A state-of-the-art review on single drop study in liquid-liquid extraction: Experiments and simulations

doi:10.1016/j.cjche.2019.03.025

Abstract

Abstract: The experimental and numerical investigations of single drop in liquid/liquid extraction system have been reviewed with particular focus on experimental techniques and computational fluid dynamic simulation approaches. Comprehensive surveys of available experimental techniques and numerical approaches for single drop rising and falling were given. Subsequently, single drop mass transfer was also reviewed both experimentally and numerically. Additionally, single drop breakage and coalescence process and the influencing factors were summarized and compared, so as to establish sub-models for population balance model. Future directions on single drop mass transfer, drop breakage and coalescence were suggested. It is believed that the single drop is a powerful tool to assist extraction process design from lab-scale to pilot-scale.

Key words: Solvent extraction, Mass transfer, Single drop, Drop breakage and coalescence, CFD simulation, Population balance model

摘要： The experimental and numerical investigations of single drop in liquid/liquid extraction system have been reviewed with particular focus on experimental techniques and computational fluid dynamic simulation approaches. Comprehensive surveys of available experimental techniques and numerical approaches for single drop rising and falling were given. Subsequently, single drop mass transfer was also reviewed both experimentally and numerically. Additionally, single drop breakage and coalescence process and the influencing factors were summarized and compared, so as to establish sub-models for population balance model. Future directions on single drop mass transfer, drop breakage and coalescence were suggested. It is believed that the single drop is a powerful tool to assist extraction process design from lab-scale to pilot-scale.

关键词: Solvent extraction, Mass transfer, Single drop, Drop breakage and coalescence, CFD simulation, Population balance model

Jiyizhe Zhang, Yundong Wang, Geoffrey W. Stevens, Weiyang Fei. A state-of-the-art review on single drop study in liquid-liquid extraction: Experiments and simulations[J]. Chinese Journal of Chemical Engineering, 2019, 27(12): 2857-2875.

Jiyizhe Zhang, Yundong Wang, Geoffrey W. Stevens, Weiyang Fei. A state-of-the-art review on single drop study in liquid-liquid extraction: Experiments and simulations[J]. 中国化学工程学报, 2019, 27(12): 2857-2875.

References

[1] E. Müller, R. Berger, E. Blass, D. Sluyts, A. Pfennig, Liquid-Liquid Extraction, Ullmann's Encyclopedia of Industrial Chemistry, 2002.
[2] J.D. Law, T.A. Todd, Liquid-liquid extraction equipment, Hydrometallurgy 42(3) (2008) 1247-1252.
[3] S.S. Ye, Q. Tang, J.S. Qiao, Y.D. Wang, Physical properties measurements and CFD simulations in settler of different P507-kerosene systems, CIESC J. 67(2) (2016) 458-468(in Chinese).
[4] Y. Zou, Y.D. Wang, W.Y. Fei, Research progress of mixer-settler extractor, Process Equip. Piping. 51(5) (2014) 40-46(in Chinese).
[5] S. Mohanty, Modeling of liquid-liquid extraction column:A review, Rev. Chem. Eng. 16(3) (2000) 199-248.
[6] K.E. Wardle, T.R. Allen, R. Swaney, CFD simulation of the separation zone of an annular centrifugal contactor, Sep. Sci. Technol. 44(3) (2009) 517-542.
[7] N. Kopriwa, F. Buchbender, J. Ayesterán, M. Kalem, A. Pfennig, A critical review of the application of drop-population balances for the design of solvent extraction columns:I. Concept of solving drop-population balances and modelling breakage and coalescence, Solvent Extr. Ion Exch. 30(7) (2012) 683-723.
[8] D. Adinata, Single-drop based modelling of solvent extraction in high-viscosity systems, Ph. D. Thesis RWTH Achen Univ., Germany, 2011.
[9] J.S. Hadamard, Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux, Acad. Sci. 152(1911) 1735-1738(in French).
[10] W. Rybczynski, Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium, Acad. Sci. 1(1911) 40-46(in German).
[11] M. Wegener, N. Paul, M. Kraume, Fluid dynamics and mass transfer at single droplets in liquid/liquid systems, Int. J. Heat Mass Transf. 71(2014) 475-495.
[12] A.E. Hamielec, S.H. Storey, J. Whitehead, Viscous flow around fluid spheres at intermediate Reynolds numbers (II), Can. J. Chem. Eng. 41(6) (1963) 246-251.
[13] Z.G. Feng, E.E. Michaelides, Drag coefficients of viscous spheres at intermediate and high Reynolds numbers, J. Fluids Eng. 123(4) (2001) 841-849.
[14] V.Y. Rivkind, G.M. Ryskin, Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers, Fluid Dynamics 11(1) (1976) 5-12.
