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Abstract

The main topic of this study is the mathematical modelling of bubble size distributions in an aerated stirred tank using the population balance method. The air-water system consisted of a fully baffled vessel with a diameter of 0.29 m, which was equipped with a six-bladed Rushton turbine. The secondary phase was introduced through a ring sparger situated under the impeller. Calculations were performed with the CFD software CFX 14.5. The turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the MUSIG method with 24 bubble size groups. For the bubble size distribution modelling, the breakup model by Luo and Svendsen (1996) typically has been used in the past. However, this breakup model was thoroughly reviewed and its practical applicability was questioned. Therefore, three different breakup models by Martínez-Bazán et al. (1999a, b), Lehr et al. (2002) and Alopaeus et al. (2002) were implemented in the CFD solver and applied to the system. The resulting Sauter mean diameters and local bubble size distributions were compared with experimental data.

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Authors and Affiliations

Zbyněk Kálal
Milan Jahoda
Ivan Fořt
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Abstract

In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

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Authors and Affiliations

Jerzy Bałdyga
Grzegorz Tyl
Mounir Bouaifi
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Abstract

The paper presents a photographic analysis of the break-up of gas bubbles flowing out of the outlets of a self-aspirating disk impeller. It was found that bubbles detached from the interfacial surface most often disintegrate to form several daughter bubbles. Further in the work, the population balance model was verified for several formulas describing the bubble break-up rate. It has been found that a good fit to the experimental data is provided by the formula given by Laakkonen for 5 daughter bubbles. The possibility of using the Monte Carlo method to model the bubble break-up processwas also determined. For this method, a good agreement of results was achieved for the division into a maximum of 10 daughter bubbles. In the case of this method it was also found necessary to use the function of break-up frequency at a higher rate for smaller bubbles.

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Authors and Affiliations

Jacek Stelmach
ORCID: ORCID
Radosław Musowski
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Abstract

Modelling of titanium dioxide deagglomeration in the mixing tank equipped with a high shear impeller is presented in this study. A combination of computational fluid dynamics with population balance was applied for prediction of the final particle size. Two approaches are presented to solve population balance equations. In the first one, a complete population balance breakage kinetics were implemented in the CFD code to simulate size changes in every numerical cell in the computational domain. The second approach uses flow field and properties of turbulence to construct a mechanistic model of suspension flow in the system. Such approach can be considered as an attractive alternative to CFD simulations, because it allows to greatly reduce time required to obtain the results, i.e., the final particle size distribution of the product. Based on experiments shattering breakage mechanism was identified. A comparison of the mechanistic model and full CFD does not deviate from each other. Therefore the application of a much faster mechanistic model has comparable accuracy with full CFD. The model of particle deagglomeration does not predict a very fast initial drop of particle size, observed in the experiment, but it can predict, with acceptable accuracy, the final particle size of the product.
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Bibliography

Atiemo-Obeng V.A., Calabrese R.V., 2004. Rotor–stator mixing devices, In: Paul E.L., Atiemo-Obeng V.A., Kresta S.M. (Eds.), Handbook of industrial mixing. DOI: 10.1002/0471451452.ch8.

Bałdyga J., Makowski Ł., OrciuchW., Sauter C., Schuchmann H.P., 2008a. Deagglomeration processes in high-shear devices. Chem. Eng. Res. Des., 86, 1369–1381. DOI: 10.1016/j.cherd.2008.08.016.

Bałdyga J., Orciuch W., Makowski Ł., Malik K., Özcan-Taskin G., Eagles W., Padron G., 2008b. Dispersion of nanoparticle clusters in a rotor-stator mixer. Ind. Eng. Chem. Res., 47, 3652–3663. DOI: 10.1021/ie070899u.

Bałdyga J., Orciuch W., Makowski Ł., Malski-Brodzicki M., Malik K., 2007. Break up of nano-particle clusters in high-shear devices. Chem. Eng. Process. Process Intensif., 46, 851–861. DOI: 10.1016/j.cep.2007.05.016.

Boverhof D.R., Bramante C.M., Butala J.H., Clancy S.F., LafranconiW.M.,West J., Gordon S.C., 2015. Comparative assessment of nanomaterial definitions and safety evaluation considerations. Regul. Toxicol. Pharm., 73, 137–150. DOI: 10.1016/j.yrtph.2015.06.001.

Chung C.J., Lin H.I., Tsou H.K., Shi Z.Y., He J.L., 2008. An antimicrobial TiO2 coating for reducing hospitalacquired infection. J. Biomed. Mater. Res. Part B, 85b, 220–224. DOI: 10.1002/jbm.b.30939.

Fujishima A., Rao T.N., Tryk D.A., 2000. Titanium dioxide photocatalysis. J. Photochem. Photobiol., C, 1, 1–21. DOI: 10.1016/S1389-5567(00)00002-2.

