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Original Articles

Population Balances for Extraction Column Simulations—An Overview

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References

  • Hanson, C. Recent Advances in Liquid-Liquid Extraction; Pergamon Press: New York, 1971.
  • Godfrey, J.; Slater, M. J. Liquid-liquid Extraction Equipment; John Wiley & Sons: New York, 1994.
  • Bart, H.-J. Reactive Extraction; Springer: Heidelberg, 2001.
  • Bart, H.-J.; Stevens, G. Reactive Solvent Extraction. In Ion Exchange and Solvent Extraction; Marcus, Y.; SenGupta, A. K., Eds.; New York: Marcel Dekker; 2004. p. 37–83.
  • Lo, T. C.; Baird, M. H. I.; Hanson, C. Handbook of Solvent Extraction; Wiley: New York, 1983.
  • Pilhofer, T.; Mewes, D. Siebbodenextraktionskolonnen: Vorausberechnung unpulsierter Kolonnen. Verlag Chemie: Weinheim (Germany); 1979.
  • Fair, J.; Humphrey, J. Liquid-Liquid Extraction: Possible Alternative to Distillation. Solvent Extr. Ion Exch. 1984, 2(3), 323–352. DOI: 10.1080/07366298408918451.
  • Casamatta, G.; Vogelpohl, A. Modelling of Fluid Dynamics and Mass Transfer in Extraction Columns. Ger. Chem. Eng. 1985, 8(2), 96–103.
  • Henley, E.; Seader, J.; Roper, D. Separation Process Principles: Chemical and Biochemical Operations, 3rd ed. ed.; Hoboken Wiley: New Jersey, 2011.
  • Steinmetz, T.; Bart, H.-J. Scale-up of Mini-Plant Extractors on Energy Dissipation-Based Population Balances. Chem. Eng. Technol. 2009, 32(5), 693–709. DOI: 10.1002/ceat.200800610.
  • Chesters, A. Modelling of Coalescence Processes in Fluid-Liquid Dispersions. A Review of Current Understanding. Chem. Eng. Res. Des. 1991, 69(4), 259–270.
  • Simon, M.;, Koaleszenz Von Tropfen Und Tropfenschwärmen. Dissertation, TU Kaiserslautern, Germany, 2004.
  • Eiswirth, R. Binary Coalescence of Free Rising Droplets. Dissertation, TU Kaiserslautern, Germany, 2015.
  • Kamp, J.; Kraume, M. Influence of Drop Size and Superimposed Mass Transfer on Coalescence in Liquid/Liquid Dispersions—Test Cell Design for Single Drop Investigations. Chem. Eng. Res. Des. 2014, 92(4), 635–643. DOI: 10.1016/j.cherd.2013.12.023.
  • Villwock, J.; Gebauer, F.; Kamp, J.; Bart, H.-J.; Kraume, M. Systematic Analysis of Single Droplet Coalescence. Chem. Eng. Technol. 2014, 37(7), 1103–1111. DOI: 10.1002/ceat.v37.7.
  • Kopriwa, N. Quantitative Beschreibung von Koaleszenzvorgängen in Extraktionskolonnen. Dissertation, RWTH Aachen, Germany, 2013.
  • Bapat, P. M.; Tavlarides, L. L. Mass Transfer in a Liquid-Liquid CFSTR. AIChE J. 1985, 31(4), 659–666. DOI: 10.1002/(ISSN)1547-5905.
  • Maaß, S. Experimental Analysis, Modeling and Simulation of Drop Breakage in Agitated Turbulent Liquid/Liquid-Dispersions. Dissertation, TU Berlin, Germany, 2011.
  • Schmidt, S. A.; Simon, M.; Bart, H.-J. Tropfenpopulationsmodellierung—Einfluss von Stoffsystem und technischen Geometrien. Chem. Ing. Technol. 2003, 75(1–2), 62–68. DOI: 10.1002/cite.200390023.
  • Schmidt, S. A.; Simon, M.; Attarakih, M. M.; Lagar, L. G.; Bart, H.-J. Droplet Population Balance Modelling—Hydrodynamics and Mass Transfer. Chem. Eng. Sci. 2006, 61, 246–256. DOI: 10.1016/j.ces.2005.02.075.
  • Henschke, M.;, Auslegung Pulsierter Siebboden-Extraktionskolonnen, Habilitationsschrift, RWTH Aachen, Germany, 2004.
  • Klinger, S. Messung Und Modellierung Des Spaltungs- Und Koaleszenzverhaltens Von Tropfen Bei Der Extraktion. Dissertation, RWTH Aachen, Germany, 2008.
  • Attarakih, M. M.; Bart, H.-J.; Lagar, L. G.; Faqir, N. LLECMOD: A Windows-based Program for Hydrodynamics Simulation of Liquid–Liquid Extraction Columns. Chem. Eng. Process. 2006, 45, 113–123. DOI: 10.1016/j.cep.2005.03.012.
  • Jildeh, H. Liquid-Liquid Extraction Columns. Parameter Estimation, Dissertation, TU Kaiserslautern, Germany, 2015.
  • Drumm, C.; Attarakih, M. M.; Hlawitschka, M. W.; Bart, H.-J. One-Group Reduced Population Balance Model for CFD Simulation of a Pilot-Plant Extraction Column. Ind. Eng. Chem. Res. 2010, 49(7), 3442–3451. DOI: 10.1021/ie901411e.
  • Bart, H.-J.; Drumm, C.; Attarakih, M. M. Process Intensification with Reactive Extraction Columns. Chem. Eng. Process. Process. Intensif. 2008, 47(5), 745–754. DOI: 10.1016/j.cep.2007.11.005.
  • Ramkrishna, D.;. The Status of Population Balances. Rev. Chem. Eng. 1985, 3(1), 49–95. DOI: 10.1515/REVCE.1985.3.1.49.
  • Ramkrishna, D.; Mahoney, A.; Population balance modeling. Promise for the Future. Chem. Eng. Sci. 2002, 57(4), 595–606. DOI: 10.1016/S0009-2509(01)00386-4.
  • Yeoh, G.; Chrung, C.; Tu, J. Multiphase Flow Analysis Using Population Balance Modeling: Bubbles, Drops and Particles; Butterworth-Heinemann: Amsterdam, 2014.
  • Hulburt, H.; Katz, S. Some Problems in Particle Technology: A Statistical Mechanical Formulation. Chem. Eng. Sci. 1964, 19(8), 555–574. DOI: 10.1016/0009-2509(64)85047-8.
  • Randolph, A.; Larson, M. Transient and Steady State Size Distributions in Continuous Mixed Suspension Crystallizers. AIChE J. 1962, 8(5), 639–645. DOI: 10.1002/(ISSN)1547-5905.
  • Ramkrishna, D.;. Population Balances: Theory and Applications to Particulate Systems in Engineering; Academic Press: San Diego, 2000.
  • Costa, C. B. B.; Maciel, M. R. W.; Filho, R. Considerations on the Crystallization Modeling: Population Balance Solution. Comput. Chem. Eng. 2007, 31(3), 206–218. DOI: 10.1016/j.compchemeng.2006.06.005.
  • Henson, A.; Dynamic Modeling of Microbial Cell Populations. Curr. Opin. Biotechnol. 2003, 14(5), 460–467. DOI: 10.1016/S0958-1669(03)00104-6.
  • Buffo, A.; Vanni, M.; Marchisio, D. L. Multidimensional Population Balance Model for the Simulation of Turbulent Gas–Liquid Systems in Stirred Tank Reactors. Chem. Eng. Sci. 2012, 70, 31–44. DOI: 10.1016/j.ces.2011.04.042.