[15] A. Saboni, S. Alexandrova, Numerical study of the drag on a fluid sphere, AIChE J 48(12) (2002) 2992-2994.
[16] H. Brauer, Particle/fluid transport processes, Fortschritte in der Verfahrenstechnik, VDI, Verlag, Düsseldorf, 1979, (Band 17).
[17] A.D. Polyanin, V.V. Dilman, Methods of Modeling Equations and Analogies in Chemical Engineering, CRC Pr I Llc, City, 1994.
[18] R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops, and Particles, Academic Press, 1978.
[19] J.R. Grace, Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Chem. Eng. Res. Des. 54(1976) 167-173.
[20] M. Henschke, A. Pfennig, Mass-transfer enhancement in single-drop extraction experiments, AIChE J. 45(10) (1999) 2079-2086.
[21] S. Hu, R.C. Kinter, The fall of single liquid drops through water, AIChE J. 1(1) (1955) 42-48.
[22] A.J. Klee, R.E. Treybal, Rate of rise or fall of liquid drops, AIChE J. 2(4) (1956) 444-447.
[23] R.R. Schroeder, R.C. Kintner, Oscillations of drops falling in a liquid field, AIChE J. 11(1) (1965) 5-8.
[24] G. Thorsen, R.M. Stordalen, S.G. Terjesen, On the terminal velocity of circulating and oscillating liquid drops, Chem. Eng. Sci. 23(5) (1968) 413-426.
[25] R.M. Edge, C.D. Grant, The terminal velocity and frequency of oscillation of drops in pure systems, Chem. Eng. Sci. 26(7) (1971) 1001-1012.
[26] M. Yamaguchi, T. Fujimoto, T. Katayama, Experimental studies of mass transfer rate in the dispersed phase and moving behavior for single oscillating drops in liquidliquid systems, J. Chem. Eng. Jpn 8(5) (1975) 361-366.
[27] M. Wegener, M. Kraume, A.R. Paschedag, Terminal and transient drop rise velocity of single toluene droplets in water, AIChE J. 56(1) (2010) 2-10.
[28] K. Bäumler, M. Wegener, A.R. Paschedag, E. Bänsch, Drop rise velocities and fluid dynamic behavior in standard test systems for liquid/liquid extraction-Experimental and numerical investigations, Chem. Eng. Sci. 66(3) (2011) 426-439.
[29] R.M. Griffith, The effect of surfactants on the terminal velocity of drops and bubbles, Chem. Eng. Sci. 17(12) (1962) 1057-1070.
[30] R.M. Edge, C.D. Grant, The motion of drops in water contaminated with a surfaceactive agent, Chem. Eng. Sci. 27(9) (1972) 1709-1721.
[31] M.D. Leven, J. Newman, The effect of surfactant on the terminal and interfacial velocities of a bubble or drop, AIChE J. 22(4) (1976) 695-701.
[32] X.J. Li, Z.S. Mao, W. Fei, Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems, Chem. Eng. Sci. 58(16) (2003) 3793-3806.
[33] T. Misek, R. Berger, J. Schröter, Standard Test Systems for Liquid Extraction Studies, EFCE Publ. Ser, 1985.
[34] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39(1) (1981) 201-225.
[35] S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79(1) (1988) 12-49.
[36] E. Bertakis, S. Groß, J. Grande, O. Fortmeier, A. Reusken, A. Pfennig, Validated simulation of droplet sedimentation with finite-element and level-set methods, Chem. Eng. Sci. 65(6) (2010) 2037-2051.
[37] R.F. Engberg, E.Y. Kenig, Numerical simulation of rising droplets in liquid-liquid systems:A comparison of continuous and sharp interfacial force models, Int. J. Heat Fluid Flow 50(2014) 16-26.
[38] Z.Q. Huang, H. Wang, VOF simulation studies on single droplet fluid dynamic behavior in liquid-liquid flow process, J. Chem. Eng. Jpn 51(1) (2018) 33-48.
[39] W. Dijkhuizen, M. van Sint Annaland, H. Kuipers, Numerical investigation of closures for interface forces in dispersed flows using a 3D front tracking model, Fourth International Conference on CFD in the Oil and Gas, Metallurgical & Process Industries, Trondheim, Norway, 2005.
[40] G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, A fronttracking method for the computations of multiphase flow, J. Comput. Phys. 169(2) (2001) 708-759.
[41] A.E. Komrakova, D. Eskin, J.J. Derksen, Lattice Boltzmann simulations of a single nbutanol drop rising in water, Phys. Fluids 25(4) (2013), 042102.
[42] M. Adekojo Waheed, M. Henschke, A. Pfennig, Simulating sedimentation of liquid drops, Int. J. Numer. Methods Eng. 59(14) (2004) 1821-1837.