Gajovic A., Stubicar M., Ivanda M., Furi K., 2001. Raman spectroscopy of ball-milled TiO2. J. Mol. Struct., 563–564, 315–320. DOI: 10.1016/S0022-2860(00)00790-0.

Gavi E., Kubicki D., Padron G.A., Özcan-Taskın N.G., 2018. Breakup of nanoparticle clusters using Microfluidizer M110-P. Chem. Eng. Res. Des., 132, 902–912. DOI: 10.1016/j.cherd.2018.01.011.

Gázquez M.J., Bolívar J.P., Garcia-Tenorio R., Vaca F., 2014. A review of the production cycle of titanium dioxide pigment. Mater. Sci. Appl., 5, 441–458. DOI: 10.4236/msa.2014.57048.

Hansen S., Khakhar D.V., Ottino J.M., 1998. Dispersion of solids in nonhomogeneous viscous flows. Chem. Eng. Sci., 53, 1803–1817. DOI: 10.1016/S0009-2509(98)00010-4.

Hass G., 1952. Preparation, properties and optical applications of thin films of titanium dioxide. Vacuum, 2, 331–345. DOI: 10.1016/0042-207X(52)93783-4.

Kamaly S.W., Tarleton A.C., Özcan-Taskın N.G., 2017. Dispersion of clusters of nanoscale silica particles using batch rotor-stators. Adv. Powder Technol., 28, 2357–2365. DOI: 10.1016/j.apt.2017.06.017.

Krzosa R., Makowski Ł., OrciuchW., Adamek R., 2021. Population balance application in TiO2 particle deagglomeration process modeling. Energies, 14, 3523. DOI: 10.3390/en14123523.

Mandzy N., Grulke E., Druffel T., 2005. Breakage of TiO2 agglomerates in electrostatically stabilized aqueous dispersions. Powder Technol., 160, 121–126. DOI: 10.1016/j.powtec.2005.08.020.

Marchisio D.L., Fox R.O., 2005. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci., 36, 43–73. DOI: 10.1016/j.jaerosci.2004.07.009.

Marchisio D.L., Vigil R.D., Fox R.O., 2003. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci., 258, 322–334. DOI: 10.1016/S0021-9797(02)00054-1.

Martínez-de Jesús G., Ramírez-Munoz J., García-Cortés D., Cota L.G., 2018. Computational fluid dynamics study of flow induced by a grooved high-shear impeller in an unbaffled tank. Chem. Eng. Technol., 41, 580–589. DOI: 10.1002/ceat.201700091.

McGraw R., 1997. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol., 27, 255–265. DOI: 10.1080/02786829708965471.

Meacock G., Taylor K.D.A., Knowles M.J., Himonides A., 1997. The improved whitening of minced cod flesh using dispersed titanium dioxide. J. Sci. Food Agric., 73, 221–225. DOI: 10.1002/(SICI)1097-0010(199702)73:2221::AID-JSFA708>3.0.CO;2-U.

Middlemas S., Fang Z.Z., Fan P., 2015. Life cycle assessment comparison of emerging and traditional Titanium dioxide manufacturing processes. J. Clean. Prod., 89, 137–147. DOI: 10.1016/j.jclepro.2014.11.019.

Mikulášek P., Wakeman R.J., Marchant J.Q., 1997. The influence of pH and temperature on the rheology and stability of aqueous titanium dioxide dispersions. Chem. Eng. J., 67, 97–102. DOI: 10.1016/S1385-8947(97)00026-0.

Özcan-Taskin N.G., Padron G., Voelkel A., 2009. Effect of particle type on the mechanisms of break up of nanoscale particle clusters. Chem. Eng. Res. Des., 87, 468–473. DOI: 10.1016/j.cherd.2008.12.012.

Özcan-Taskın N.G., Padron G.A., Kubicki D., 2016. Comparative performance of in-line rotor-stators for deagglomeration processes. Chem. Eng. Sci., 156, 186–196. DOI: 10.1016/j.ces.2016.09.023.

Randolph A.D., Larson M.A., 1962. Transient and steady state size distributions in continuous mixed suspension crystallizers. AIChE J., 8, 639–645. DOI: 10.1002/aic.690080515.

Reck E., Richards M., 1999. TiO2 manufacture and life cycle analysis. Pigm. Resin Technol., 28, 149–157. DOI: 10.1108/03699429910271297.

Rodgers T.L., Cooke M., Siperstein F.R., Kowalski A., 2009. Mixing and dissolution times for a cowles disk agitator in large-scale emulsion preparation. Ind. Eng. Chem. Res., 48, 6859–6868. DOI: 10.1021/ie900286s.

Sen S., Ram M.L., Roy S., Sarkar B.K., 1999. The structural transformation of anatase TiO2 by high-energy vibrational ball milling. J. Mater. Res., 14, 841–848. DOI: 10.1557/JMR.1999.0112.

