Investigation of discrete population balance models and breakage kernels for dilute emulsification systems

Industrial and Engineering Chemistry Research

Volumn 50, Issue 19, 2011, Pages 11358-11374

  Becker, Per Julian ^a   Puel, François ^a   Henry, Reynald ^a   Sheibat Othman, Nida ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AGITATION RATES; AUTOMATED IMAGE ANALYSIS; BREAKAGE KERNEL; CELL AVERAGES; DISPERSED PHASE; EXPERIMENTAL DATA; FINITE VOLUME; FIXED PIVOT; IN-SITU; LIQUID-LIQUIDS; LOG-NORMAL; MEAN DIAMETER; NUMERICAL DISCRETIZATION; POPULATION BALANCE MODELS; RATE KERNEL; STANDARD DEVIATION;

DISCRETE EVENT SIMULATION; ETHYLENE GLYCOL; LIQUIDS; NORMAL DISTRIBUTION; SIZE DISTRIBUTION; STAINLESS STEEL; SURFACE ACTIVE AGENTS;

EMULSIFICATION;

EID: 84860210502     PISSN: 08885885     EISSN: 15205045     Source Type: Journal    
DOI: 10.1021/ie2006033     Document Type: Article

References (52)

1. Ramkrishna, D. Population Balances-Theory and Applications to Particulate Systems in Engineering; Academic Press: San Diego, CA, 2000.
2. Ramkrishna, D.; Mahony, A. W. Population Balance Modeling. Promise for the Future. Chem. Eng. Sci. 2002, 57, 59.
3. Lasheras, J. C.; Eastwood, C.; Martinez-Bazan, C.; Montanes, J. L. A Review of Statistical Models for Break-up of an Immiscible Fluid Immersed into a Fully Developed Turbulent Flow. Int. J. Multiphase Flow 2002, 28, 247.
4. Patruno, L. E.; Dorao, C. A.; Svendsen, H. F.; Jakobsen, H. A. Analysis of breakage kernels for population balance modeling. Chem. Eng. Sci. 2009, 64, 501.
5. Liao, Y.; Lucas, D. A Litterature Review of Theoretical Models for Drop and Bubble Breakup in Turbulent Dispersions. Chem. Eng. Sci. 2009, 64, 3389-3406.
6. Coulaloglou, C. A.; Tavlarides, L. L. Description of Interaction Processes in Agitated Liquid-Liquid Dispersions. Chem. Eng. Sci. 1977, 32, 1289.
7. Alopaeus, V.; Koskinen, J.; Keskinen, K. I. Simulation of the Population Balance for Liquid-Liquid Systems in a Nonideal Stirred Tank. Part 1 Description and Qualitative Validation of the Model. Chem. Eng. Sci. 1999, 54 (24), 5887.
8. Sathyagal, A. N.; Ramkrishna, D. Droplet Breakage in Stirred Dispersions. Breakage Functions from Experimental Drip-size Distributions. Chem. Eng. Sci. 1996, 51, 1377.
9. Baldyga, J.; Podgorska, W. Drop breakup in intermittent turbulence. Maximum stable and transient sizes of drops. Can. J. Chem. Eng. 1998, 76, 456.
10. Narsimhan, G.; Gupta, J. P. A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions. Chem. Eng. Sci. 1979, 34, 257.
11. Lee, C. H.; Erickson, L. E.; Glasgow, L. A. Bubble Breakup and Coalescence in Turbulent Gas-Liquid Dispersions. Chem. Eng. Commun. 1987, 59, 65.
12. Lee, C. H.; Erickson, L. E.; Glasgow, L. A. Bubble Breakup and Coalescence in Turbulent Gas-Liquid Dispersions. Chem. Eng. Commun. 1987, 61, 181-195.
13. Prince, M. J.; Blanch, H. W. Bubble Coalescence and Break-up in Air Sparged Bubble Columns. AIChE J. 1990, 31, 1485.
14. Luo, H.; Svendsen, H. F. Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J. 1996, 42 (5), 1225.
