[1] S. Parvizi, E. Keshavarz Alamdari, S.H. Hashemabadi, S. Aosati, CFD simulation and experimental study of impeller speed and cearance effects in the mixer of copper solvent extraction unit, Indian J. Sci. Technol. 9(S1) (2016) DOI: 10.17485/ijst/2016/v9iS1/99815.
[2] F. Azizi, A. Al-Taweel, Turbulently flowing liquid-liquid dispersions. Part I: drop breakage and coalescence, Chem. Eng. J. 166 (2011) 715-725.
[3] A.W. Mahoney, D. Ramkrishna, Efficient solution of population balance equations with discontinuities by finite elements, Chem. Eng. Sci. 57 (2002) 1107-1119.
[4] D. Ramkrishna, A.W. Mahoney, Population balance modeling. Promise for the future, Chem. Eng. Sci. 57 (2002) 595-606.
[5] M.M. Attarakih, H.J. Bart, N.M. Faqir, Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions, Chem. Eng. Sci. 59 (2004) 2567-2592.
[6] R. Andersson, B. Andersson, F. Chopard, T. Norén, Development of a multi-scale simulation method for design of novel multiphase reactors, Chem. Eng. Sci. 59 (2004) 4911-4917.
[7] S. Parvizi, E. Keshavarz Alamdari, S.H. Hashemabadi, M. Kavousi, A. Sattari, Investigating factors affecting on the efficiency of dynamic mixers, Min. Proc. Ext. Met. Rev. 37 (2016) 342-368.
[8] F. Azizi, A. Al-Taweel, Algorithm for the accurate numerical solution of PBE for drop breakup and coalescence under high shear rates, Chem. Eng. Sci. 65 (2010) 6112-6127.
[9] E. Madadi-Kandjani, A. Passalacqua, An extended quadrature-based moment method with log-normal kernel density functions, Chem. Eng. Sci. 131 (2015) 323-339.
[10] A. Passalacqua, F. Laurent, E. Madadi-Kandjani, J.C. Heylmun, R.O. Fox, An open-source quadrature-based population balance solver for OpenFOAM, Chem. Eng. Sci. 176 (2018) 306-318.
[11] G.H. Yeoh, C.P. Cheung, J. Tu, Multiphase flow analysis using population balance modeling: Bubbles, drops and particles, Butterworth-Heinemann, Oxford, 2014.
[12] G. Narsimhan, J. Gupta, D. Ramkrishna, A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions, Chem. Eng. Sci. 34 (1979) 257-265.
[13] E.L. Paul, V.A. Atiemo-Obeng, S.M. Kresta, Handbook of industrial mixing: Science and practice, John Wiley & Sons, NJ, 2004.
[14] S.L. Ross, F.H. Verhoff, R.L. Curl, Droplet breakage and coalescence processes in an agitated dispersion. 2: Measurement and interpretation of mixing experiments, Ind. Eng. Chem. Fund. 17 (1978) 101-108.
[15] C. Coulaloglou, L. Tavlarides, Drop size distributions and coalescence frequencies of liquid‐liquid dispersions in flow vessels, AIChE J. 22 (1976) 289-297.
[16] 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 (2014) 635-643.
[17] S. Das, Development of a coalescence model due to turbulence for the population balance equation, Chem. Eng. Sci. 137 (2015) 22-30.
[18] A. Bąk, W. Podgórska, Investigation of drop breakage and coalescence in the liquid-liquid system with nonionic surfactants Tween 20 and Tween 80, Chem. Eng. Sci. 74 (2012) 181-191.
[19] N.B. Raikar, S.R. Bhatia, M.F. Malone, M.A. Henson, Experimental studies and population balance equation models for breakage prediction of emulsion drop size distributions, Chem. Eng. Sci. 64 (2009) 2433-2447.
[20] N. Metta, M. Ierapetritou, R. Ramachandran, A multiscale DEM-PBM approach for a continuous comilling process using a mechanistically developed breakage kernel, Chem. Eng. Sci. 178 (2018) 211-221.
[21] F. Xiao, H. Xu, X.Y. Li, D. Wang, Modeling particle-size distribution dynamics in a shear-induced breakage process with an improved breakage kernel: Importance of the internal bonds, Colloid. Surface. A, 468 (2015) 87-94.
