Solid-liquid mixing analysis in stirred vessels

References

Abrahamson J. Collision rates of small particles in a vigorously turbulent fluid. Chem Eng Sci 1975; 30: 1371–1379.10.1016/0009-2509(75)85067-6Search in Google Scholar

Abu-Farah L, Al-Qaessi F, Schönbucher A. Cyclohexane/water dispersion behaviour in a stirred batch vessel experimentally and with CFD simulation. Procedia Comput Sci 2010; 1: 655–664.10.1016/j.procs.2010.04.070Search in Google Scholar

AEAT. CFX5 Flow solver user guide, CFD services, Oxfordshire, UK: AEA Industrial Technology, 2003.Search in Google Scholar

Alipchenkov VM, Zaichik LI. Particle clustering in isotropic turbulent flow. Fluid Dyn 2003; 38: 417–432.10.1023/A:1025198006731Search in Google Scholar

Amsallem D, Farhat C. On the stability of reduced-order linearized computational fluid dynamics models based on POD and galerkin projection: descriptor vs non-descriptor forms. In: Quarteroni A, Rozza G, editors. Reduced order methods for modeling and computational reduction. Switzerland: Springer International Publishing, 2012: 215–233.Search in Google Scholar

Andersson B. Fluid/particle mass transport in slurries. Encycl Fluid Mech 1986; 5: 189–211.Search in Google Scholar

Arastoopour H, Wang CH, Weil SA. Particle-particle interaction force in a dilute gas-solid system. Chem Eng Sci 1982; 37: 1379–1386.10.1016/0009-2509(82)85010-0Search in Google Scholar

Armenante PM, Nagamine EU. Effect of low off-bottom impeller clearance on the minimum agitation speed for complete suspension of solids in stirred tanks. Chem Eng Sci 1998; 53: 1757–1775.10.1016/S0009-2509(98)00001-3Search in Google Scholar

Bakker A, Fasano JB, Myers KJ. Effects of flow pattern on the solids distribution in a stirred tank. IChemE Symp Ser 1994; 136: 1–7.Search in Google Scholar

Baldi GR, Conti R, Alaria E. Complete suspension of particles in mechanically agitated vessels. Chem Eng Sci 1978; 33: 21–25.10.1016/0009-2509(78)85063-5Search in Google Scholar

Barrue H, Xuereb C, Bertrand JA. Computational study on solids suspension in a stirred vessel. Proceedings of ECCE 1, Italy, May 1997: 1843–1846.Search in Google Scholar

Bell RA, Witt PJ, Easton AK, Schwarz MP. Comparison of representations for particle-particle interactions in a gas-solid fluidised bed. International Conference on CFD in Mineral & Metal Processing and Power Generation, CSIRO, 1997: 361–368.Search in Google Scholar

Bittorf KJ, Kresta SM. Three-dimensional wall jets: axial flow in a stirred tank. AIChE J 2001; 47: 1227–1284.Search in Google Scholar

Bittorf KJ, Kresta SM. Prediction of cloud height for solid suspensions in stirred tanks. Chem Eng Res Des 2003; 81: 568–577.10.1205/026387603765444519Search in Google Scholar

Bohnet M, Niesmak G. Distribution of solids in stirred suspension. Ger Chem Eng 1980; 3: 57.Search in Google Scholar

Brucato A, Ciofalo M, Godfrey J, Grisafi F, Micale G. Experimental and CFD simulation of solids distribution in stirred vessels. Proceedings of 5th International Conference Multiphase Flow in Industrial Plants, Amalfi, September 1996: 323–334.Search in Google Scholar

Brucato A, Ciofalo M, Grisafi F, Magelli F, Torretta F. On the simulation of solid particle distribution in multiple impeller agitated tanks via computational fluid dynamics. Proceedings of ECCE 1, Italy, May 1997; 4–7: 1723–1726.Search in Google Scholar