  • Valentas, K. J.; Amundson, N. R. Breakage and Coalescence in Dispersed Phase Systems. Ind. Eng. Chem. Fundam. 1966, 5(4), 533–542. DOI: 10.1021/i160020a018.
  • Jiřičný, V.; Krátký, M. Procházka, J. Counter-Current Flow of Dispersed and Continuous Phase I: Discrete Polydispersed Model. J. Chem. Eng. Sci. 1979, 34(9), 1141–1149. DOI: 10.1016/0009-2509(79)85020-4.
  • Jiřičný, V.; Krátký, M.; Procházka, J. Counter-Current Flow of Dispersed and Continuous Phase II: Simulation of Hold-up and Particle Size Distribution Profiles. Chem. Eng. Sci. 1979, 34(9), 1151–1158. DOI: 10.1016/0009-2509(79)85021-6.
  • Jiřičný, V.; Procházka, J. Counter-Current Flow of Dispersed and Continuous Phase III Measurements of Hold-up Profiles and Particle Size Distributions in a Vibrating Plate Contactor. Chem. Eng. Sci. 1980, 35(11), 2237–2245. DOI: 10.1016/0009-2509(80)87001-1.
  • Casamatta, G. Comportement De La Population Des Gouttes Dans Une Colonne d’Extraction: Transport, Rupture, Coalescence, Transfert De Matière (Behaviour of the Drop Population in an Extraction Column. Transport, Rupture, Coalescence, Transfer of Matter), Dissertation, Institut du Génie Chimique, Toulouse, France, 1981.
  • Casamatta, G.; Vogelpohl, A. Modellierung der Fluiddynamik und des Stoffübergangs in Extraktionskolonnen. Chem. Ing. Technol. 1984, 56(3), 230–231. DOI: 10.1002/cite.330560313.
  • Bart, H.-J.; Garthe, D.; Grömping, T.; Pfennig, A.; Schmidt, S.; Stichlmair, J. Vom Einzeltropfenexperiment zur Extraktionskolonne. AiF final report No. 40 ZN: 01.01.2001-31.10.2004, January 14, 2014. http://www.avt.rwth-aachen.de/AVT/fileadmin/redaktion/avt/TVT/AIF_40_ZN_1_2_3_2005.pdf (accessed Oct 19, 2019).
  • Hoting, B. Untersuchungen zur Fluiddynamik und Stoffübertragang in Extraktionskolonnen mit strukturierten Packungen. Dissertation, TU Clausthal, Germany, 1996.
  • Haverland, H.; Vogelpohl, A.; Gourdon, C.; Casamatta, G. Simulation of Fluid Dynamics in a Pulsed Sieve Plate Column. Chem. Eng. Technol. 1987, 10(1), 151–157. DOI: 10.1002/(ISSN)1521-4125.
  • Haverland, H. Untersuchungen zur Tropfendispergierung in flüssigkeitspulsierten Siebboden-Extraktionskolonnen, Dissertation, TU Clausthal, Germany, 1988.
  • Gourdon, C.; Casamatta, G. Influence of Mass Transfer Direction on the Operation of a Pulsed Sieve-Plate Pilot Column. Chem. Eng. Sci. 1991, 46(11), 2799–2808. DOI: 10.1016/0009-2509(91)85149-R.
  • Toutain, J.; Le Lann, J. M.; Gourdon, C. Joulia, Maxwell-Stefan Approach Coupled Drop Population Model for the Dynamic Simulation of Liquid-liquid Extraction Pulsed Column-Comput. Chem. Eng. 1998, 22, 379–386.
  • Jaradat, M.; Attarakih, M. M.; Bart, H.-J. Advanced Prediction of Pulsed (Packed and Sieve Plate) Extraction Columns Performance Using Population Balance Modelling. Chem. Eng. Res. Des. 2011, 89(12), 2752–2760. DOI: 10.1016/j.cherd.2011.05.009.
  • Alzyod, S.; Attarakih, M. M.; Bart, H.-J. CFD Modeling of Pulsed Sieve Plate Liquid Extraction Columns Using OPOSPM as a Reduced Population Balance Model: Hydrodynamics and mass transfer. Comput. Aided Chem. Eng. 2018, 43, 451–456.
  • Attarakih, M. M.; Bart, H.-J.; Faqir, N. Numerical Solution of the Spatially Distributed Population Balance Equation Describing the Hydrodynamics of Interacting Liquid-Liquid Dispersions. Chem. Eng. Sci. 2004, 59(12), 2567–2592. DOI: 10.1016/j.ces.2004.03.005.
  • Attarakih, M. M.; Bart, H.-J.; Faqir, N. Solution of the Droplet Breakage Equation for Interacting Liquid-Liquid Dispersions: A Conservative Discretization Approach. Chem. Eng. Sci. 2004, 59(12), 2547–2565. DOI: 10.1016/j.ces.2004.03.004.
  • Attarakih, M. M.; Bart, H.-J.; Faqir, N. Numerical Solution of the Bivariate Population Balance Equation for the Interacting Hydrodynamics and Mass Transfer in Liquid-Liquid Extraction Columns. Chem. Eng. Sci. 2006, 61(1), 113–123. DOI: 10.1016/j.ces.2004.12.055.
  • Attarakih, M. M.; Bart, H.-J.; Steinmetz, T.; Dietzen, M.; Faqir, N. LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid-Liquid Extraction Columns. Open Chem. Eng. J. 2008, 2, 10–34. DOI: 10.2174/1874123100802010010.
  • Attarakih, M. M.; Jaradat, M.; Bart, H.-J.; Kuhnert, J.; Drumm, C.; Tiwari, S.; Sharma, V.; Klar, A. A Multivariate Sectional Quadrature Method of Moments for the Solution of the Population Balance Equation. In 20th European Symposium on Computer Aided Process Engineering; Pierucci, S., Ferraris, G. B., Eds.; Elsevier: Amsterdam, 2010; Vol. 2010, pp 1551–1556.
  • Attarakih, M. M.; Jildeh, H. B.; Mickler, M.; Bart, H.-J. The OPOSPM as a Nonlinear Autocorrelation Population Balance Model for Dynamic Simulation of Liquid Extraction Columns. In 11th International Symposium on Process Systems Engineering; Karimi, I. A., Srinivasan, R., Eds.; Elsevier: Amsterdam, 2012; pp 1216–1220.
  • Attarakih, M. M.; Al-Zyod, S.; Abu-Khader, M.; Bart, H.-J. PPBLAB: A New Multivariate Population Balance Environment for Particulate System Modelling and Simulation. Procedia Engineering. 2012, 42, 1445–1462. DOI: 10.1016/j.proeng.2012.07.538.
  • Attarakih, M. M.; Abu-Khader, M.; Bart, H.-J. Modeling and Dynamic Analysis of a Rotating Disc Contactor (RDC) Extraction Column Using One Primary and One Secondary Particle Method (OPOSPM). Chem. Eng. Sci. 2013, 91, 180–196. DOI: 10.1016/j.ces.2013.01.032.
  • Attarakih, M. M.; Bart, H.-J. Solution of the Population Balance Equation Using the Differential Maximum Entropy Method (Dmaxentm): An Application to Liquid Extraction Columns. Chem. Eng. Sci. 2014, 108, 123–133. DOI: 10.1016/j.ces.2013.12.031.