[43] R.T. Eiswirth, H.J. Bart, T. Atmakidis, E.Y. Kenig, Experimental and numerical investigation of a free rising droplet, Chem. Eng. Process. 50(7) (2011) 718-727.
[44] R.F.Engberg,E.Y.Kenig,Aninvestigationoftheinfluenceofinitialdeformationon fluid dynamics of toluene droplets in water, Int. J. Multiphase Flow 76(2015) 144-157.
[45] M.J. Brodkorb, D. Bosse, C. Von Reden, A. Gorak, M.J. Slater, Single drop mass transfer in ternary and quaternary liquid-liquid extraction systems, Chem. Eng. Process. Process Intensif. 42(11) (2003) 825-840.
[46] J. Temos, H.R.C. Pratt, G.W. Stevens, Mass transfer to freely-moving drops, Chem. Eng. Sci. 51(1) (1996) 27-36.
[47] T.K. Sherwood, J.E. Evans, J.V.A. Longcor, Extraction in spray and packed columns, Ind. Eng. Chem. 31(9) (1939) 1144-1150.
[48] F.B. West, P.A. Robinson, A.C. Morgenthaler, T.R. Beck, D.K. McGregor, Liquid-liquid extraction from single drops, Ind. Eng. Chem. 43(1) (1951) 234-238.
[49] A.H.P. Skelland, R.M. Wellek, Resistance to mass transfer inside droplets, AIChE J. 10(4) (1964) 491-496.
[50] M.J. Slater, M.H.I. Baird, T.B. Liang, Drop phase mass transfer coefficients for liquid-liquid systems and the influence of packings, Chem. Eng. Sci. 43(2) (1988) 233-245.
[51] L. Steiner, G. Oezdemir, S. Hartland, Single-drop mass transfer in the water-toluene-acetone system, Ind. Eng. Chem. Res. 29(7) (1990) 1313-1318.
[52] T. Al-Hassan, C.J. Mumford, G.V. Jeffreys, A study of mass transfer from single large oscillating drops, Chem. Eng. Technol. 15(3) (1992) 186-192.
[53] M. Henschke, A. Pfennig, Influence of sieve trays on the mass transfer of single drops, AIChE J. 48(2) (2002) 227-234.
[54] Y.L. Lee, Surfactants effects on mass transfer during drop-formation and drop falling stages, AIChE J. 49(7) (2003) 1859-1869.
[55] M. Wegener, M. Kraume, A.R. Paschedag, Influence of Marangoni convection on mass transfer at non-spherical droplets, Chem. Eng. Trans. 17(2009) 525-530.
[56] M. Wegener, A.R. Paschedag, M. Kraume, Mass transfer enhancement through Marangoni instabilities during single drop formation, Int. J. Heat Mass Transf. 52(11-12) (2009) 2673-2677.
[57] Z. Azizi, A. Rahbar, H. Bahmanyar, Investigation of packing effect on mass transfer coefficient in a single drop liquid extraction column, Iran. J. Chem. Chem. Eng. 7(4) (2010) 3-11.
[58] M. Wegener, A.R. Paschedag, Mass transfer enhancement at deformable droplets due to Marangoni convection, Int. J. Multiphase Flow 37(1) (2011) 76-83.
[59] M. Wegener, A.R. Paschedag, The effect of soluble anionic surfactants on rise velocity and mass transfer at single droplets in systems with Marangoni instabilities, Int. J. Heat Mass Transf. 55(5-6) (2012) 1561-1573.
[60] H. Zheng, W. Ren, K. Chen, Y. Gu, Z. Bai, S. Zhao, Influence of Marangoni convection on mass transfer in the n-propyl acetate/acetic acid/water system, Chem. Eng. Sci. 111(2014) 278-285.
[61] Z. Huang, C. Ye, L. Li, X. Zhang, T. Qiu, Measurement and correlation of the mass transfer coefficient for a liquid-liquid system with high density difference, Braz. J. Chem. Eng. 33(4) (2016) 897-906.
[62] Z. Azizi, M. Rezaeimanesh, Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid, Chem. Eng. Res. Des. 115(2016) 44-52.
[63] Z. Wang, P. Lu, Y. Wang, C. Yang, Z.S. Mao, Experimental investigation and numerical simulation of Marangoni effect induced by mass transfer during drop formation, AIChE J. 59(11) (2013) 4424-4439.
[64] A.T. Popovich, R.E. Jervis, O. Trass, Mass transfer during single drop formation, Chem. Eng. Sci. 19(5) (1964) 357-365.
[65] A.H.P. Skelland, S.S. Minhas, Dispersed phase mass transfer during drop formation and coalescence in liquid-liquid extraction, AIChE J. 17(6) (1971) 1316-1324.