Brucato A, Grisafi F, Montante G. Particle drag coefficients in turbulent fluids. Chem Eng Sci 1998; 53: 3295–3314.10.1016/S0009-2509(98)00114-6Search in Google Scholar

Buffo A, Vanni M, Marchisio DL. Multidimensional population balance model for the simulation of turbulent gas-liquid systems in stirred tank reactors. Chem Eng Sci 2011; 70: 31–44.10.1016/j.ces.2011.04.042Search in Google Scholar

Bujalski W, Takenaka K, Paoleni S, Jahoda M, Paglianti A, Takahashi K, Nienow AW, Etchells AW. Suspension and liquid homogenization in high solids concentration stirred chemical reactors. Chem Eng Res Des 1999; 77: 241–247.10.1205/026387699526151Search in Google Scholar

Decker S, Sommerfeld M. Calculation of particle suspension in agitated vessels with the Euler-Lagrange approach. IChemE Symp Ser 1996; 140: 71–82.Search in Google Scholar

Delafosse A, Line A, Morchain J, Guiraud P. LES and URANS simulations of hydrodynamics in mixing tank: comparison to PIV experiments. Chem Eng Res Des 2008; 86: 1322–1330.10.1016/j.cherd.2008.07.008Search in Google Scholar

Derksen JJ. Numerical simulation of solids suspension in a stirred tank. AIChE J 2003; 49: 2700–2714.10.1002/aic.690491104Search in Google Scholar

Derksen J, Van den Akker HEA. Large eddy simulations on the flow driven by a Rushton turbine. AIChE J 1999; 45: 209–221.10.1002/aic.690450202Search in Google Scholar

Ding J, Gidaspow D. Bubbling fluidization model using kinetic theory of granular flow. AIChE J 1990; 36: 523–538.10.1002/aic.690360404Search in Google Scholar

Ding J, Wang X, Zhou X, Ren N, Guo W. CFD optimization of continuous stirred-tank (CSTR) reactor for biohydrogen production. Bioresour Technol 2010; 101: 7005–7013.10.1016/j.biortech.2010.03.146Search in Google Scholar PubMed

Elghobashi S. On predicting particle-laden turbulent flows. Appl Sci Res 1994; 52: 309–329.10.1007/BF00936835Search in Google Scholar

Ergun S. Fluid flow through packed columns. Chem Eng Prog 1952; 48: 89–94.Search in Google Scholar

Fajner D, Pinelli D, Ghadge RS, Montante G, Paglianti A, Magelli F. Solids distribution and rising velocity of buoyant solid particles in a vessel stirred with multiple impellers. Chem Eng Sci 2008; 63: 5876–5882.10.1016/j.ces.2008.08.033Search in Google Scholar

Farhat C, Rallu A, Wang K, Belytschko T. Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly non-linear compressible fluid-structure interaction problems. Int J Numer Methods Eng 2010; 84: 73–107.10.1002/nme.2883Search in Google Scholar

Farzpourmachiani A, Shams M, Shadaram A, Azidehak F. Eulerian-Lagrangian 3-D simulations of unsteady two-phase gas-liquid flow in a rectangular column by considering bubble interactions. Int J Non-Linear Mech 2011; 46: 1049–1056.10.1016/j.ijnonlinmec.2011.04.024Search in Google Scholar

Feng X, Li X, Cheng J, Yang C, Mao Z. Numerical simulation of solid-liquid turbulent flow in a stirred tank with a two-phase explicit algebraic stress model. Chem Eng Sci 2012; 82: 272–284.10.1016/j.ces.2012.07.044Search in Google Scholar

Fletcher DF, Brown GJ. Numerical simulation of solid suspension via mechanical agitation: effect of the modelling approach, turbulence model and hindered settling drag law. Int J Comput Fluid Dyn 2013; 23: 173–187.Search in Google Scholar