  • Attarakih, M. M.; Hasseine, A.; Bart, H.-J. CFD Modelling of Bubbly Gas Flow Using Coupled OPOSPM-Two-Fluid Model. Comput. Aided Chem. Eng. 2016, 38, 403–406.
  • Attarakih, M. M.; Alzyod, S.; Fricke, A. Population Balance Modelling of Pulsed Packed Bed Extraction Columns Using PPPLab Software. Comput. Aided Chem. Eng. 2017, 40, 67–72.
  • Modes, G. Grundlegende Studie zur Populationsdynamik einer Extraktionskolonne auf Basis von Einzeltropfenuntersuchungen. Dissertation, TU Kaiserslautern, Germany, 2000.
  • Modes, G.; Bart, H.-J.; Rodriguez-Perancho, D.; Bröder, D. Simulation of the Fluid Dynamics of Solvent Extraction Columns from Single Droplet Parameters. Chem. Eng. Technol. 1999, 3, 231–236. DOI: 10.1002/(SICI)1521-4125(199903)22:3<231::AID-CEAT231>3.0.CO;2-C.
  • Schmidt, S. A. Populationsdynamische Simulation gerührter Extraktionskolonnen auf Basis von Einzeltropfen- und Tropfenschwarmuntersuchungen. Dissertation, TU Kaiserslautern, Germany, 2006.
  • Zamponi, G. Das dynamische Verhalten einer gerührten Solventextraktionskolonne. Dissertation, TU München, Germany, 1996.
  • Kolb, P. Hydrodynamik und Stoffaustausch in einem gerührten Miniplantextraktor der Bauart Kühni. Dissertation, TU Kaiserslautern, Germany, 2004.
  • Steinmetz, T. Tropfenpopulationsbilanzgestütztes Auslegungsverfahren zur Skalierung einer gerührten Mini-Plant Extraktionskolonne. Dissertation, TU Kaiserslautern, Germany, 2007.
  • Alzyod, S. A Coupled SQMOM-CFD Population Balance Framework for Modelling and Simulation of Liquid-liquid Extraction Equipment. Dissertation, TU Kaiserslautern, Germany, 2018.
  • Drumm, C. Coupling of Computational Fluid Dynamics and Population Balance Modelling for Liquid-Liquid Extraction. Dissertation, TU Kaiserslautern, Germany, 2010.
  • Hlawitschka, M. W. Computational Fluid Dynamics Aided Design of Stirred Liquid-Liquid Extraction Columns. Dissertation, TU Kaiserslautern, Germany, 2013.
  • Jildeh, H.; Hlawitschka, M. W.; Attarakih, M. M.; Bart, H.-J. Solution of Inverse Problem with the One Primary and One Secondary Particle Model (OPOSPM) Coupled with Computational Fluid Dynamics (CFD). Procedia Engineering. 2012, 42, 1692–1710. DOI: 10.1016/j.proeng.2012.07.562.
  • Vikhansky, A.; Kraft, M. Modelling of a RDC Using a Combined CFD-population Balance Approach. Chem. Eng. Sci. 2004, 59, 2597–2606. DOI: 10.1016/j.ces.2004.02.016.
  • Drumm, C.; Bart, H.-J. In 6th Int. Conference on Multiphase Flow; Sommerfeld, M., Tropea, C., Eds.; Leipzig; 2007, p S6.
  • Drumm, C.; Attarakih, M. M.; Bart, H.-J. Coupling of CFD with DPBM for an RDC Extractor. Chem. Eng. Sci. 2009, 64(4), 721–732. DOI: 10.1016/j.ces.2008.05.041.
  • Hlawitschka, M. W.; Bart, H.-J. Determination of Local Velocity, Energy Dissipation and Phase Fraction with LIF- and PIV-Measurement in a Kühni Miniplant Extraction Column. Chem. Eng. Sci. 2012, 69(1), 138–145. DOI: 10.1016/j.ces.2011.10.019.
  • McGraw, R.;. Description of Aerosol Dynamics by the Quadrature Method of Moments. Aerosol. Sci. Technol. 1997, 27(2), 255–265. DOI: 10.1080/02786829708965471.
  • Mohanty, S.;. Modeling of Liquid-Liquid Extraction Column: A Review. Rev. Chem. Eng. 2000, 16(3), 199–248. DOI: 10.1515/REVCE.2000.16.3.199.
  • Attarakih, M. M. Solution Methodologies for the Population Balance Equations Describing the Hydrodynamics of Liquid-Liquid Extraction Contactors. Dissertation, TU Kaiserslautern, Germany, 2004.
  • Marchisio, D. L.; Fox, R. O. Solution of Population Balance Equations Using the Direct Quadrature Method of Moments. J. Aerosol. Sci. 2005, 36(1), 43–73. DOI: 10.1016/j.jaerosci.2004.07.009.
  • Dorao, C.; Jakobsen, H. Solution of Population Balance Equations Using the Direct Quadrature Method of Moments. J. Comput. Appl. Math. 2006, 196(2), 619–633. DOI: 10.1016/j.cam.2005.10.015.
  • Su, J.; Gu, Z.; Xu, X.; Advances in Numerical Methods for the Solution of Population Balance Equations for Disperse Phase Systems. Sci. China Ser. B. 2009, 52(8), 1063–1079. DOI: 10.1007/s11426-009-0164-2.
  • Kronberger, T. Numerische Simulation von Tropfenpopulationen in Extraktionskolonnen. Dissertation, JK University Linz, Austria, 1995.
  • Ortner, A. Numerische Simulation instationärer Transportphänomene bei der Solvent-Extraktion in Gegenstromkolonnen. Dissertation, JK University Linz, Austria, 1995.
  • Wulkow, M.; Gerstlauer, A.; Nieken, U. Modeling and Simulation of Crystallization Processes Using Parsival. Chem. Eng. Sci. 2001, 56(7), 2575–2588. DOI: 10.1016/S0009-2509(00)00432-2.
  • Kumar, S.; Ramkrishna, D. On the Solution of Population Balance Equations by Discretization—I A Fixed Pivot Technique. Chem. Eng. Sci. 1996, 51(8), 1311–1332. DOI: 10.1016/0009-2509(96)88489-2.
  • Kumar, S.; Ramkrishna, D. On the Solution of Population Balance Equations by Discretization—II A Moving Pivot Technique. Chem. Eng. Sci. 1996, 51(8), 1333–1342. DOI: 10.1016/0009-2509(95)00355-X.
  • Attarakih, M. M.; Bart, H.-J. On the Solution of the Smoluchowski Coagulation Equation Using a Conservative Discretization Approach (CDA). Comput. Aided Chem. Eng. 2019, 46, 691–696.
  • Jaradat, M.; Attarakih, M. M.; Steinmetz, T.; Bart, H.-J. LLECMOD: A Bivariate Population Balance Simulation Tool for Pulsed Liquid-Liquid Extraction Columns. Open Chem. Eng. J. 2012, 6, 8–31. DOI: 10.2174/1874123101206010008.
  • Zhao, H.; Maisels, A.; Matsoukas, T.; Zheng, C. Analysis of Four Monte Carlo Methods for the Solution of Population Balances in Dispersed Systems. Powder Technol. 2007, 173(1), 38–50. DOI: 10.1016/j.powtec.2006.12.010.
  • Liffman, K.;. A Direct Simulation Monte-Carlo Method for Cluster Coagulation. J. Comput. Phys. 1992, 100(1), 116–127. DOI: 10.1016/0021-9991(92)90314-O.
