Journal articles: 'Population balance modelling'

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Nopens, I., and C. A. Biggs. "Advances in population balance modelling." Chemical Engineering Science 61, no. 1 (January 2006): 1–2. http://dx.doi.org/10.1016/j.ces.2005.05.026.

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Utomo, Johan, Nicoleta Balliu, and Moses O. Tadé. "CHALLENGES OF MODELLING A POPULATION BALANCE USING WAVELET." IFAC Proceedings Volumes 39, no. 2 (2006): 643–48. http://dx.doi.org/10.3182/20060402-4-br-2902.00643.

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Tan, H. S., M. J. V. Goldschmidt, R. Boerefijn, M. J. Hounslow, D. Salman, and J. A. M. Kuipers. "Population Balance Modelling of Fluidized Bed Melt Granulation." Chemical Engineering Research and Design 83, no. 7 (July 2005): 871–80. http://dx.doi.org/10.1205/cherd.04347.

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Coufort, Carole, Denis Bouyer, Alain Liné, and Benoît Haut. "Modelling of flocculation using a population balance equation." Chemical Engineering and Processing: Process Intensification 46, no. 12 (December 2007): 1264–73. http://dx.doi.org/10.1016/j.cep.2006.10.012.

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Liu, Jing J., Cai Y. Ma, Yang D. Hu, and Xue Z. Wang. "Modelling protein crystallisation using morphological population balance models." Chemical Engineering Research and Design 88, no. 4 (April 2010): 437–46. http://dx.doi.org/10.1016/j.cherd.2009.08.015.

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Pougatch, Konstantin, Sean Delfel, Majid Hosseini, Benny Moyls, Ardalan Sadighian, and Adrian Revington. "Population balance modelling of dense clay slurries flocculation." Chemical Engineering Science 231 (February 2021): 116260. http://dx.doi.org/10.1016/j.ces.2020.116260.

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Rollié, Sascha, Heiko Briesen, and Kai Sundmacher. "Discrete bivariate population balance modelling of heteroaggregation processes." Journal of Colloid and Interface Science 336, no. 2 (August 2009): 551–64. http://dx.doi.org/10.1016/j.jcis.2009.04.031.

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Schmidt, Stephan A., Martin Simon, Menwer M. Attarakih, Luis Lagar G., and Hans-Jörg Bart. "Droplet population balance modelling—hydrodynamics and mass transfer." Chemical Engineering Science 61, no. 1 (January 2006): 246–56. http://dx.doi.org/10.1016/j.ces.2005.02.075.

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Patruno, L. E., C. A. Dorao, H. F. Svendsen, and H. A. Jakobsen. "Analysis of breakage kernels for population balance modelling." Chemical Engineering Science 64, no. 3 (February 2009): 501–8. http://dx.doi.org/10.1016/j.ces.2008.09.029.

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Attarakih, Menwer M., Hans-Jörg Bart, Tilmann Steinmetz, Markus Dietzen, and Naim M. Faqir. "LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns." Open Chemical Engineering Journal 2, no. 1 (March 4, 2008): 10–34. http://dx.doi.org/10.2174/1874123100802010010.

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The population balance equation finds many applications in modelling poly-dispersed systems arising in many engineering applications such as aerosols dynamics, crystallization, precipitation, granulation, liquid-liquid, gas-liquid, combustion processes and microbial systems. The population balance lays down a modern approach for modelling the complex discrete behaviour of such systems. Due to the industrial importance of liquid-liquid extraction columns for the separation of many chemicals that are not amenable for separation by distillation, a Windows based program called LLECMOD is developed. Due to the multivariate nature of the population of droplets in liquid –liquid extraction columns (with respect to size and solute concentration), a spatially distributed population balance equation is developed. The basis of LLECMOD depends on modern numerical algorithms that couples the computational fluid dynamics and population balances. To avoid the solution of the momentum balance equations (for the continuous and discrete phases), experimental correlations are used for the estimation of the turbulent energy dissipation and the slip velocities of the moving droplets along with interaction frequencies of breakage and coalescence. The design of LLECMOD is flexible in such a way that allows the user to define droplet terminal velocity, energy dissipation, axial dispersion, breakage and coalescence frequencies and the other internal geometrical details of the column. The user input dialog makes the LLECMOD a user-friendly program that enables the user to select the simulation parameters and functions easily. The program is reinforced by a parameter estimation package for the droplet coalescence models. The scale-up and simulation of agitated extraction columns based on the populations balanced model leads to the main application of the simulation tool.