Gidaspow D. Multiphase flow and fluidization: continuum and kinetic theory descriptions. New York, USA: Academic Press, 1994.Search in Google Scholar

Gidaspow D, Syamlal M, Seo Y. Hydrodynamics of fluidization of single and binary size particles: super computing modeling. In Fluidization V: Proceedings of the 5th Engineering Foundation Conference on Fluidization, Eds. Ostergaard K, Sorensen A. Engineering Foundation, New York, 1986: 1–8.Search in Google Scholar

Gogate PR, Beenackers AACM, Pandit AB. Multiple-impeller systems with a special emphasis on bioreactors: a critical review. Biochem Eng J 2000; 6: 109–144.10.1016/S1369-703X(00)00081-4Search in Google Scholar

Grétarsson JT, Kwatra N, Fedkiw R. Numerically stable fluid-structure interactions between compressible flow and solid structures. J Comput Phys 2011; 230: 3062–3084.10.1016/j.jcp.2011.01.005Search in Google Scholar

Guha D, Ramachandran PA, Dudukovic MP, Derksen JJ. Evaluation of large eddy simulation and Euler-Euler CFD models for solids flow dynamics in a stirred tank reactor. AIChE J 2008; 54: 766–778.10.1002/aic.11417Search in Google Scholar

Hamill IS, Hawkins R, Jones IP, Lo SM, Splawski BA, Fontenot K. The application of CFDS-FLOW 3D to single- and multi-phase flows in mixing vessels. AIChE Symp Ser Book 305 1995; 91: 150–160.Search in Google Scholar

Hartmann H, Derksen JJ, Montavon C, Pearson J, Hamill IS, Van den Akker HEA. Assessment of large eddy and RANS stirred tank simulations by means of LDA. Chem Eng Sci 2004; 59: 2419–2432.10.1016/j.ces.2004.01.065Search in Google Scholar

Hicks MT, Myers KJ, Bakker A. Cloud height in solids suspension agitation. Chem Eng Commun 1997; 160: 137–155.10.1080/00986449708936610Search in Google Scholar

Hosseini S, Patel D, Ein-Mozaffari F, Mehrvar M. Study of solid-liquid mixing in agitated tanks through computational fluid dynamics modeling. Ind Eng Chem Res 2010; 49: 4426–4435.10.1021/ie901130zSearch in Google Scholar

Hu C, Mei R. Effect of inertia on the particle collision coefficient in Gaussian turbulence. In CDROM Proceedings, ASME Fluid Engineering Div. Summer Meeting, 1997.Search in Google Scholar

Ishii M, Zuber N. Drag coefficient, relative velocity in bubbly, droplet or particulate flows. AIChE J 1979; 25: 843–855.10.1002/aic.690250513Search in Google Scholar

Jaworski Z, Bujalski W, Otomo N, Nienow AW. CFD study of homogenization with dual Rushton turbines – comparison with experimental results: part I: initial studies. Chem Eng Res Des 2000; 78: 327–333.10.1205/026387600527437Search in Google Scholar

Joshi JB, Nere NK, Rane CV, Murthy BN, Mathpati CS, Patwardhan AW, Ranade VV. CFD simulation of stirred tanks: comparison of turbulence models. part I: radial flow impellers. Can J Chem Eng 2011; 89: 23–82.10.1002/cjce.20446Search in Google Scholar

Kasat GR, Khopkar AR, Ranade VV, Pandit AB. CFD simulation of liquid-phase mixing in solid-liquid stirred reactor. Chem Eng Sci 2008; 63: 3877–3885.10.1016/j.ces.2008.04.018Search in Google Scholar

Kee NCS, Tan RBH. CFD simulation of solids suspension in mixing vessels. Can J Chem Eng 2002; 80: 1–6.Search in Google Scholar

Khazam O, Kresta SM. Mechanisms of solids drawdown in stirred tanks. Can J Chem Eng 2008; 86: 622–634.10.1002/cjce.20077Search in Google Scholar