  • Garcia, A.; van den Broeck, C.; Aertsens, M.; Serneels, R. A Monte Carlo Simulation of Coagulation. Phys. A. 1987, 143(3), 535–546. DOI: 10.1016/0378-4371(87)90164-6.
  • Altunok, M.; Grömping, T.; Pfennig, A. ReDrop—An Efficient Simulation Tool for Describing Solvent and Reactive Extraction Columns, In: Computer Aided Chemical Engineering. In 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering; Marquardt, W., Pantelides, C., Eds.; Elsevier: Amsterdam, 2006; pp 665–670.
  • Kalem, M.; Buchbender, F.; Pfennig, A. Simulation of Hydrodynamics in RDC Extraction Columns Using the Simulation Tool “Redrop”. Chem. Eng. Res. Des. 2011, 89(1A), 1–9. DOI: 10.1016/j.cherd.2010.05.001.
  • Goodson, M.; Kraft, M. Simulation of Coalescence and Breakage: An Assessment of Two Stochastic Methods Suitable for Simulating Liquid-Liquid Extraction. Chem. Eng. Sci. 2004, 59(18), 3865–3881. DOI: 10.1016/j.ces.2004.05.029.
  • Vikhansky, A.; Kraft, M.; Simon, M.; Schmidt, S.; Bart, H.-J. Droplets Population Balance in a Rotating Disc Contactor: An Inverse Problem Approach. AIChE J. 2006, 52(4), 1441–1450. DOI: 10.1002/(ISSN)1547-5905.
  • Adinata, D.; Ayesterán, J.; Buchbender, F.; Kalem, M.; Kopriwa, N.; Pfennig, A. Tropfenpopulationsbilanzen zur Auslegung von Extraktionskolonnen. Chem. Ing. Technol. 2011, 83(7), 952–964. DOI: 10.1002/cite.201100016.
  • Marchisio, D.; Pikturna, J.; Fox, R.; Vigil, R. D.; Barresi, A. Quadrature Method of Moments for Population-Balance Equations. AIChE J. 2003, 49(5), 1266–1276. DOI: 10.1002/(ISSN)1547-5905.
  • Marchisio, D.; Vigil, R. D.; Fox, R. Implementation of the Quadrature Method of Moments in CFD Codes for Aggregation–Breakage Problems. Chem. Eng. Sci. 2003, 58(15), 3337–3351. DOI: 10.1016/S0009-2509(03)00211-2.
  • Marchisio, D.; Vigil, R. D.; Fox, R. Quadrature Method of Moments for Aggregation–Breakage Processes. J. Colloid Interface Sci. 2003, 258(2), 322–334. DOI: 10.1016/S0021-9797(02)00054-1.
  • Buffo, A.; Vanni, M.; Marchisio, D.; Fox, R. Multivariate Quadrature-Based Moments Methods for Turbulent Polydisperse Gas–Liquid Systems. Int. J. Multiphase Flow. 2013, 50, 41–57. DOI: 10.1016/j.ijmultiphaseflow.2012.09.005.
  • Attarakih, M. M.; Drumm, C.; Bart, H.-J. Solution of the Population Balance Equation Using the Sectional Quadrature Method of Moments (SQMOM). Chem. Eng. Sci. 2009, 64(4), 742–752. DOI: 10.1016/j.ces.2008.05.006.
  • Yuan, C.; Fox, R. Conditional Quadrature Method of Moments for Kinetic Equations. J. Comput. Phys. 2011, 230(22), 8216–8246. DOI: 10.1016/j.jcp.2011.07.020.
  • Attarakih, M. M.; Jaradat, M.; Allaboun, H.; Bart, H.-J.; Faqir, N. M. Dynamic Modeling of a Rotating Disk Contactor Using the Primary and Secondary Particle Method (PSPM). In 6th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, S. T. Johansen, J. E. Olsen, A. Ashrafian, Eds.; SINTEF/NTNU:Trondheim, Norway, 2008.
  • Attarakih, M. M.; Jaradat, M.; Drumm, C.; Bart, H.-J.; Tiwari, S.; Sharma, V. Solution of the Population Balance Equation Using the One Primary One Secondary Particle Method (OPOSPM). In 19th European Symposium on Computer Aided Process Engineering; Jezowski, J., Thullie, J., Eds.; Elsevier: Amsterdam, 2009; pp 1333–1338.
  • Jildeh, H.; Attarakih, M. M.; Bart, H.-J. Coalescence Parameter Estimation in Liquid Extraction Column Using OPOSPM. In 11th International Symposium on Process Systems Engineering; Karimi, I. A., Srinivasa, R., Eds.; Elsevier: Amsterdam, 2012; pp 960–964.
  • Jildeh, H.; Attarakih, M. M.; Mickler, M.; Bart, H.-J. An Online Inverse Problem for the Simulation of Extraction Columns Using Population Balances. In 22nd European Symposium on Computer Aided Process Engineering; Bogle, I. D. L., Fairweather, M., Eds.; Elsevier: Amsterdam, 2012; pp 1043–1047.
  • Jildeh, H.; Attarakih, M. M.; Mickler, M.; Bart, H.-J. Parameter Optimisation and Validation for Droplet Population Balances. Can. J. Chem. Eng. 2014, 92(2), 210–219. DOI: 10.1002/cjce.21892.
  • Bart, H.-J.; Mickler, M.; Jildeh, H. Optical Image Analysis and Determination of Dispersed Multi Phase Flow for Simulation and Control. In Optical Imaging: Technology, Methods and Applications; Tanaka, A., Nakamura, B., Eds.; Nova Science: New York, 2012; pp 1–63.
  • Mickler, M.; Jildeh, H.; Attarakih, M. M.; Bart, H.-J. Online Monitoring, Simulation and Prediction of Multiphase Flows. Can. J. Chem. Eng. 2014, 92(2), 307–317. DOI: 10.1002/cjce.21893.
  • Attarakih, M. M.; Jaradat, M.; Hlawitschka, M. W.; Bart, H.-J.; Kuhnert, J. Integral Formulation of the Population Balance Equation Using the Cumulative QMOM. In 21st European Symposium on Computer Aided Process Engineering; Pistikopoulos, E. N., Georgiadis, M. C., Kokossis, A. C., Eds.; Elsevier: Amsterdam, 2011; pp 81–85.
  • Attarakih, M. M. Integral Formulation of the Population Balance Equation: Application to Particulate Systems with Particle Growth. Comput. Chem. Eng. 2013, 48, 1–13. DOI: 10.1016/j.compchemeng.2012.08.001.
  • Attarakih, M. M.; Kuhnert, J.; Wächtler, T.; Abu-Khader, M.; Bart, H.-J. Solution of the Population Balance Equation using the Normalized QMOM (NQMOM). In 8th Int. Conference on CFD in Oil & Gas, Metallurgical and Process Industry; Johannsen, S. T., Eds: SINTEF/NTNN: Trondheim, Norway, 2011.
  • Wächtler, T.; Kuhnert, J.; Attarakih, M. M.; Tiwari, S.; Klar, A.; Bart, H.-J. The Normalized Quadrature Method of Moments Coupled with Finite Pointset Method. In 2nd Int. Conf. Particle-based Methods—Fundamentals and Applications; Onate, E., Owen, D. R. J., Eds.: Barcelona, 2011.
  • Wächtler, T. Numerical Simulation of Turbulent Dispersions in Liquid-Liquid Extraction Columns, Dissertation, TU Kaiserslautern, Germany, 2014.