Shamlou P.A., Titchener-Hooker N., 1993. Turbulent aggregation and breakup of particles in liquids in stirred vessels, In: Shamlou P.A. (Ed.), Processing of Solid–Liquid Suspensions. Butterworth-Heinemann Ltd. 1–25. DOI: 10.1016/b978-0-7506-1134-3.50005-3.

Tang S., Ma Y., Shiu C., 2001. Modelling the mechanical strength of fractal aggregates. Colloids Surf., A, 180, 7–16. DOI: 10.1016/S0927-7757(00)00743-3.

Unadkat H., Rielly C.D., Nagy Z.K., 2011. PIV study of the flow field generated by a sawtooth impeller. Chem. Eng. Sci., 66, 5374–5387. DOI: 10.1016/j.ces.2011.07.046.

Weir A., Westerhoff P., Fabricius L., Hristovski K., Von Goetz N., 2012. Titanium dioxide nanoparticles in food and personal care products. Environ. Sci. Technol., 46, 2242–2250. DOI: 10.1021/es204168d.

Xie L., Rielly C.D., Eagles W., Özcan-Taskin G., 2007. Dispersion of nano-particle clusters using mixed flow and high shear impellers in stirred tanks. Chem. Eng. Res. Des., 85, 676–684. DOI: 10.1205/cherd06195.

Xie L., Rielly C.D., Özcan-Taskin G., 2008. Break-Up of nanoparticle agglomerates by hydrodynamically limited processes. J. Dispers. Sci. Technol., 29, 573–579. DOI: 10.1080/01932690701729211.

Yang H.G., Li C.Z., Gu H.C., Fang T.N., 2001. Rheological behavior of titanium dioxide suspensions. J. Colloid Interface Sci., 236, 96–103. DOI: 10.1006/jcis.2000.7373.

Yu J., Zhao X., Zhao Q.,Wang G., 2001. Preparation and characterization of super-hydrophilic porous TiO2 coating films. Mater. Chem. Phys., 68, 253–259 DOI: 10.1016/S0254-0584(00)00364-3.

Zhang J., Xu S., Li W., 2012. High shear mixers: A review of typical applications and studies on power draw, flow pattern, energy dissipation and transfer properties. Chem. Eng. Process., 57–58, 25–41. DOI: 10.1016/j.cep.2012.04.004.
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Authors and Affiliations

Radosław Krzosa
1
Krzysztof Wojtas
1
Jakub Golec
1
Łukasz Makowski
1
Wojciech Orciuch
1
Radosław Adamek
2

  1. Warsaw University of Technology, Faculty of Chemical and Process Engineering, ul.Warynskiego 1, 00-645 Warsaw, Poland
  2. ICHEMAD–Profarb, ul. Chorzowska 117, 44–100 Gliwice, Poland
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Abstract

In this paper aggregation of small solid particles in the perikinetic and orthokinetic regimes is considered. An aggregation kernel for colloidal particles is determined by solving the convection-diffusion equation for the pair probability function of the solid particles subject to simple shear and extensional flow patterns and DLVO potential field. Using the solution of the full model the applicability regions of simplified collision kernels from the literature are recognized and verified for a wide range of Péclet numbers. In the stable colloidal systems the assumption which considers only the flow pattern in a certain boundary layer around central particle results in a reasonable accuracy of the particle collision rate. However, when the influence of convective motion becomes more significant one should take into account the full flow field in a more rigorous manner and solve the convection-diffusion equation directly. Finally, the influence of flow pattern and process parameters on aggregation rate is discussed.
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Authors and Affiliations

Grzegorz Tyl
1
Juliusz Kondracki
2
Magdalena Jasińska
1

  1. Faculty of Chemical and Process Engineering, Warsaw University of Technology, ul. Warynskiego 1, 00-645 Warsaw, Poland
  2. Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
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Abstract

The work concerns numerical simulations of a cone mill used for emulsion preparation. Hydrodynamics, power consumption and population balance are investigated for various operating conditions at high phase volume emulsions and for different rheologies. Cone mills are usually simplified as a simple gap between rotor and stator but by increasing the complexity of the geometry till it represents the commercial device identifies a wealth of additional features such as recirculation zones above (which enhance breakage) and below (which allow for coalescence) the rotor-stator gap. Two separate sets of population balance modelling constants are required to capture all the experiment results – even with the most complex geometries. Some suggestions are made for improvements and further studies will consider other rotor-stator devices.
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Authors and Affiliations

Guido Lupieri
1
Ioannis Bagkeris
1
Jo J.M. Janssen
2
Adam J. Kowalski
1

  1. Unilever R&D, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral CH63 3JW, UK
  2. Unilever Foods Innovation Centre, Bronland 14, 6708WH Wageningen, The Nederlands

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