Khopkar AR, Kasat GR, Pandit AB, Ranade VV. Computational fluid dynamics simulation of the solid suspension in a stirred slurry reactor. Ind Eng Chem Res 2006; 45: 4416–4428.10.1021/ie050941qSearch in Google Scholar

Kitagawa A, Murai Y, Yamamoto F. Two-way coupling of Eulerian-Lagrangian model for dispersed multiphase flows using filtering functions. Int J Multiph Flow 2001; 27: 2129–2153.10.1016/S0301-9322(01)00040-4Search in Google Scholar

Klenov OP, Noskov AS. Solid dispersion in the slurry reactor with multiple impellers. Chem Eng J 2011; 176–177: 75–82.10.1016/j.cej.2011.07.056Search in Google Scholar

Kruis FE, Kusters KA. The collision rate of particles in turbulent flow. Chem Eng Commun 1997; 158: 201–230.10.1080/00986449708936589Search in Google Scholar

Lahey RT, Lopez de Bertodano M, Jones OC. Phase distribution in complex geometry conduits. Nucl Eng Des 1993; 141: 177–201.10.1016/0029-5493(93)90101-ESearch in Google Scholar

Lane GL, Schwarz MP, Evans GM. Numerical modelling of gas-liquid flow in stirred tanks. Chem Eng Sci 2005; 60: 2203–2214.10.1016/j.ces.2004.11.046Search in Google Scholar

Larson M, Jonsson L. Mixing in a 2-layer stably stratified fluid by a turbulent jet. J Hydraul Res 1994; 32: 271–289.10.1080/00221686.1994.10750041Search in Google Scholar

Lea J. Suspension Mixing tank-design heuristic. Chemical Product and Process Modeling, 2009; 4. DOI: 10.2202/1934-2659.1334.10.2202/1934-2659.1334Search in Google Scholar

Leng DE, Calabrese RV. Immiscible liquid-liquid systems. In: Paul EL, Atiemo-Obeng VA, Kresta SM, editors. Handbook of industrial mixing: science and practice. New Jersey, USA: Wiley-Interscience, 2004.Search in Google Scholar

Li J, Farhat C, Avery P, Tezaur R. A dual-primal FETI method for solving a class of fluid-structure interaction problems in the frequency domain. Int J Numer Methods Eng 2012; 89: 418–437.10.1002/nme.3243Search in Google Scholar

Ljungqvist M, Rasmuson A. Numerical simulation of the two-phase flow in an axially stirred vessel. Chem Eng Res Des 2001; 79: 533–546.10.1205/02638760152424307Search in Google Scholar

Lopez de Bertodano MA. Two fluid model for two-phase turbulent jets. Nucl Eng Des 1998; 179: 65–74.10.1016/S0029-5493(97)00244-6Search in Google Scholar

Magelli F, Fajner D, Nocentini M, Pasquali G. Solid distribution in vessels stirred with multiple impellers. Chem Eng Sci 1990; 45: 615–625.10.1016/0009-2509(90)87005-DSearch in Google Scholar

Mak ATC. Solid-liquid mixing in mechanically agitated vessels (PhD Thesis). London, England: University College London, 1992.Search in Google Scholar

Mersmann A, Werner F, Maurer S, Bartosch K. Theoretical prediction of the minimum stirrer speed in mechanically agitated suspensions. Chem Eng Process 1998; 37: 503–510.10.1016/S0255-2701(98)00057-9Search in Google Scholar

Meyer CJ, Deglon DA. Particle collision modeling – a review. Miner Eng 2011; 24: 719–730.10.1016/j.mineng.2011.03.015Search in Google Scholar

Micale G, Grisafi F, Rizzuti L, Brucato A. CFD simulation of particle suspension height in stirred vessels. Chem Eng Res Des 2004; 82: 1204–1213.10.1205/cerd.82.9.1204.44171Search in Google Scholar