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Nopens, Ingmar, Elena Torfs, Joel Ducoste, Peter A. Vanrolleghem, and Krist V. Gernaey. "Population balance models: a useful complementary modelling framework for future WWTP modelling." Water Science and Technology 71, no. 2 (December 9, 2014): 159–67. http://dx.doi.org/10.2166/wst.2014.500.

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Population balance models (PBMs) represent a powerful modelling framework for the description of the dynamics of properties that are characterised by distributions. This distribution of properties under transient conditions has been demonstrated in many chemical engineering applications. Modelling efforts of several current and future unit processes in wastewater treatment plants could potentially benefit from this framework, especially when distributed dynamics have a significant impact on the overall unit process performance. In these cases, current models that rely on average properties cannot sufficiently capture the true behaviour and even lead to completely wrong conclusions. Examples of distributed properties are bubble size, floc size, crystal size or granule size. In these cases, PBMs can be used to develop new knowledge that can be embedded in our current models to improve their predictive capability. Hence, PBMs should be regarded as a complementary modelling framework to biokinetic models. This paper provides an overview of current applications, future potential and limitations of PBMs in the field of wastewater treatment modelling, thereby looking over the fence to other scientific disciplines.

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Rigopoulos, S. "Population balance modelling of polydispersed particles in reactive flows." Progress in Energy and Combustion Science 36, no. 4 (August 2010): 412–43. http://dx.doi.org/10.1016/j.pecs.2009.12.001.

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Liu, L. X., D. J. Robinson, and J. Addai-Mensah. "Population balance based modelling of nickel laterite agglomeration behaviour." Powder Technology 223 (June 2012): 92–97. http://dx.doi.org/10.1016/j.powtec.2011.06.020.

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Patruno, L. E., C. A. Dorao, P. M. Dupuy, H. F. Svendsen, and H. A. Jakobsen. "Identification of droplet breakage kernel for population balance modelling." Chemical Engineering Science 64, no. 4 (February 2009): 638–45. http://dx.doi.org/10.1016/j.ces.2008.05.015.

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Süle, Zoltán, Béla G. Lakatos, Csaba Mihálykó, and Éva Orbán-Mihálykó. "Modelling of Heat Transfer Processes with Compartment/Population Balance Model." Periodica Polytechnica Chemical Engineering 57, no. 1–2 (2013): 3. http://dx.doi.org/10.3311/ppch.2163.

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Cheung, Sherman C. P., Guan Heng Yeoh, and Jiyuan Tu. "A Review of Population Balance Modelling for Isothermal Bubbly Flows." Journal of Computational Multiphase Flows 1, no. 2 (June 2009): 161–99. http://dx.doi.org/10.1260/175748209789563928.

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Süle, Z., B. G. Lakatos, and Cs Mihálykó. "Modelling of Heat Transfer Processes with Compartment/Population Balance Model." SNE Simulation Notes Europe 18, no. 3-4 (December 2009): 25–32. http://dx.doi.org/10.11128/sne.19.tn.09945.

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Crundwell, F. K., and A. W. Bryson. "The modelling of particulate leaching reactors— the population balance approach." Hydrometallurgy 29, no. 1-3 (June 1992): 275–95. http://dx.doi.org/10.1016/0304-386x(92)90018-u.

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Chimwani, Ngonidzashe, and Murray M. Bwalya. "Milling Studies in an Impact Crusher I: Kinetics Modelling Based on Population Balance Modelling." Minerals 11, no. 5 (April 30, 2021): 470. http://dx.doi.org/10.3390/min11050470.

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A number of experiments were conducted on a laboratory batch impact crusher to investigate the effects of particle size and impeller speed on grinding rate and product size distribution. The experiments involved feeding a fixed mass of particles through a funnel into the crusher up to four times, and monitoring the grinding achieved with each pass. The duration of each pass was approximately 20 s; thus, this amounted to a total time of 1 min and 20 s of grinding for four passes. The population balance model (PBM) was then used to describe the breakage process, and its effectiveness as a tool for describing the breakage process in the vertical impact crusher is assessed. It was observed that low impeller speeds require longer crushing time to break the particles significantly whilst for higher speeds, longer crushing time is not desirable as grinding rate sharply decreases as the crushing time increases, hence the process becomes inefficient. Results also showed that larger particle sizes require shorter breakage time whilst smaller feed particles require longer breakage time.