15. Martinez-Bazan, C.; Montanes, J. L.; Lasheras, J. C. On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow. Part 1. Breakup Frequency. J. Fluid Mech. 1999, 401, 157.
16. Lehr, F.; Millies, M.; Mewes, D. Bubble-Size Distribution and Flow Fields in Bubble Columns. AIChE J. 2002, 48 (11), 2426.
17. Wang, T.; Wang, J.; Jin, Y. A Novel Theoretical Breakup Kernel Function for Bubbles/Droplets in a Turbulent Flow. Chem. Eng. Sci. 2003, 58, 4629.
18. Zhao, H.; Ge, W. A Theoretical Bubble Breakup Model for Slurry Beds or Three-phase Fluidized Beds under High Pressure. Chem. Eng. Sci. 2007, 62, 109.
19. (a) Baldyga, J.; Bourne, J. R. Chapter 15: Further Applications, in Turbulent Mixing and Chemical Reactions; John Wiley & Sons: Chichester, U.K., 1999.
20. (b) Baldyga, J.; Bourne, J. R. Chapter 5: Theory of Turbulence and Models of Turbulent Flow, in Turbulent Mixing and Chemical Reactions; John Wiley & Sons: Chichester, U.K., 1999.
21. Tsouris, C.; Tavlarides, L. L. Breakage and Coalescence Models for Drops in Tubrulent Dispersions. AIChE J. 1994, 40 (3), 395.
22. Liao,Y.; Lucas,D.ALitteratureReviewonMechanisms andModels for the Coalescence Process of Fluid Particles. Chem. Eng. Sci. 2010, 65, 2851.
23. Simon, M. Coalescence of drops and drop swarming, Koaleszenz von Tropfen und Tropfenschwärmen, PhD. Dissertation, Technische Universität Kaiserslautern, Kaiserslautern, Germany, 2004.
24. Diemer, R. B.; Olson, J. H. A moment methodology for coagulation and breage problems: part 3-generalized daughter distribution functions. Chem. Eng. Sci. 2002, 57 (19), 4187.
25. Marchisio, D. L.; Vigil, R. D.; Fox, R. O. Implementation of the Quadrature Method of Moments in CFD Codes for Aggregation-Breakage Problems. Chem. Eng. Sci. 2003, 58, 3337.
26. Bapt, P. M.; Talarides, L. L.; Smith, G. W. Mont Carlo simulation of mass transfer in liquid-liquid dispersions. Chem. Eng. Sci. 1983, 38 (12), 2003.
27. Mahoney, A. W.; Ramkrishna, D. Efficient solution of population balance equations with discontinuouties by finite elements. Chem. Eng. Sci. 2002, 57, 1107.
28. Vanni, M. Approximate population balance equations for aggregation-breakage processes. J. Colloid Interface Sci. 2000, 221 (2), 143.
29. Kostoglou, M.; Karableas, A. J. On Sectional Techniques for the Solution of the Breakage Equation. Comput. Chem. Eng. 2009, 33, 112.
30. Kumar, S.; Ramkrishna, D. On the Solution of Population Balance Equations by Discretization - I. A Fixed Pivot Technique. Chem. Eng. Sci. 1996, 51 (8), 13311.
31. Fibert, F.; Laurenc-ot, P. Numerical Simulation of the Smoluchowski Coagulation Equation. SIAM J. Sci. Comput. 2004, 25 (6), 2004.
32. Kumar, S.; Ramkrishna, D. On the Solution of Population Balance Equations by Discretization - II. A moving pivot technique. Chem. Eng. Sci. 1996, 51 (8), 1333.
33. Kumar, J.; Peglow, M.; Warnecke, G.; Heinrich, S.; Mörl, L. Improved Accuracy and Convergence of Discretized Population Balance for Aggregation: The Cell Average Technique. Chem. Eng. Sci. 2006, 61, 3327.
34. Kumar, J.; Warnecke, G.; Peglow, M.; Heinrich, S. Comparison of Numerical Methods for Solving Population Balance Equations Incorporating Aggregation and Breakage. Powder Technol. 2009, 189, 218.