Micheletti M, Nikiforaki L, Lee KC, Yianneskis M. Particle concentration and mixing characteristics of moderate-to-dense solid-liquid suspensions. Ind Eng Chem Res 2003; 42: 6236–6249.10.1021/ie0303799Search in Google Scholar

Molerus O, Latzel W. Suspension of solid particles in agitated vessels – II. Archimedes numbers >40, reliable prediction of minimum stirrer angular velocities. Chem Eng Sci 1987; 42: 1423–1430.10.1016/0009-2509(87)85014-5Search in Google Scholar

Monaghan JJ. Smoothed particle hydrodynamics. Rep Prog Phys 2005; 68: 1703–1759.10.1088/0034-4885/68/8/R01Search in Google Scholar

Montante G, Magelli F. Modelling of solids distribution in stirred tanks: analysis of simulation strategies and comparison with experimental data. Int J Comput Fluid Dyn 2005; 19: 253–262.10.1080/10618560500081795Search in Google Scholar

Montante G, Magelli F. Mixed solids distribution in stirred vessels: experiments and computational fluid dynamics simulations. Ind Eng Chem Res 2007; 46: 2885–2891.10.1021/ie060616iSearch in Google Scholar

Montante G, Lee KC, Brucato A, Yianneskis M. Numerical simulations of the dependency of flow pattern on impeller clearance in stirred vessels. Chem Eng Sci 2001a; 56: 3751–3770.10.1016/S0009-2509(01)00089-6Search in Google Scholar

Montante G, Micale G, Magelli F, Brucato A. Experiments and CFD predictions of solid particle distribution in a vessel agitated with four pitched blade turbines. Chem Eng Res Des 2001b; 79: 1005–1010.10.1205/02638760152721253Search in Google Scholar

Montante G, Pinelli D, Magelli F. Scale-up criteria for the solids distribution in slurry reactors stirred with multiple impellers. Chem Eng Sci 2003; 58: 5363–5372.10.1016/j.ces.2003.09.021Search in Google Scholar

Montante G, Paglianti A, Magelli F. Analysis of dilute solid-liquid suspensions in turbulent stirred tanks. Chem Eng Res Des 2012; 90: 1448–1456.10.1016/j.cherd.2012.01.009Search in Google Scholar

Murthy BN, Ghadge RS, Joshi JB. CFD simulations of gas-liquid-solid stirred reactor: prediction of critical impeller speed for solid suspension. Chem Eng Sci 2007; 62: 7184–7195.10.1016/j.ces.2007.07.005Search in Google Scholar

Myers KJ, Bakker A, Fasano JB. Simulation and experimental verification of liquid-solid agitation performance. AIChE Symp Ser Book 305 1995; 91: 139–145.Search in Google Scholar

Narayanan S, Bhatia VK, Guha DK, Rao MN. Suspension of solids by mechanical agitation. Chem Eng Sci 1969; 24: 223–230.10.1016/0009-2509(69)80031-XSearch in Google Scholar

Ochieng A, Lewis AE. CFD simulation of nickel solids concentration distribution in a stirred tank. Miner Eng 2006a; 19: 180–189.10.1016/j.mineng.2005.09.028Search in Google Scholar

Ochieng A, Lewis AE. CFD simulation of solids off-bottom suspension and cloud height. Hydrometallurgy 2006b; 82: 1–12.10.1016/j.hydromet.2005.11.004Search in Google Scholar

Ochieng A, Onyango MS. Drag models, solids concentration and velocity distribution in a stirred tank. Powder Technol 2008; 181: 1–8.10.1016/j.powtec.2007.03.034Search in Google Scholar

Ochieng A, Onyango MS. CFD simulation of solid suspension in stirred tanks: review. Hem Ind 2010; 64: 365–374.10.2298/HEMIND100714051OSearch in Google Scholar