  • Attarakih, M. M.; Bart, H.-J. A Novel MaxEnt Method for the Solution of Two-Dimensional Population Balance Equation with Particle Growth. In 24th European Symposium on Computer Aided Process Engineering; Klemeš, J. J., Varbanov, P. S., Liew, P. Y., Eds.; Elsevier: Amsterdam, 2014; pp 901–906.
  • Cruz-Pinto, J.; Korchinsky, W. Drop Breakage in Counter Current Flow Liquid-Liquid Extraction Columns. Chem. Eng. Sci. 1981, 36(4), 695–703. DOI: 10.1016/0009-2509(81)85084-1.
  • Weiss, J.; Steiner, L.; Hartland, S. Determination of Actual Drop Velocities in Agitated Extraction Columns. Chem. Eng. Sci. 1995, 50(2), 255–261. DOI: 10.1016/0009-2509(94)00237-L.
  • Wegener, M.; Paul, N.; Kraume, M.; Fluid Dynamics and Mass Transfer at Single Droplets in Liquid/Liquid Systems. Int. J. Heat Mass Transfer. 2014, 71, 475–495. DOI: 10.1016/j.ijheatmasstransfer.2013.12.024.
  • Cauwenberg, V.; Degrève, J.; Slater, M. The Interaction of Solute Transfer, Contaminants and Drop Break-up in Rotating Disc Contactors: Part II the Coupling of the Mass Transfer and Breakage Processes via Interfacial Tension. Can. J. Chem. Eng. 1997, 75(6), 1056–1066.
  • Cauwenberg, V.; Degreve, J.; Slater, M. The Interaction of Solute Transfer, Contaminants and Drop Break-up in Rotating Disc Contactors: Part I. Correlation of Drop Breakage Probabilities, Can. J. Chem. Eng. 1997, 75, 1046–1055.
  • Wegener, M. Der Einfluss der Konzentrationsinduzierten Marangonikonvektion auf den instationären Impuls- und Stofftransport an Einzeltropfen. Dissertation, TU Berlin, Germany, 2009.
  • Heine, J.Bart, H.-J., Visualization Of Mass Transfer during Droplet Formation, Chem.Eng. Technol. 2019, 42(7), 1–8.
  • Wagner, I. Der Einfluss der Viskosität auf den Stoffübergang in Flüssig-flüssig-Extraktionskolonnen. Dissertation, TU München, Germany, Hieronymus Verlag, München, Germany, 1999.
  • Lewis, W.; Whiteman, W. Principles of Gas Absorption, Ind. Eng. Chem. 1924, 16(12), 1215–1220.
  • Kumar, A.; Hartland, S. Correlations for Prediction of Mass Transfer Coefficients in Single Drop Systems and Liquid–Liquid Extraction Columns, S. Chem. Eng. Res. Des. 1999, 77(5), 372–384. DOI: 10.1205/026387699526359.
  • Kumar, A. Hydrodynamics and Mass Transfer in Kühni Extractor. Dissertation, ETH Zürich, Switzerland, 1985.
  • Heertjes, P.; Holve, W.; Talsma, H. Mass Transfer between Isobutanol and Water in a Spray-Column. Chem. Eng. Sci. 1954, 3(3), 122–142. DOI: 10.1016/0009-2509(54)80017-0.
  • Handlos, A.; Baron, T. Mass and Heat Transfer from Drops in Liquid-Liquid Extraction. AIChE J. 1957, 3(1), 127–136. DOI: 10.1002/(ISSN)1547-5905.
  • Blass, E. Engineering Design and Calculation of Extractors for Liquid-Liquid Systems. In Principles and Practices of Solvent Extraction; Rydberg, J.; Musikas, C.; Choppin, G. R., eds; Marcel Dekker: New York; 1992. p. 267–314.
  • Kronig, R.; Brink, J. On the Theory of Extraction from Falling Droplets. Appl. Sci. Res. 1951, 2(1), 142–154. DOI: 10.1007/BF00411978.
  • Garner, F.; Tayeban, M. The Importance of the Wake in Mass Transfer from Both Continuous and Dispersed Phase Systems. Ann. Real. Soc. Esp. Fis. Quim. (Madrid). 1960, 56(5), 479–480.
  • Treybal, R. Liquid Extraction; McGraw-Hill: New York, 1963.
  • Newman, A.; The Drying of Porous Solids: Diffusion and Surface Emission Equations. AIChE J. 1931, 27, 203–220.
  • Skelland, A. H. P.; Wellek, R. M. Resistance to Mass Transfer inside Droplets. AIChE J. 1964, 10(4), 491–496. DOI: 10.1002/(ISSN)1547-5905.
  • Korchinsky, W.; Cruz-Pinto, J. Mass Transfer Coefficients—Calculation for Rigid and Oscillating Drops in Extraction Columns. Chem. Eng. Sci. 1979, 34(4), 551–561. DOI: 10.1016/0009-2509(79)85100-3.
  • Bart, H.-J.; Extraction Columns in hydrometallurgy. Hydrometallurgy. 2005, 78(1–2), 21–29. DOI: 10.1016/j.hydromet.2004.12.008.
  • Bart, H.-J.; Slater, M. European Federation of Chemical Engineering (EFCE) - Test Systems for Liquid Extraction: Standard Test System for Reactive Extraction—Zinc/D2EHPA. 2014. http://www.processnet.org/processnet_media/EFCE_Testsysteme-p-88.pdf. (accessed Oct 10, 2019).
  • Sainz-Diaz, C.; Klocker, H.; Marr, R.; Bart, H.-J. New Approach in the Modelling of the Extraction Equilibrium of Zinc with Bis-(2-Ethylhexyl) Phosphoric Acid. Hydrometallurgy. 1996, 42(1), 1–11. DOI: 10.1016/0304-386X(95)00075-R.
  • Corsi, C.; Gnagnarelli, G.; Slater, M.; Vegliò, F. A Study of the Kinetics of Zinc Stripping for the System Zn/H2SO4/D2EHPA/n-heptane in A Hancil Constant Interface Cell and A Rotating Disc Contactor. Hydrometallurgy. 1998, 50(2), 125–141. DOI: 10.1016/S0304-386X(98)00050-4.
  • Wachter, B. A Possible Recommended Reactive Liquid/Liquid System Zinc/Di (2-ethyhexyl) Phosphoric Acid/n-Dodecane: Modelling of Equilibrium by Means of Simulsolv. Dissertation, TU Graz, Austria; 1996.
  • Mansur, M.; Slater, M.; Biscaia, E. Kinetic Equilibrium Analysis of the Reactive Liquid-Liquid Test System ZnSO4/D2EHPA/n-Heptane. Hydrometallurgy. 2002, 63(2), 117–126. DOI: 10.1016/S0304-386X(01)00211-0.
  • Mansur, M.; Slater, M.; Biscaia, E. Kinetic Analysis of the Reactive Liquid-Liquid Test System ZnSO4/D2EHPA/n-heptane. Hydrometallurgy. 2002, 63(2), 107–116. DOI: 10.1016/S0304-386X(01)00210-9.
  • Mansur, M.; Slater, M.; Biscaia, E. Reactive Extraction of Zinc Sulfate with Bis(2-ethylhexyl)phosphoric Acid in a Short Kühni Column Used in Batch Mode. Ind. Eng. Chem. Res. 2003, 42(17), 4068–4076. DOI: 10.1021/ie020883y.
  • Neto, P.; Mansur, M. Transient Modeling of Zinc Extraction with D2EHPA in a Kühni Column. Chem. Eng. Res. Des. 2013, 91(12), 2323–2332. DOI: 10.1016/j.cherd.2013.05.014.