35. Crombie, R. L. Cold Pearl surfactant-based blends. Int. J. Cosmet. Sci. 1997, 19, 205.
36. Khalil, A.; Puel, F.; Chevalier, Y.; Galven, J. M.; Rivoire, A.; Klein, J. P. Study of Droplet Size Distribution during an Emulsification Process using in situ Video Probe Coupled with an Automatic Image Analysis. Chem. Eng. J. 2010, 165, 946.
37. Brown, D. A. R.; Jones, P. N.; Middleton, J. C. Part A: Measuring tools and techniques for mixing and flow visualization studies. In Handbook of Industrial Mixing; Paul, E. L., Atiemo-Obeng, V. A., Kresta, S. M., Eds.; John Wiley & Sons: Hoboken, NJ, 2004; p 145.
38. Illingworth, J.; Kittler, J. A Survey of the Hough Transform. Comput. Vision, Graphics Image Process. 1988, 44, 87.
39. Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 1941, 30, 301.
40. Leng, D. E.; Calabrese, R. V. Immiscible liquid-liquid systems. In Handbook of Industrial Mixing; Paul, E. L., Atiemo-Obeng, V. A., Kresta, S. M., Eds.; John Wiley & Sons: Hoboken, NJ, 2004; p 639.
41. Baldyga, J.; Bourne, J. R.; Pacek, A. W.; Amanullah, A.; Nienow, A. W. Effect of agitation and scale-up on drop size in turbulent dispersions: allowance for intermittency. Chem. Eng. Sci. 2001, 56, 3377.
42. Konno, M.; Aoki, M.; Saito, S. Scale Effects on Breakup Process in Liquid-Liquid Agitated Tanks. J. Chem. Eng. Jpn. 1983, 16, 312.
43. Martinez-Bazan, C.; Montanes, J. L.; Lasheras, J. C. On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow. Part 2. Size PDF of the Resulting Daughter Bubble. J. Fluid Mech. 1999, 401, 183.
44. Coulaloglou, C. A.; Tavlarides, L. L. Drop size distributions and coalescence frequencies of liquid-liquid dispersions in flow vessels. AIChE J. 1976, 22 (2), 289.
45. Sun, N.; Immanuel, C. D. Efficient Solution of Population Balance Models Employing a Hierarchical Solution Strategy based on a Multi-level Discretization. Trans. Inst. Meas. Control 2005, 27 (5), 347.
46. Kiparissides, C.; Krallis, A.; Meimaroglou, D.; Pladis, P.; Baltsas, A. From Molecular to Plant-Scale Modeling of Polymerization Processes: A Digital High-Pressure Low-Density Polyethylene Production Paradigm. Chem. Eng. Technol. 2010, 33 (11), 1754.
47. Gunawan, R.; Fusman, I.; Braaz, R. D. High resolution algorithms for multidimensional population balance equations. AIChE J. 2004, 50 (11), 2738.
48. Tanaka, H.; Inaba, S.; Nakaza, K. Steady-State Size Distribution for the Self-Similar Collision Cascade. ICARUS 1996, 123, 450.
49. Alopaeus, V.; Koskinen, J.; Keskinen, K. I. Simulation of the Population Balance for Liquid-Liquid Systems in a Nonideal Stirred Tank. Part 2. Parameter Fitting and the Use id the Multiblock Model for Dense Dispersions. Chem. Eng. Sci. 2002, 57 (10), 1815.
50. Zhou, G.; Kresta, S. M. Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank. Chem. Eng. Sci. 1998, 53, 2063.
51. Zhou, G.; Kresta, S. M. Evolution of drop size distributions in liquid-liquid dispersions for various impellers. Chem. Eng. Sci. 1998, 53, 2099.
52. Pacek, A. W.; Chamsart, S.; Nienow, A. W.; Bakker, A. The influence of impeller type on mean drop size and drop size distribution in an agitated vessel. Chem. Eng. Sci. 1999, 54, 4211.