Ochieng A, Onyango M, Kiriamiti K. Experimental measurement and computational fluid dynamics simulation of mixing in a stirred tank: a review. S Afr J Sci 2009; 105: 11–12.Search in Google Scholar

Oshinowo LM, Bakker A. CFD modelling of solid suspensions in stirred tanks. Symposium on Computational Modelling of Metals, Minerals and Materials, TMS Annual Meeting. Seattle, WA, 2002: 234–242.Search in Google Scholar

Osman J, Varley J. The use of computational fluid dynamics (CFD) to estimate mixing times in a stirred tank. IChemE Symp Ser 1999; 146: 15–22.Search in Google Scholar

Panneerselvam R, Savithri S, Surender GD. CFD modeling of gas-liquid-solid mechanically agitated contactor. Chem Eng Res Des 2008; 86: 1331–1344.10.1016/j.cherd.2008.08.008Search in Google Scholar

Petitti M, Nasuti A, Marchisio DL, Vanni M, Baldi G, Mancini N, Podenzani F. Bubble size distribution modeling in stirred gas-liquid reactors with QMOM augmented by a new correction algorithm. AIChe J 2010; 56: 36–53.10.1002/aic.12003Search in Google Scholar

Pinelli D, Nocentini M, Magelli F. Solids distribution in stirred slurry reactors: influence of some mixer configurations and limits to the applicability of a simple model for predictions. Chem Eng Commun 2001; 188: 91–107.10.1080/00986440108912898Search in Google Scholar

Pinelli D, Montante G, Magelli F. Dispersion coefficients and settling velocities of solids in slurry vessels stirred with different types of multiple impellers. Chem Eng Sci 2009; 59: 3081–3089.10.1016/j.ces.2004.04.033Search in Google Scholar

Qi N, Zhang H, Zhang K, Xu G, Yang Y. CFD simulation of particle suspension in a stirred tank. Particuology 2012; 11: 317–326.10.1016/j.partic.2012.03.003Search in Google Scholar

Rieger F, Ditl P. Suspension of solid particles. Chem Eng Sci 1994; 49: 2219–2227.10.1016/0009-2509(94)E0029-PSearch in Google Scholar

Saffman PG, Turner JS. On the collision of drops in turbulent clouds. J Fluid Mech 1956; 1: 16–30.10.1017/S0022112056000020Search in Google Scholar

Sajjadi B, Abdul Raman AA, Ibrahim S, Raja Ehsan Shah RSS. Review on gas-liquid mixing analysis in multiscale stirred vessel using CFD. Rev Chem Eng 2012; 28: 171–189.10.1515/revce-2012-0003Search in Google Scholar

Sajjadi B, Abdul Raman AA, Raja Ehsan Shah RSS, Ibrahim S. Review on applicable breakup/coalescence models in turbulent liquid-liquid flows. Rev Chem Eng 2013; 29: 131–158.10.1515/revce-2012-0014Search in Google Scholar

Sankaran V, Sitaraman J, Flynt B, Farhat C. Development of a coupled and unified solution method for fluid-structure interactions. In: Choi H, Choi HG, Yoo J, editors. Computational fluid dynamics 2008. Berlin: Springer Berlin Heidelberg, 2009: 147–152.Search in Google Scholar

Sardeshpande MV, Ranade VV. Computational fluid dynamics modelling of solid suspension in stirred tanks. Curr Sci 2012; 102: 1530–1551.Search in Google Scholar

Sardeshpande MV, Juvekar VA, Ranade VV. Hysteresis in cloud heights during solid suspension in stirred tank reactor: experiments and CFD simulations. AIChE J 2010; 56: 2795–2804.10.1002/aic.12191Search in Google Scholar

Schiller L, Naumann Z. A drag coefficient correlation. Z Ver Deutsch Ing 1935; 77: 51.Search in Google Scholar