  • Ji, J.; Mensforth, K.; Perera, J.; Stevens, G. The Role of Kinetics in the Extraction of Zinc with D2EHPA in a Packed Column. Hydrometallurgy. 2006, 84(3–4), 139–148. DOI: 10.1016/j.hydromet.2006.03.062.
  • Kalem, M.; Altunok, M. Y.; Pfennig, A. Sedimentation Behavior of Droplets for the Reactive Extraction of Zinc with D2EHPA. AIChE J. 2010, 56(1), 160–167.
  • Altunok, M.; Kalem, M.; Pfennig, A. Investigation of Mass Transfer on Single Droplets for the Reactive Extraction of Zinc with D2EHPA. AIChE J. 2012, 58(5), 1346–1355. DOI: 10.1002/aic.v58.5.
  • Altunok, M. Zur Auslegung von Siebbodenextraktionskolonnen für die Reaktivextraktion basierend auf Versuchen im Labormassstab. Dissertation, RWTH Aachen, Germany; 2009.
  • Korb, C.; Bart, H.-J. Solvent Extraction in Columns in a Droplet Breakage Domain. Hydrometallurgy. 2017, 173, 71–79. DOI: 10.1016/j.hydromet.2017.08.009.
  • Korb, C. Extraktionskolonnen für Reaktivextraktion. Dissertation, TU Kaiserslautern, Kaiserslautern, 2019.
  • Nitsch, W. Transportprozesse und chemische Reaktionen an fluiden Phasengrenzflächen; DECHEMA Monographie. VCH Verlagsgesellschaft mbH: Weinheim, 1989.
  • Cianetti, C.; Danesi, P. R. Kinetics and Mechanism of the Interfacial Mass Transfer of Zn 2+, Co 2+, Ni 2+ in the System: Bis(2-Ethylhexyl)Phosphoric Acid, n-Dodecane - Kno 3, Water. Solvent Extr. Ion Exch. 1983, 1(1), 9–26. DOI: 10.1080/07366298308918390.
  • Klocker, H.; Bart, H.-J.; Marr, R.; Müller, M. Mass Transfer Based on Chemical Potential Theory: ZnSO4/H2SO4/D2EHPA. AIChE J. 1997, 43(10), 2479–2487. DOI: 10.1002/aic.690431011.
  • Willersinn, S.; Bart, H.-J. Reactive Mass Transfer in a Membrane-based Microcontactor. Chem. Eng. Process. Process Intensif. 2015, 95, 186–194. DOI: 10.1016/j.cep.2015.05.015.
  • Willersinn, S.; Bart, H.-J. Kinetics of Ge(IV) Extraction Using a Microstructured Membrane Contactor. Int. J. Chem. Kinet. 2016, 48(10), 609–621. DOI: 10.1002/kin.2016.48.issue-10.
  • Willersinn, S. Reactive Extraction Kinetics in a Membrane-based Microcontactor. Dissertation, TU Kaiserslautern, Kaiserslautern, 2017.
  • VDI e.V. VDI Heat Atlas; Berlin: Springer; 2010.
  • Ruff, K.; Pilhofer, T.; Mersmann, A. Vollständige Durchströmung von Lochböden bei der Fluid-Dispergierung. Chem. Ing. Technol. 1976, 48(9), 759–764. DOI: 10.1002/cite.330480906.
  • Mersmann, A.;. Auslegung und Maßstabsvergrößerung von Blasen- und Tropfensäulen. Chem. Ing. Technol. 1977, 49(9), 679–691. DOI: 10.1002/cite.330490902.
  • Blaß, E.;. Bildung und Koaleszenz von Blasen und Tropfen. Chem. Ing. Technol. 1988, 60(12), 935–947. DOI: 10.1002/cite.330601203.
  • Möhring, D.; Weiss, S. Zur Effektivität von Flüssigkeitsverteilern in Extraktionskolonnen. Teil 1: Problemstellung Und Experimente. Chem. Ing. Technol. 1997, 69(6), 812–816. DOI: 10.1002/cite.330690610.
  • Koch, J.; Vogelpohl, A. Ein lastunabhäniger Verteiler für die Flüssig/Flüssig-Extraktion. Chem. Ing. Technol. 2000, 72(11), 1356–1358. DOI: 10.1002/1522-2640(200011)72:11<1356::AID-CITE1356>3.0.CO;2-G.
  • Vignes, A.;. Hydrodynamique Des Dispersions - Mouvement D´un Globule Dans Un Fluide Immobile Et Infini. Genie Chim. 1965, 93(5), 129–142.
  • Klee, A.; Treybal, R. Rate of Rise or Fall of Liquid Drops. AIChE J. 1956, 2(4), 444–447. DOI: 10.1002/(ISSN)1547-5905.
  • Grace, J.; Wairegi, T.; Nguyen, T. Shapes and Velocities of Single Drops and Bubbles Moving Freely through Immiscible Liquids. Trans. Inst. Chem. Eng. 1976, 54(3), 167–173.
  • Clift, R.; Grace, J.; Weber, M. E. Bubbles, Drops, and Particles., 3rd ed. ed.; Academic Press: New York, NY, 1992.
  • Wesselingh, J. A.; Bohlen, M.; Particles, S. Bubbles and Drops. Chem. Eng. Res. Des. 1999, 77(2), 89–96. DOI: 10.1205/026387699525954.
  • Godfrey, J.; Slater, M. J. Slip Velocity Relationships for Liquid-Liquid Extraction Columns. Chem. Eng. Res. Des. 1991, 69(2), 130–141.
  • Bailes, P.; Gledhill, J.; Godfrey, J.; Slater, M. J. Hydrodynamic Behaviour of Packed, Rotating Disc and Kühni Liquid/Liquid Extraction Columns. Chem. Eng. Res. Des. 1986, 64(1), 43–55.
  • Fang, J.; Godfrey, J.; Mao, Z.-Q.; Slater, M. J.; Gourdon, C. Single Liquid Drop Breakage Probabilities and Characteristic Velocities in Kühni Columns. Chem. Eng. Technol. 1995, 18(1), 41–48. DOI: 10.1002/(ISSN)1521-4125.
  • Seikova, I.; Gourdon, C.; Casamatta, G. Single-Drop Transport in a Kühni Extraction Column. Chem. Eng. Sci. 1992, 47(15–16), 4141–4154. DOI: 10.1016/0009-2509(92)85164-7.
  • Gourdon, C.; Casamatta, G.; Angelino, H. Single Drop experiments with Liquid Test Systems: A Way of Comparing Two Types of Mechanically Agitated Extraction Columns. Chem. Eng. J. 1991, 46(3), 137–148. DOI: 10.1016/0300-9467(91)87005-U.
  • Haunold, C.; Cabassud, M.; Gourdon, C.; Casamatta, G. Drop Behaviour in a Kühni Column for a Low Interfacial Tension System. Can. J. Chem. Eng. 1990, 68(3), 407–414. DOI: 10.1002/cjce.v68:3.
  • Bahmanyar, H.; Slater, M. Studies of Drop Break-up in Liquid-Liquid Systems in a Rotating Disc Contactor. Part I: Conditions of No Mass Transfer. Chem. Eng. Technol. 1991, 14(2), 79–89. DOI: 10.1002/(ISSN)1521-4125.
  • Garthe, D. Fluiddynamics and Mass Transfer of Single Particles and Swarms of Particles in Extraction Columns. Dissertation, TU München, Germany, 2006.