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Hosseini, Seyed Ali, and Nilay Shah. "Modelling enzymatic hydrolysis of cellulose part I: Population balance modelling of hydrolysis by endoglucanase." Biomass and Bioenergy 35, no. 9 (October 2011): 3841–48. http://dx.doi.org/10.1016/j.biombioe.2011.04.026.

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Skorych, Vasyl, Nilima Das, Maksym Dosta, Jitendra Kumar, and Stefan Heinrich. "Application of Transformation Matrices to the Solution of Population Balance Equations." Processes 7, no. 8 (August 14, 2019): 535. http://dx.doi.org/10.3390/pr7080535.

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The development of algorithms and methods for modelling flowsheets in the field of granular materials has a number of challenges. The difficulties are mainly related to the inhomogeneity of solid materials, requiring a description of granular materials using distributed parameters. To overcome some of these problems, an approach with transformation matrices can be used. This allows one to quantitatively describe the material transitions between different classes in a multidimensional distributed set of parameters, making it possible to properly handle dependent distributions. This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes. The finite volume method for spatial discretization and the second-order Runge–Kutta method were used to obtain the complete discretized form of the PBE and to calculate the transformation matrices. The proposed method was implemented in the flowsheet modelling framework Dyssol to demonstrate and prove its applicability. Hence, it was revealed that this new approach allows the modelling of complex processes involving materials described by several interconnected distributed parameters, correctly taking into consideration their interdependency.

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22

Li, Zhen Liang. "Modelling the Activated Sludge Flocculation Process Using Population Balance Model (PBM)." Advanced Materials Research 610-613 (December 2012): 1372–76. http://dx.doi.org/10.4028/www.scientific.net/amr.610-613.1372.

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This paper describes the application of population balance models to activated sludge flocculation process. It presents the development and selection of appropriate expressions for aggregation and breakage kinetics within the population balance framework to describe the evolution of mean size and steady state distribution of flocs under shear conditions. A size and velocity gradient dependent collision efficiency is introduced into the aggregation expression. In the model, only 2 parameters need to be estimated: collision efficiency coefficient and the breakage frequency coefficient. They are obtained by the “best fit” with the experimental data, and keep unchanged under different shear condition for the same flocs. The modelling results indicate that the population balance models coupled with suitable aggregation and breakage kinetics is appropriate for describing activated sludge flocculation dynamics.

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Puel, F., and G. Févotte. "Two-Dimensional Population Balance Modelling of Semi-Batch Organic Solution Crystallization." IFAC Proceedings Volumes 37, no. 1 (January 2004): 595–600. http://dx.doi.org/10.1016/s1474-6670(17)38797-9.

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24

Jeldres, Ricardo I., Phillip D. Fawell, and Brendan J. Florio. "Population balance modelling to describe the particle aggregation process: A review." Powder Technology 326 (February 2018): 190–207. http://dx.doi.org/10.1016/j.powtec.2017.12.033.

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25

X. Liu, L., and J. D. Litster. "Population balance modelling of granulation with a physically based coalescence kernel." Chemical Engineering Science 57, no. 12 (June 2002): 2183–91. http://dx.doi.org/10.1016/s0009-2509(02)00110-0.

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Vollmer, Ulrich, and Jörg Raisch. "Population balance modelling and H∞—controller design for a crystallization process." Chemical Engineering Science 57, no. 20 (October 2002): 4401–14. http://dx.doi.org/10.1016/s0009-2509(02)00354-8.

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Liu, L. "Population balance modelling for high concentration nanoparticle sizing with ultrasound spectroscopy." Powder Technology 203, no. 3 (November 2010): 469–76. http://dx.doi.org/10.1016/j.powtec.2010.06.008.

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Szilágyi, Botond, Norbert Muntean, Réka Barabás, Oana Ponta, and Béla G. Lakatos. "Reaction precipitation of amorphous calcium phosphate: Population balance modelling and kinetics." Chemical Engineering Research and Design 93 (January 2015): 278–86. http://dx.doi.org/10.1016/j.cherd.2014.04.003.

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Bartolini, Edoardo, Harry Manoli, Eleonora Costamagna, Hari Athitha Jeyaseelan, Mouna Hamad, Mohammad R. Irhimeh, Ali Khademhosseini, and Ali Abbas. "Population balance modelling of stem cell culture in 3D suspension bioreactors." Chemical Engineering Research and Design 101 (September 2015): 125–34. http://dx.doi.org/10.1016/j.cherd.2015.07.014.