Sha Z, Palosaari S. Modeling and simulation of crystal size distribution in imperfectly mixed suspension crystallization. J Chem Eng Jpn 2002; 35: 1188–1195.10.1252/jcej.35.1188Search in Google Scholar

Sha Z, Oinas P, Louhi-Kultanen M, Yang G, Palosaari S. Application of CFD simulation to suspension crystallization – factors affecting size-dependent classification. Powder Technol 2001; 121: 20–25.10.1016/S0032-5910(01)00369-2Search in Google Scholar

Shamlou PA, Zolfagharian A. Incipient solid motion in liquids in mechanically agitated vessels. In: Proceedings of the 3rd Fluid Mixing Conference 1987: 195–208.Search in Google Scholar

Sharma RN, Shaikh AA. Solids suspension in stirred tanks with pitched blade turbines. Chem Eng Sci 2003; 58: 2123–2140.10.1016/S0009-2509(03)00023-XSearch in Google Scholar

Singh H, Fletcher DF, Nijdam JJ. An assessment of different turbulence models for predicting flow in a baffled tank stirred with a Rushton turbine. Chem Eng Sci 2011; 66: 5976–5988.10.1016/j.ces.2011.08.018Search in Google Scholar

Smith FG. A model of transient mixing in a stirred tank. Chem Eng Sci 1997; 52: 1459–1478.10.1016/S0009-2509(96)00472-1Search in Google Scholar

Špidla M, Moštěk M, Sinevič V, Jahoda M, Machoň V. Experimental assessment and CFD simulations of local solid concentration profiles in a pilot-scale stirred tank. Chem Pap 2005; 59: 386–393.Search in Google Scholar

Sundaram S, Collins LR. Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J Fluid Mech 1997; 335: 75–109.10.1017/S0022112096004454Search in Google Scholar

Syamlal M. The particle-particle drag term in a multiparticle model of fluidization. Springfield, VA: National Technical Information Service, 1987: 188.Search in Google Scholar

Taghavi M, Zadghaffari R, Moghaddas J, Moghaddas Y. Experimental and CFD investigation of power consumption in a dual Rushton turbine stirred tank. Chem Eng Res Des 2011; 89: 280–290.10.1016/j.cherd.2010.07.006Search in Google Scholar

Tamburini A, Cipollina A, Micale G, Ciofalo M, Brucato A. Dense solid-liquid off-bottom suspension dynamics: simulation and experiment. Chem Eng Res Des 2009; 87: 587–597.10.1016/j.cherd.2008.12.024Search in Google Scholar

Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M. CFD simulations of dense solid-liquid suspensions in baffled stirred tanks: prediction of suspension curves. Chem Eng J 2011; 178: 324–341.10.1016/j.cej.2011.10.016Search in Google Scholar

Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M. CFD Simulations of dense solid-liquid suspensions in baffled stirred tanks: prediction of the minimum impeller speed for complete suspension. Chem Eng J 2012; 193–194: 234–255.10.1016/j.cej.2012.04.044Search in Google Scholar

Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M. CFD simulations of dense solid-liquid suspensions in baffled stirred tanks: prediction of solid particle distribution. Chem Eng J 2013; 223: 875–890.10.1016/j.cej.2013.03.048Search in Google Scholar

Tamburini A, Cipollina A, Micale G, Brucato A, Ciofalo M. Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels. Chem Eng Res Des 2014; 92: 1045–1063.10.1016/j.cherd.2013.10.020Search in Google Scholar

Van den Akker HEA. The details of turbulent mixing process and their simulation. Adv Chem Eng 2006; 31: 151–229.10.1016/S0065-2377(06)31003-4Search in Google Scholar

van Wachem BGM, Almstedt AE. Methods for multiphase computational fluid dynamics. Chem Eng J 2003; 96: 81–98.10.1016/j.cej.2003.08.025Search in Google Scholar

Wadnerkar D, Utikar RP, Tade MO, Pareek VK. CFD simulation of solid-liquid stirred tanks. Adv Powder Technol 2012; 23: 445–453.10.1016/j.apt.2012.03.007Search in Google Scholar