[66] W.J. Heideger, M.W. Wright, Liquid extraction during drop formation:effect of formation time, AIChE J. 32(8) (2010) 1372-1376.
[67] J.D. Thornton, T.J. Anderson, K.H. Javed, S.K. Achwal, Surface phenomena and mass transfer interactions in liquid-liquid systems, AIChE J. 31(7) (1985) 1069-1076.
[68] A.B. Newman, The drying of porous solid:Diffusion and surface emission effects, Trans. AIChE 27(1931) 203-216.
[69] R. Kronig, J.C. Brink, On the theory of extraction from falling droplets, Appl. Sci. Res. 2(1) (1951) 142.
[70] A.E. Handlos, T. Baron, Mass and heat transfer from drops in liquid-liquid extraction, AIChE J. 3(1) (1957) 127-136.
[71] T.W. Li, Z.S. Mao, J.Y. Chen, W.Y. Fei, Terminal effect of drop coalescence on single drop mass transfer measurements and its minimization, Chin. J. Chem. Eng. 9(2) (2001) 204-207.
[72] T.W. Li, Experimental and Simulation Study of Steady Mass Transfer in Single Drop at Medium Reynolds Number, Ph. D. Thesis, Institute of Chemical Metallurgy Chinese Academy of Sciences, China, 1998.
[73] K.H. Javed, J.D. Thornton, T.J. Anderson, Surface phenomena and mass transfer rates in liquid-liquid systems:Part 2, AIChE J. 35(7) (1989) 1125-1136.
[74] K.P. Lindland, S.G. Terjesen, The effect of a surface-active agent on mass transfer in falling drop extraction, Chem. Eng. Sci. 5(1) (1956) 1-12.
[75] W.S. Huang, R.C. Kintner, Effects of surfactants on mass transfer inside drops, AIChE J. 15(5) (1969) 735-744.
[76] L.H. Chen, Y.L. Lee, Adsorption behavior of surfactants and mass transfer in singledrop extraction, AIChE J. 46(1) (2000) 160-168.
[77] L.K. Mudge, W.J. Heideger, The effect of surface active agents on liquid-liquid mass transfer rates, AIChE J. (1970) 602-608.
[78] F.H. Garner, A.H.P. Skelland, Effects of surface active agents on extraction from droplets, Ind. Eng. Chem. 48(1) (1956) 51-58.
[79] C.A.P. Bakker, F.F. Van Vlissingen, W.J. Beek, The influence of the driving force in liquid-liquid extraction-A study of mass transfer with and without interfacial turbulence under well-defined conditions, Chem. Eng. Sci. 22(10) (1967) 1349-1355.
[80] A. Beitel, W.J. Heideger, Surfactant effects on mass transfer from drops subject to interfacial instability, Chem. Eng. Sci. 26(5) (1971) 711-717.
[81] A.H.P. Skelland, C.L. Caenepeel, Effects of surface active agents on mass transfer during droplet formation, fall, and coalescence, AIChE J. 18(6) (1972) 1154-1163.
[82] J. Saien, S. Daliri, Mass transfer from single drops and the influence of temperature, Ind. Eng. Chem. Res. 51(21) (2012) 7364-7372.
[83] J. Saien, S. Daliri, Mass transfer coefficient in liquid-liquid extraction and the influence of aqueous phase pH, Ind. Eng. Chem. Res. 47(1) (2008) 171-175.
[84] J. Saien, S. Daneshamoz, Experimental studies on the effect of ultrasonic waves on single drop liquid-liquid extraction, Ultrason. Sonochem. 40(2018) 11-16.
[85] M.A. Waheed, M. Henschke, A. Pfennig, Mass transfer by free and forced convection from single spherical liquid drops, Int. J. Heat Mass Transf. 45(22) (2002) 4507-4514.
[86] W.H. Piarah, A. Paschedag, M. Kraume, Numerical simulation of mass transfer between a single drop and an ambient flow, AIChE J. 47(7) (2001) 1701-1704.
[87] Z.S. Mao, T.W. Li, J.Y. Chen, Numerical simulation of steady and transient mass transfer to a single drop dominated by external resistance, Int. J. Heat Mass Transf. 44(6) (2001) 1235-1247.
[88] K.B. Deshpande, W.B. Zimmerman, Simulation of interfacial mass transfer by droplet dynamics using the level set method, Chem. Eng. Sci. 61(19) (2006) 6486-6498.
[89] J. Wang, P. Lu, Z. Wang, C. Yang, Z.S. Mao, Numerical simulation of unsteady mass transfer by the level set method, Chem. Eng. Sci. 63(12) (2008) 3141-3151.
[90] M. Wegener, A numerical parameter study on the impact of Marangoni convection on the mass transfer at buoyancy-driven single droplets, Int. J. Heat Mass Transf. 71(2014) 769-778.