[22] A. Falola, A. Borissova, X.Z. Wang, Extended method of moment for general population balance models including size dependent growth rate, aggregation and breakage kernels, Comput. Chem. Eng. 56 (2013) 1-11.
[23] M. Mirzaie, A. Sarrafi, H.H. Pour, A. Baghaie, M. Molaeinasab, Experimental investigation and CFD modeling of hydrodynamic parameters in a pulsed packed column, Solvent Extr. Ion Exc. 34 (2016) 643-660.
[24] H. Luo, H.F. Svendsen, Theoretical model for drop and bubble breakup in turbulent dispersions, AIChE J. 42 (1996) 1225-1233.
[25] L.E. Patruno, C.A. Dorao, P.M. Dupuy, H.F. Svendsen, H.A. Jakobsen, Identification of droplet breakage kernel for population balance modelling, Chem. Eng. Sci. 64 (2009) 638-645.
[26] R. Xie, J. Li, Y. Jin, D. Zou, M. Chen, Simulation of drop breakage in liquid-liquid system by coupling of CFD and PBM: Comparison of breakage kernels and effects of agitator configurations, Chinese J. Chem. Eng. 27 (2019) 1001-1014.
[27] P.J. Becker, F. Puel, H.A. Jakobsen, N. Sheibat-Othman, Development of an improved breakage kernel for high dispersed viscosity phase emulsification, Chem. Eng. Sci. 109 (2014) 326-338.
[28] M.E. Gheshlaghi, A.S. Goharrizi, A.A. Shahrivar, H. Abdollahi, Modeling industrial thickener using computational fluid dynamics (CFD), a case study: Tailing thickener in the Sarcheshmeh copper mine, Int. J. Min. Sci. Technol. 23 (2013) 885-892.
[29] N. Yang, Q. Xiao, A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors, Chem. Eng. Sci. 170 (2017) 241-250.
[30] J. Kamp, M. Kraume, Coalescence efficiency model including electrostatic interactions in liquid/liquid dispersions, Chem. Eng. Sci. 126 (2015) 132-142.
[31] M. Mirzaie, A. Sarrafi, H. Hashemipour, A. Baghaie, M. Molaeinasab, CFD simulation and experimental investigation of the copper solvent extraction in a pilot plant pulsed packed column in Sarcheshmeh Copper Complex, Heat Mass Transfer, 53 (2017) 1995-2008.
[32] V. Rewatkar, J. Joshi, Effect of impeller design on liquid phase mixing in mechanically agitated reactors, Chem. Eng. Commun. 102 (1991) 1-33.
[33] F. Lehr, D. Mewes, A transport equation for the interfacial area density applied to bubble columns. Chem. Eng. Sci. 56 (2001) 1159-1166.
[34] L. Müller, A. Klar, F. Schneider, A numerical comparison of the method of moments for the population balance equation, arXiv preprint arXiv:1706.05854 (2017).
[35] L. Liu, J. Litster, Population balance modelling of granulation with a physically based coalescence kernel, Chem. Eng. Sci. 57 (2002) 2183-2191.
[36] C.A. Coulaloglou, Dispersed phase interactions in an agitated flow vessel, PhD Thesis, Illinois Institute of Technology, Chicago, IL, USA, 1975.
[37] M.A. Hsia, The modeling of liquid-liquid extraction in stirred tanks by a simulation approach, PhD Thesis, Illinois Institute of Technology, Chicago, IL, USA, 1981.
[38] P.M. Bapat, L.L. Tavlarides, Mass transfer in a liquid-liquid CFSTR, AIChE J. 31 (1985) 659-666.
[39] L.M. Ribeiro, P.F.R. Regueiras, M.M.L. Guimaraes, C.M.N. Madureira, J.J.C. Cruz-Pinto, Dynamic behaviour of liquid-liquid agitated dispersions. I: The hydrodynamics, Comput. Chem. Eng. 19 (1995) 333-343.
[40] Z. Gao, D. Li, A. Buffo, W. Podgórska, D.L. Marchisio, Simulation of droplet breakage in turbulent liquid-liquid dispersions with CFD-PBM: comparison of breakage kernels, Chem. Eng. Sci. 142 (2016) 277-288.
[41] S. Parvizi, S. Aosati, E. Keshavarz Alamdari, Experimental study of the effect of impeller geometrical parameters on fluid hydrodynamics in copper solvent extraction mixer, Int. J. Adv. Des. Manuf. Technol. 10 (2017) 21-25.