChE J., 42, 1673 (1996).
32. Turner, S., Wick, N., Hanel, R., Sedivy, R. and L. Huber, "Anomalous Diffusion on Dynamical Networks: a Model for Interacting Epithelial Cell Migration," Physica A., 320, 475 (2003).
33. Vanni, M., "Discretization Procedure for the Breakage Equation," AIChE J., 45, 916 (1999).
34. Wachi, S., and A. G. Jones, "Mass Transfer with Chemical Reaction and Precipitation," Chem. Eng. Sci., 46, 1027 (1991).
35. McCoy, B.J., and M. Wang, "Continuous-Mixture Fragmentation Kinetics: Particle Size Reduction and Molecular Cracking," Chem. Eng. Sci., 49, 3773 (1994).
36. Wang, M., Smith, J. M., and B. J. McCoy, "Continuous Kinetics for Thermal Degradation of Polymer in Solution," AIChE J., 41, 1521 (1995).
37. Williams, M. M. R., and S. K. Loyalka, Aerosol Science, Pergamon Press, New York (1991).
38. Ziff, R. M., and E. D. McGrady, "Kinetics of Polymer Degradation," Macromolecules, 19, 2513 (1986).