  • Narsimhan, G.; Nejfelt, G.; Ramkrishna, D. Breakage Functions for Droplets in Agitated Liquid-Liquid Dispersions. AIChE J. 1984, 30(3), 457–467. DOI: 10.1002/(ISSN)1547-5905.
  • Li, N.; Ziegler, E. N. Effect of Axial Mixing on Mass Transfer in Extraction Columns. Ind. Eng. Chem. 1967, 59(3), 30–36. DOI: 10.1021/ie51402a008.
  • Macías-Salinas, R.; Fair, J. Axial Mixing in Modern Packings, Gas and Liquid Phases: I. Single-Phase Flow. AIChE J. 1999, 45(2), 222–239. DOI: 10.1002/(ISSN)1547-5905.
  • Langmuir, I.;. The Velocity of Reactions in Gases Moving through Heated Vessels and the Effect of Convection and Diffusion. J. Am. Chem. Soc. 1908, 30(11), 1742–1754.
  • Breysse, J.; Bühlmann, U.; Godfrey, C. Axial Mixing Characteristics of Industrial and Pilot Scale Kühni Columns. AIChE Symp. Ser. 1984, 80(238), 94–101.
  • Bauer, R. Die Längsvermischung beider Phasen in einer gerührten Fest-Flüssig-Extraktionskolonne. Dissertation, ETH Zürich. Zürich, 1976.
  • Kumar, A.; Hartland, S. Prediction of Axial Mixing Coefficients in Rotating Disc and Asymmetric Rotating Disc Extraction Columns. Can. J. Chem. Eng. 1992, 70(1), 77–87. DOI: 10.1002/cjce.v70:1.
  • Strand, C. P.; Olney, R. B.; Ackerman, G. H. Fundamental Aspects of Rotating Disk Contactor Performance. AIChE J. 1962, 8(2), 252–261. DOI: 10.1002/(ISSN)1547-5905.
  • Sovová, H.;. Breakage and Batch Coalescence of Drops in a Stirred Vessel-II Comparison of Model and Experiments. Chem. Eng. Sci. 1981, 36(9), 15671573.
  • Coulaloglou, C.; Tavlarides, L. L. Description of Interaction Processes in Agitated Liquid-Liquid Dispersions. Chem. Eng. Sci. 1977, 32(11), 1289–1297. DOI: 10.1016/0009-2509(77)85023-9.
  • Tsouris, C.; Tavlarides, L. L. Breakage and Coalescence Models for Drops in Turbulent Dispersions. AIChE J. 1994, 40(3), 395–406. DOI: 10.1002/(ISSN)1547-5905.
  • Kumar, A.; Hartland, S. A Unified Correlation for the Prediction of Dispersed-Phase Hold-Up in Liquid-Liquid Extraction Columns. Ind. Eng. Chem. Res. 1995, 34(11), 3925–3940. DOI: 10.1021/ie00038a032.
  • Drumm, C.; Hlawitschka, M. W.; Bart, H.-J. CFD Simulations and Particle Image Velocimetry Measurements in an Industrial Scale Rotating Disc Contactor. AIChE J. 2011, 57(1), 10–26. DOI: 10.1002/aic.12249.
  • Burghoff, S.; Kenig, E. Y. A CFD Model for Mass Transfer and Interfacial Phenomena on Single Droplets. AIChE J. 2006, 52(12), 4071–4078. DOI: 10.1002/(ISSN)1547-5905.
  • Hinze, J. O.; Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes. AIChE J. 1955, 1(3), 289–295. DOI: 10.1002/(ISSN)1547-5905.
  • Liao, Y.; Lucas, D. A Literature Review of Theoretical Models for Drop and Bubble Breakup in Turbulent Dispersions. Chem. Eng. Sci. 2009, 64(15), 3389–3406. DOI: 10.1016/j.ces.2009.04.026.
  • Buchbender, F. Single-Drop-Based Modelling of Drop Residence Times in Kühni Columns. Dissertation, RWTH Aachen, Germany, 2013.
  • Kolmogorov, A. N.;. Sammelband zur statistischen Theorie der Turbulenz; Akademieverlag: Berlin, 1958.
  • Narsimhan, G.; Gupta, J.; Ramkrishna, D. A Model for Transitional Breakage Probability of Droplets in Agitated Lean Liquid-Liquid Dispersions. Chem. Eng. Sci. 1979, 34(2), 257–265. DOI: 10.1016/0009-2509(79)87013-X.
  • Laso, M. A Model for the Dynamic Simulation of Liquid-Liquid Dispersion. Dissertation, ETH Zürich, Switzerland, 1986.
  • Hesketh, R. P.; Etchells, A. W.; Russell, T. W. F. Bubble Breakage in Pipeline Flow. Chem. Eng. Sci. 1991, 46(1), 1–9. DOI: 10.1016/0009-2509(91)80110-K.
  • Kentish, S.; Stevens, G.; Pratt, H. Estimation of Coalescence and Breakage Rate Constants within a Kühni Column. Ind. Eng. Chem. Res. 1998, 37(3), 1099–1106. DOI: 10.1021/ie970336q.
  • Martínez-Bazán, C.; Montanés, J.; Lasheras, J. On the Breakup of an Air Bubble Injected into a Fully Developed Turbulent Flow. Part 1. Breakup Frequency. J. Fluid. Mech. 1999, 401, 157–182. DOI: 10.1017/S0022112099006680.
  • Alopaeus, V.; Koskinen, J.; Keskinen, K.; Majander, J. Simulation of the Population Balances for Liquid–Liquid Systems in a Nonideal Stirred Tank. Part 2—Parameter Fitting and the Use of the Multiblock Model for Dense Dispersions. Chem. Eng. Sci. 2002, 57(10), 1815–1825. DOI: 10.1016/S0009-2509(02)00067-2.
  • Lehr, F.; Millies, M.; Mewes, D. Bubble-Size Distributions and Flow Fields in Bubble Columns. AIChE J. 2002, 48(11), 2426–2443. DOI: 10.1002/(ISSN)1547-5905.
  • Laso, M.; Steiner, L.; Hartland, S. Dynamic Simulation of Liquid-Liquid Agitated Dispersions-I. Derivation of a Simplified Model. Chem. Eng. Sci. 1987, 42(10), 2429–2436. DOI: 10.1016/0009-2509(87)80116-1.
  • Maaß, S.; Kraume, M. Determination of Breakage Rates Using Single Drop Experiments. Chem. Eng. Sci. 2012, 70, 146–164. DOI: 10.1016/j.ces.2011.08.027.
  • Chen, Z.; Prüss, J.; Warnecke, H.-J. A Population Balance Model for Disperse Systems: Drop Size Distribution in Emulsion. Chem. Eng. Sci. 1998, 53(5), 1059. DOI: 10.1016/S0009-2509(97)00328-X.
  • Bahmanyar, H.; Dean, D.; Dowling, I.; Ramlochan, K.; Slater, M.; Yu, W. Studies of Drop Break-up in Liquid-Liquid Systems in a Rotating Disc Contactor. Part II: Effects of Mass Transfer and Scale-up. Chem. Eng. Technol. 1991, 14(3), 178–185. DOI: 10.1002/(ISSN)1521-4125.
  • Simon, M.; Schmidt, S.; Bart, H.-J. Bestimmung von Zerfalls- und Koaleszenzparametern in Flüssig/Flüssig-Systemen auf der Grundlage von Einzeltropfenexperimenten. Chem. Ing. Technol. 2002, 74(3), 247–256. DOI: 10.1002/1522-2640(200203)74:3<247::AID-CITE247>3.0.CO;2-B.