[91] Z.S. Mao, J.Y. Chen, Numerical simulation of the Marangoni effect on mass transfer to single slowly moving drops in the liquid-liquid system, Chem. Eng. Sci. 59(8-9) (2004) 1815-1828.
[92] S. Ubal, C.H. Harrison, P. Grassia, W.J. Korchinsky, Numerical simulation of mass transfer in circulating drops, Chem. Eng. Sci. 65(10) (2010) 2934-2956.
[93] M. Wegener, T. Eppinger, K. Bäumler, M. Kraume, A.R. Paschedag, E. Bänsch, Transient rise velocity and mass transfer of a single drop with interfacial instabilities-Numerical investigations, Chem. Eng. Sci. 64(23) (2009) 4835-4845.
[94] R.F. Engberg, M. Wegener, E.Y. Kenig, The influence of Marangoni convection on fluid dynamics of oscillating single rising droplets, Chem. Eng. Sci. 117(2014) 114-124.
[95] R.F. Engberg, M. Wegener, E.Y. Kenig, A Numerical Investigation of the Impact of Marangoni Convection on Oscillating Rising Droplets in Liquid/Liquid Systems, International Solvent Extraction Conference, Wurzburg, Germany, 2014.
[96] M.R. Davidson, M. Rudman, Volume-of-fluid calculation of heat or mass transfer across deforming interfaces in two-fluid flow, Numer. Heat Transfer, Part B 41(3-4) (2002) 291-308.
[97] J.F. Wang, C. Yang, Z.S. Mao, Numerical simulation of Marangoni effect in single droplet mass transfer by level-set method, Sci. China (Ser. A:Chem) 38(2) (2008) 150-160(in Chinese).
[98] P. Lu, Z. Wang, C. Yang, Z.S. Mao, Experimental investigation and numerical simulation of mass transfer during drop formation, Chem. Eng. Sci. 65(20) (2010) 5517-5526.
[99] K. Bäumler, M. Wegener, E. Bänsch, A.R. Paschedag, 2D simulations of interfacial instabilities at deformable single droplets, Seventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries, Melbourne, 2009.
[100] S. Burghoff, E.Y. Kenig, CFD modelling of mass transfer and interfacial phenomena on single droplets, AIChE J. 20(2005) 103-108.
[101] J. Kamp, J. Villwock, M. Kraume, Drop coalescence in technical liquid/liquid applications:a review on experimental techniques and modeling approaches, Rev. Chem. Eng. 33(1) (2017) 1-47.
[102] J. Kamp, M. Kraume, From single drop coalescence to droplet swarms-Scale-up considering the influence of collision velocity and drop size on coalescence probability, Chem. Eng. Sci. 156(2016) 162-177.
[103] H.M. Hulburt, S. Katz, Some problems in particle technology:A statistical mechanical formulation, Chem. Eng. Sci. 19(8) (1964) 555-574.
[104] Y. Liao, D. Lucas, A literature review of theoretical models for drop and bubble breakup in turbulent dispersions, Chem. Eng. Sci. 64(15) (2009) 3389-3406.
[105] Y. Liao, D. Lucas, A literature review on mechanisms and models for the coalescence process of fluid particles, Chem. Eng. Sci. 65(10) (2010) 2851-2864.
[106] K.J. Valentas, O. Bilous, N.R. Amundson, Analysis of breakage in dispersed phase systems, Ind. Eng. Chem. Fundam. 5(2) (1966) 271-279.
[107] M. Attarakih, Solution methodologies for the population balance equations describing the hydrodynamics of liquid-liquid extraction contactors, Ph. D. Thesis, T.U. Kaiserslautern, Germany, 2004.
[108] D. Ramkrishna, Population Balances:Theory and Applications to Particulate Systems in Engineering, Elsevier, 1975.
[109] M. Goodson, M. Kraft, Simulation of coalescence and breakage:an assessment of two stochastic methods suitable for simulating liquid-liquid extraction, Chem. Eng. Sci. 59(18) (2004) 3865-3881.
[110] E.W. Barega, E. Zondervan, A.B. de Haan, A combined lossy capacitor population balance model (LCPBM) for calculating the influence of frequency on electric field enhanced coalescence in a static-mixer settler setup, Chem. Eng. Sci. 104(2013) 727-741.
[111] A. Misra, L.G.M. de Souza, M. Illner, L. Hohl, M. Kraume, J.U. Repke, D. Thévenin, Simulating separation of a multiphase liquid-liquid system in a horizontal settler by CFD, Chem. Eng. Sci. 167(2017) 242-250.
[112] A. Vikhansky, M. Kraft, Modelling of a RDC using a combined CFD-population balance approach, Chem. Eng. Sci. 59(13) (2004) 2597-2606.