Waghmare Y, Falk R, Graham L, Koganti V. Drawdown of floating solids in stirred tanks: scale-up study using CFD modeling. Int J Pharm 2011; 418: 243–253.10.1016/j.ijpharm.2011.05.039Search in Google Scholar PubMed

Wang LP, Wexler AS, Zhou Y. Statistical mechanical descriptions of turbulent coagulation. Phys Fluids 1998; 10: 2647–2651.10.1063/1.869777Search in Google Scholar

Wang LP, Wexler AS, Zhou Y. Statistical mechanical description and modelling of turbulent collision of inertial particles. J Fluid Mech 2000; 415: 117–153.10.1017/S0022112000008661Search in Google Scholar

Wang F, Mao Z, Shen X. Numerical study of solid-liquid two-phase flow in stirred tanks with Rushton impeller (II) prediction of critical impeller speed. Chin J Chem Eng 2004; 12: 610–614.Search in Google Scholar

Wang F, Mao Z, Wang Y, Yang C. Measurement of phase holdups in liquid-liquid-solid three-phase stirred tanks and CFD simulation. Chem Eng Sci 2006; 61: 7535–7550.10.1016/j.ces.2006.08.046Search in Google Scholar

Wang L, Yifei Zhang, Li X, Zhang Y. Experimental investigation and CFD simulation of liquid-solid-solid dispersion in a stirred reactor. Chem Eng Sci 2010; 65: 5559–5572.10.1016/j.ces.2010.08.002Search in Google Scholar

Wang K, Rallu A, Gerbeauand J-F, Farhat C. Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid-structure interaction problems. Int J Numer Methods Fluids 2011; 67: 1175–1206.10.1002/fld.2556Search in Google Scholar

Wang K, Grétarsson J, Main A, Farhat C. Computational algorithms for tracking dynamic fluid-structure interfaces in embedded boundary methods. Int J Numer Methods Fluids 2012; 70: 515–535.10.1002/fld.3659Search in Google Scholar

Wen CY, Yu YH. Mechanics of fluidization. Chem Eng Prog Symp Ser 1966; 62: 100–111.Search in Google Scholar

Wichterle K. Conditions for suspension of solids in agitated vessels. Chem Eng Sci 1988; 43: 467–471.10.1016/0009-2509(88)87007-6Search in Google Scholar

Williams JJE, Crane RI. Particle collision rate in turbulent flow. Int J Multiphase Flow 1983; 9: 421–435.10.1016/0301-9322(83)90098-8Search in Google Scholar

Yeoh SL, Papadakis G, Yianneskis M. Determination of mixing time and degree of homogeneity in stirred vessels with large eddy simulation. Chem Eng Science 2005; 60: 2293–2302.10.1016/j.ces.2004.10.048Search in Google Scholar

Yuu S. Collision rate of small particles in a homogeneous and isotropic turbulence. AIChE J 1984; 30: 802–807.10.1002/aic.690300515Search in Google Scholar

Zaichik LI, Alipchenkov VM. Pair dispersion and preferential concentration of particles in isotropic turbulence. Phys Fluids 2003; 15: 1776–1787.10.1063/1.1569485Search in Google Scholar

Zaichik LI, Simonin O, Alipchenkov VM. Collision rates of bidisperse inertial particles in isotropic turbulence. Phys Fluids 2006; 18: 035110.10.1063/1.2187548Search in Google Scholar

Zhou Y, Wexler AS, Wang L-P. Modelling turbulent collision of bidisperse inertial particles. J Fluid Mech 2001; 433: 77–104.10.1017/S0022112000003372Search in Google Scholar

Zwietering TN. Suspending of solid particles in liquid by agitators. Chem Eng Sci 1958; 8: 244–253.10.1016/0009-2509(58)85031-9Search in Google Scholar