  • Hasseine, A.; Meniai, A.-H.; Korichi, M.; Lehocine, M.; Bart, H.-J. A Genetic Algorithm Based Approach Coalescence Parameters: Estimation in Liquid-Liquid Extraction Columns. Chem. Eng. Technol. 2006, 29(12), 1416–1423. DOI: 10.1002/ceat.200600218.
  • Cauwenberg, V. Hydrodynamics and Physico-chemical Aspects of Liquid-liquid Extraction. Dissertation, Catholic University Leuven, Belgium, 1995.
  • Eid, K.; Gourdon, C.; Casamatta, G.; Muratet, G. Drop Breakage in a Pulsed Sieve-Plate Column. Chem. Eng. Sci. 1991, 46(7), 1595–1608. DOI: 10.1016/0009-2509(91)87008-Z.
  • Leu, J. T. Beitrag zur Fluiddynamik von Extraktionskolonnen mit geordneten Packungen. Dissertation, TU Clausthal, Germany, 1995.
  • Lasheras, J.; Eastwood, C.; Martı́nez-Bazán, C.; Montañés, J. A Review of Statistical Models for the Break-up of an Immiscible Fluid Immersed into A Fully Developed Turbulent Flow. Int. J. Multiphase Flow. 2002, 28(2), 247–278. DOI: 10.1016/S0301-9322(01)00046-5.
  • Cabassud, M.; Gourdon, C.; Casamatta, G. Single Drop Break-up in a Kühni Column. Chem. Eng. J. 1990, 44(1), 27–41. DOI: 10.1016/0300-9467(90)80051-D.
  • Hančil, V.; Rod, V. Break-up of a Drop in a Stirred Tank. Chem. Eng. Process. Process Intensif. 1988, 23(3), 189–193. DOI: 10.1016/0255-2701(88)80015-1.
  • Eiswirth, R. T.; Bart, H.-J. Investigation of Binary Droplet-Coalescence in Liquid-Liquid-Systems. In Forschungsberichte, VDI-Reihe 3 (920); Schneider, F. P., ed.; Düsseldorf: VDI-Verlag; 2011. p. 15–26.
  • Tobin, T.; Ramkrishna, D. Coalescence of Charged Droplets in Agitated Liquid-Liquid Dispersions. AIChE J. 1992, 38(8), 1199–1205. DOI: 10.1002/(ISSN)1547-5905.
  • Pfennig, A.; Schwerin, A. Influence of Electrolytes on Liquid−Liquid Extraction. Ind. Eng. Chem. Res. 1998, 37(8), 3180–3188. DOI: 10.1021/ie970866m.
  • Tobin, T.; Ramkrishna, D. Modeling the Effect of Drop Charge on Coalescence in Turbulent Liquid—Liquid Dispersions. Can. J. Chem. Eng. 1999, 77(6), 1090–1104. DOI: 10.1002/cjce.v77:6.
  • Villwock, J. Systematische Analyse des Koaleszenzverhaltens von zweiphasigen Flüssigsystemen bei der Ionenzugabe. Dissertation, TU Berlin, Germany, 2019.
  • Liao, Y.; Lucas, D. A Literature Review on Mechanisms and Models for the Coalescence Process of Fluid Particles. Chem. Eng. Sci. 2010, 65(10), 2851–2864. DOI: 10.1016/j.ces.2010.02.020.
  • Mickler, M. Inline-Analyse, Simulation und Vorhersage von flüssigen Mehrphasenströmungen in Extraktionskolonnen. Dissertation, TU Kaiserslautern, Germany, 2014.
  • Lane, G. L.; Schwarz, M. P.; Evans, G. M. Numerical Modelling of Gas–Liquid Flowin Stirred Tanks. Chem. Eng. Sci. 2005, 60, 2203–2214. DOI: 10.1016/j.ces.2004.11.046.
  • Wright, H.; Ramkrishna, D. Factors Affecting Coalescence Frequency of Droplets in a Stirred Liquid-Liquid Dispersion. AIChE J. 1994, 40(5), 767–776. DOI: 10.1002/(ISSN)1547-5905.
  • Alopaeus, V.; Koskinen, J.; Keskinen, K. Simulation of the Population Balances for Liquid–Liquid Systems in a Nonideal Stirred Tank. Chem. Eng. Sci. 1999, 54(24), 5887–5899. DOI: 10.1016/S0009-2509(99)00170-0.
  • Gomes, L.; Guimarães, M.; Regueiras, P.; Stichlmair, J.; Cruz Pinto, J. Simulated and Experimental Dispersed-Phase Breakage and Coalescence Behavior in a Kühni Liquid−Liquid Extraction ColumnSteady State. Ind. Eng. Chem. Res. 2006, 45(11), 3955–3968. DOI: 10.1021/ie051453l.
  • Jaradat, M.; Attarakih, M. M.; Bart, H.-J. RDC Extraction Column Simulation Using the Multi-Primary One Secondary Particle Method: Coupled Hydrodynamics and Mass Transfer. Comput. Chem. Eng. 2012, 37, 22–32. DOI: 10.1016/j.compchemeng.2011.09.010.
  • Kabouche, A.; Meniai, A. H.; Hasseine, A. Estimation of Coalescence Parameters in an Agitated Extraction Column Using a Hybrid Algorithm. Chem. Eng. Technol. 2011, 34(5), 784–790. DOI: 10.1002/ceat.v34.5.
  • Garg, M.; Pratt, H. Measurement and Modelling of Droplet Coalescence and Breakage in a Pulsed-Plate Extraction Column. AIChE J. 1984, 30(3), 432–441. DOI: 10.1002/(ISSN)1547-5905.
  • Hamilton, J.; Pratt, H. Droplet Coalescence and Breakage Rates in a Packed Liquid Extraction Column. AIChE J. 1984, 30(3), 442–450. DOI: 10.1002/(ISSN)1547-5905.
  • Maaß, S.; Kraume, M., Investigation of Discrete Population Balance Models and Its Parameters for Turbulent Emulsification Processes. In 14th Europ. Conf. on Mixing, Warszawa, Poland; 2012, pp 251–256.
  • Simon, M.; Schmidt, A.; Bart, H.-J. The Droplet Population Balance Model—Estimation of Breakage and Coalescence. Chem. Eng. Technol. 2003, 26(7), 745–750. DOI: 10.1002/ceat.200306101.
  • Gomes, L.; Guimarães, M.; Stichlmair, J.; Cruz-Pinto, J. Effects of Mass Transfer on the Steady State and Dynamic Performance of a Kühni Column − Experimental Observations. Ind. Eng. Chem. Res. 2009, 48(7), 3580–3588. DOI: 10.1021/ie801034a.
  • Misek, T.; Berger, R.; Schröter, J. Standard Test Systems for Liquid Extraction: Working Party on Distillation, Absorption and Extraction. 2nd ed. Rugby: Institution of Chemical Engineers; 1985.
  • Goldmann, G. Ermittlung und Interpretation von Kennlinienfeldern einer gerührten Extraktionskolonne. Dissertation, TU München, Germany, 1986.
  • Hufnagl, H. Dynamisches Verhalten einr Flüssig-flüssig Extraktionskolonne. Dissertation, TU München, Germany, 1992.
  • Gerstlauer, A. Herleitung und Reduktion populationsdynamischer Modelle am Beispiel der Flüssig-Flüssig-Extraktion. Dissertation, Universität Stuttgart, Germany, 1999.

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