[113] M. Jaradat, M. Attarakih, H.J. Bart, Effect of phase dispersion and mass transfer direction on steady state RDC performance using population balance modelling, Chem. Eng. J. 165(2) (2010) 379-387.
[114] S. Alzyod, M. Attarakih, H.J. Bart, The Sectional Quadrature Method of Moments (SQMOM):An extension to nonhomogeneous bivariate population balances, Chem. Eng. Res. Des. 115(2016) 195-203.
[115] H. Chen, Z. Sun, X. Song, J. Yu, A pseudo-3D model with 3D accuracy and 2D cost for the CFD-PBM simulation of a pilot-scale rotating disc contactor, Chem. Eng. Sci. 139(2016) 27-40.
[116] S. Alzyod, M. Attarakih, A. Hasseine, H.J. Bart, Steady state modeling of Kühni liquid extraction column using the Spatially Mixed Sectional Quadrature Method of Moments (SM-SQMOM), Chem. Eng. Res. Des. 117(2017) 549-556.
[117] A.P. Neto, M.B. Mansur, Transient modeling of zinc extraction with D2EHPA in a Kühni column, Chem. Eng. Res. Des. 91(12) (2013) 2323-2332.
[118] A. Amokrane, S. Charton, N. Sheibat-Othman, J. Becker, J.P. Klein, F. Puel, Development of a CFD-PBE coupled model for the simulation of the drops behaviour in a pulsed column, Can. J. Chem. Eng. 92(2) (2014) 220-233.
[119] C. Korb, H.J. Bart, Solvent extraction in columns in a droplet breakage domain, Hydrometallurgy. 173(2017) 71-79.
[120] H.Q. Liu, S. Jing, Q. Fang, S.W. Li, Droplet breakup in a square-sectioned pulsed disc and doughnut column, Ind. Eng. Chem. Res. 55(7) (2016) 2242-2251.
[121] L. Peng, Z. Luo, Y.Y. Zuo, G. Yan, B. Bai, Pinch-off of liquid bridge during droplet coalescence under constrained condition, Chem. Eng. Sci. 177(2018) 471-480.
[122] J. Kamp, M. Kraume, 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. 92(4) (2014) 635-643.
[123] S. Falzone, A. Buffo, M. Vanni, D.L. Marchisio, Simulation of turbulent coalescence and breakage of bubbles and droplets in the presence of surfactants, salts, and contaminants, Adv. Chem. Eng. 52(2018) 125-188.
[124] S. Maaß, Experimental analysis, modeling and simulation of drop breakage in agitated turbulent liquid/liquid-dispersions, Ph. D. Thesis, T. U. Berlin, Germany, 2011.
[125] J. Solsvik, S. Maaß, H.A. Jakobsen, Definition of the single drop breakup event, Ind. Eng. Chem. Res. 55(10) (2016) 2872-2882.
[126] S. Galinat, O. Masbernat, P. Guiraud, C. Dalmazzone, C. Noik, Drop break-up in turbulent pipe flow downstream of a restriction, Chem. Eng. Sci. 60(23) (2005) 6511-6528.
[127] S. Galinat, L.G. Torres, O. Masbernat, P. Guiraud, F. Risso, C. Dalmazzone, C. Noik, Breakup of a drop in a liquid-liquid pipe flow through an orifice, AIChE J. 53(1) (2007) 56-68.
[128] S. Maaß, A. Gäbler, A. Zaccone, A.R. Paschedag, M. Kraume, Experimental investigations and modelling of breakage phenomena in stirred liquid/liquid systems, Chem. Eng. Res. Des. 85(5) (2007) 703-709.
[129] S. Maaß, M. Kraume, Determination of breakage rates using single drop experiments, Chem. Eng. Sci. 70(2012) 146-164.
[130] J. Solsvik, H.A. Jakobsen, Single drop breakup experiments in stirred liquid-liquid tank, Chem. Eng. Sci. 131(2015) 219-234.
[131] M. Ashar, D. Arlov, F. Carlsson, F. Innings, R. Andersson, Single droplet breakup in a rotor-stator mixer, Chem. Eng. Sci. 181(2018) 186-198.
[132] J. Jareš, J. Prochazka, Break-up of droplets in Karr reciprocating plate extraction column, Chem. Eng. Sci. 42(2) (1987) 283-292.
[133] M. Cabassud, C. Gourdon, G. Casamatta, Single drop break-up in a Kühni column, Chem. Eng. J. 44(1) (1990) 27-41.
[134] C. Gourdon, G. Casamatta, H. Angelino, Single drop experiments with liquid test systems:a way of comparing two types of mechanically agitated extraction columns, Chem. Eng. J. 46(3) (1991) 137-148.
[135] J. Fang, J.C. Godfrey, Z.Q. Mao, M.J. Slater, C. Gourdon, Single liquid drop breakage probabilities and characteristic velocities in Kühni columns, Chem. Eng. Technol. 18(1) (1995) 41-48.
[136] H. Bahmanyar, M.J. Slater, Studies of drop break-up in liquid-liquid systems in a rotating disc contactor. Part I:Conditions of no mass transfer, Chem. Eng. Technol. 14(2) (1991) 79-89.
[137] S. Nachtigall, D. Zedel, S. Maaß, A. Walle, M. Schäfer, M. Kraume, Determination of drop breakage mechanisms by experimental and numerical investigations of single drop breakages, 14th European Conference on Mixing, Poland, 2012.
[138] F. Gebauer, J. Villwock, M. Kraume, H.J. Bart, Detailed analysis of single drop coalescence-Influence of ions on film drainage and coalescence time, Chem. Eng. Res. Des. 115(2016) 282-291.
[139] N. Kopriwa, A. Pfennig, Characterization of coalescence in extraction equipment based on lab-scale experiments, Solvent Extr. Ion Exch. 34(7) (2016) 622-642.
[140] J. Villwock, F. Gebauer, J. Kamp, H.J. Bart, M. Kraume, Systematic analysis of single droplet coalescence, Chem. Eng. Technol. 37(7) (2014) 1103-1111.
[141] R. Andersson, B. Andersson, On the breakup of fluid particles in turbulent flows, AIChE J. 52(6) (2006) 2020-2030.
[142] F. Gebauer, M.W. Hlawitschka, H.J. Bart, CFD aided investigation of single droplet coalescence, Chin. J. Chem. Eng. 24(2) (2016) 249-252.
[143] R.T. Eiswirth, H.J. Bart, A.A. Ganguli, E.Y. Kenig, Experimental and numerical investigation of binary coalescence:Liquid bridge building and internal flow fields, Phys. Fluids 24(6) (2012), 062108.
[144] L.R. Mason, G.W. Stevens, D.J. Harvie, Multi-scale volume of fluid modelling of droplet coalescence, 9th International Conference on CFD in the Minerals and Process Industries, Melbourne, 2012.
[145] R. Andersson, A. Helmi, Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows, Appl. Math. Model. 38(17-18) (2014) 4186-4196.
[146] J. Płotka-Wasylka, M. Rutkowska, K. Owczarek, M. Tobiszewski, J. Namieśnik, Extraction with environmentally friendly solvents, TrAC, Trends Anal. Chem. 91(2017) 12-25.
[147] S.H. Ha, N.L. Mai, Y.M. Koo, Butanol recovery from aqueous solution into ionic liquids by liquid-liquid extraction, Process Biochem. 45(12) (2010) 1899-1903.
[148] H. Passos, M.G. Freire, J.A. Coutinho, Ionic liquid solutions as extractive solvents for value-added compounds from biomass, Green Chem. 16(12) (2014) 4786-4815.
[149] H.J. Bart, C. Drumm, M.M. Attarakih, Process intensification with reactive extraction columns, Chem. Eng. Process:Process Intensification. 47(5) (2008) 745-754.
[150] F. Buchbender, F. Onink, W. Meindersma, A. de Haan, A. Pfennig, Simulation of aromatics extraction with an ionic liquid in a pilot-plant Kühni extractor based on single-drop experiments, Chem. Eng. Sci. 82(2012) 167-176.
[151] M.M.S. Badieh, M.C. Quaresima, A. Pfennig, J. Saien, Performance study of ionic liquid in extraction based on single-drop experiments, Solvent Extr. Ion Exch. 35(7) (2017) 563-572.
[152] A.G. Teixeira, R. Agarwal, K.R. Ko, J. Grant-Burt, B.M. Leung, J.P. Frampton, Emerging biotechnology applications of aqueous two-phase systems, Adv. Healthcare Mater. 7(6) (2018) 1701036.
[153] M. Iqbal, Y. Tao, S. Xie, Y. Zhu, D. Chen, X. Wang, H.I. Hussain, Aqueous two-phase system (ATPS):An overview and advances in its applications, Biol. Proced. Online 18(1) (2016) 18.
[154] M.E. Silva, T.T. Franco, Liquid-liquid extraction of biomolecules in downstream processing-A review paper, Braz. J. Chem. Eng. 17(1) (2000) 1-17.
[155] E. Espitia-Saloma, P. Vázquez-Villegas, O. Aguilar, M. Rito-Palomares, Continuous aqueous two-phase systems devices for the recovery of biological products, Food Bioprod. Process. 92(2) (2014) 101-112.
[156] S.B. Sawant, S.K. Sikdar, J.B. Joshi, Hydrodynamics and mass transfer in two-phase aqueous extraction using spray columns, Biotechnol. Bioeng. 36(2) (1990) 109-115.
[157] P.C. Bhawsar, A.B. Pandit, S.B. Sawant, J.B. Joshi, Enzyme mass transfer coefficient in a sieve plate extraction column, Chem. Eng. J., Biochem. Eng. J. 55(1-2) (1994) B1-B17.
[158] N.D. Srinivas, A.V. Narayan, K.S.M.S. Raghavarao, Mass transfer in a spray column during two-phase extraction of horseradish peroxidase, Process Biochem. 38(3) (2002) 387-391.
[159] R.S. Barhate, G. Patil, N.D. Srinivas, K.S.M.S. Raghavarao, Drop formation in aqueous two-phase systems, J. Chromatogr. A 1023(2) (2004) 197-206.
[160] M.C. Quaresima, M. Schmidt, A. Pfennig, Solvent extraction design for highly viscous systems, The 21st International Solvent Extraction Conference, Miyazaki, 2017.
[161] P. Amani, M. Amani, G. Ahmadi, O. Mahian, S. Wongwises, A critical review on the use of nanoparticles in liquid-liquid extraction, Chem. Eng. Sci. 183(2018) 148-176.
[162] J.K. Lee, J. Koo, H. Hong, Y.T. Kang, The effects of nanoparticles on absorption heat and mass transfer performance in NH₃/H₂O binary nanofluids, Int. J. Refrig. 33(2) (2010) 269-275.
[163] J. Saien, H. Bamdadi, Mass transfer from nanofluid single drops in liquid-liquid extraction process, Ind. Eng. Chem. Res. 51(14) (2012) 5157-5166.
[164] A.M. Ghanadi, A.H. Nasab, D. Bastani, A.A.S. Kordi, The effect of nanoparticles on the mass transfer in liquid-liquid extraction, Chem. Eng. Commun. 202(5) (2015) 600-605.
[165] J. Saien, M. Zardoshti, Mass transfer intensification of nanofluid single drops with effect of temperature, Korean J. Chem. Eng. 32(11) (2015) 2311-2318.
[166] H.H. Goodarzi, M.N. Esfahany, Experimental investigation of the effects of the hydrophilic silica nanoparticles on mass transfer and hydrodynamics of single drop extraction, Sep. Purif. Technol. 170(2016) 130-137.
[167] A. Vahedi, A.M. Dehkordi, F. Fadaei, Mass transfer enhancement in single drop extraction in the presence of magnetic nanoparticles and magnetic field, AIChE J. 62(12) (2016) 4466-4479.
[168] J. Saien, R. Hasani, Hydrodynamics and mass transfer characteristics of circulating single drops with effect of different size nanoparticles, Sep. Purif. Technol. 175(2017) 298-304.
[169] A. Hatami, D. Bastani, F. Najafi, Investigation the effect of super hydrophobic titania nanoparticles on the mass transfer performance of single drop liquid-liquid extraction process, Sep. Purif. Technol. 176(2017) 107-119.
[170] J. Ayesterán, N. Kopriwa, F. Buchbender, M. Kalem, A. Pfennig, ReDrop-A simulation tool for the design of extraction columns based on single-drop experiments, Chem. Eng. Technol. 38(10) (2015) 1894-1900.
[171] M.M. Attarakih, H.J. Bart, T. Steinmetz, M. Dietzen, N.M. Faqir, LLECMOD:A bivariate population balance simulation tool for liquid-liquid extraction columns, Open Chem. Eng. J. 2(2008) 10-34.
[172] M.M. Attarakih, H.J. Bart, L. Lagar, N.M. Faqir, LLECMOD:A Windows-based program for hydrodynamics simulation of liquid-liquid extraction columns, Chem. Eng. Process. Process Intensif. 45(2) (2006) 113-123.
[173] M. Attarakih, S. Al-Zyod, M. Abu-Khader, H.J. Bart, PPBLAB:A new multivariate population balance environment for particulate system modelling and simulation, Procedia Eng. 42(2012) 1445-1462.
[174] M. Attarakih, S. Alzyod, A. Fricke, Population balance modelling of pulsed packed bed extraction columns using PPBLab software, Comput. Aided Chem. Eng. 40(2017) 67-72.
[175] M.W. Hlawitschka, M.M. Attarakih, S.S. Alzyod, H.J. Bart, CFD based extraction column design-Chances and challenges, Chin. J. Chem. Eng. 24(2) (2016) 259-263.
[176] A. Amokrane, S. Maaß, F. Lamadie, F. Puel, S. Charton, On droplets size distribution in a pulsed column. Part I:In-situ measurements and corresponding CFD-PBE simulations, Chem. Eng. J. 296(2016) 366-376.