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Gemello, Luca, Cécile Plais, Frédéric Augier, and Daniele L. Marchisio. "Population balance modelling of bubble columns under the heterogeneous flow regime." Chemical Engineering Journal 372 (September 2019): 590–604. http://dx.doi.org/10.1016/j.cej.2019.04.109.

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31

Bansal, Rohit, Pulkit Srivastava, Anurag S. Rathore, and Paresh Chokshi. "Population balance modelling of aggregation of monoclonal antibody based therapeutic proteins." Chemical Engineering Science 216 (April 2020): 115479. http://dx.doi.org/10.1016/j.ces.2020.115479.

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32

Vikhansky, Alexander, and Markus Kraft. "Modelling of a RDC using a combined CFD-population balance approach." Chemical Engineering Science 59, no. 13 (July 2004): 2597–606. http://dx.doi.org/10.1016/j.ces.2004.02.016.

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33

Yeoh, G. H., and J. Y. Tu. "Population balance modelling for bubbly flows with heat and mass transfer." Chemical Engineering Science 59, no. 15 (August 2004): 3125–39. http://dx.doi.org/10.1016/j.ces.2004.04.023.

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34

Hu, Bin, Omar K. Matar, Geoffrey F. Hewitt, and Panagiota Angeli. "Population balance modelling of phase inversion in liquid–liquid pipeline flows." Chemical Engineering Science 61, no. 15 (August 2006): 4994–97. http://dx.doi.org/10.1016/j.ces.2006.03.053.

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35

Lebaz, Noureddine, Arnaud Cockx, Mathieu Spérandio, and Jérôme Morchain. "Population balance approach for the modelling of enzymatic hydrolysis of cellulose." Canadian Journal of Chemical Engineering 93, no. 2 (December 17, 2014): 276–84. http://dx.doi.org/10.1002/cjce.22088.

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36

Biggs, C., P. Lant, and M. Hounslow. "Modelling the effect of shear history on activated sludge flocculation." Water Science and Technology 47, no. 11 (June 1, 2003): 251–57. http://dx.doi.org/10.2166/wst.2003.0612.

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The aim of this paper is to investigate the effect of shear history on activated sludge flocculation dynamics and to model the observed relationships using population balances. Activated sludge flocs are exposed to dramatic changes in the shear rate within the treatment process, as they pass through localised high and low mixing intensities within the aeration basin and are cycled through the different unit operations of the treatment process. We will show that shear history is a key factor in determining floc size, and that the floc size varies irreversibly with changes in shear rate. A population balance model of the flocculation process is also introduced and evaluated.

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Boje, Astrid, and Markus Kraft. "Stochastic population balance methods for detailed modelling of flame-made aerosol particles." Journal of Aerosol Science 159 (January 2022): 105895. http://dx.doi.org/10.1016/j.jaerosci.2021.105895.

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38

Bellinghausen, Stefan, Emmanuela Gavi, Laura Jerke, Dana Barrasso, Agba D. Salman, and James D. Litster. "Model-driven design using population balance modelling for high-shear wet granulation." Powder Technology 396 (January 2022): 578–95. http://dx.doi.org/10.1016/j.powtec.2021.10.028.

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39

Alhuthali, Sakhr, and Cleo Kontoravdi. "Population balance modelling captures host cell protein dynamics in CHO cell cultures." PLOS ONE 17, no. 3 (March 23, 2022): e0265886. http://dx.doi.org/10.1371/journal.pone.0265886.

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Monoclonal antibodies (mAbs) have been extensively studied for their wide therapeutic and research applications. Increases in mAb titre has been achieved mainly by cell culture media/feed improvement and cell line engineering to increase cell density and specific mAb productivity. However, this improvement has shifted the bottleneck to downstream purification steps. The higher accumulation of the main cell-derived impurities, host cell proteins (HCPs), in the supernatant can negatively affect product integrity and immunogenicity in addition to increasing the cost of capture and polishing steps. Mathematical modelling of bioprocess dynamics is a valuable tool to improve industrial production at fast rate and low cost. Herein, a single stage volume-based population balance model (PBM) has been built to capture Chinese hamster ovary (CHO) cell behaviour in fed-batch bioreactors. Using cell volume as the internal variable, the model captures the dynamics of mAb and HCP accumulation extracellularly under physiological and mild hypothermic culture conditions. Model-based analysis and orthogonal measurements of lactate dehydrogenase activity and double-stranded DNA concentration in the supernatant show that a significant proportion of HCPs found in the extracellular matrix is secreted by viable cells. The PBM then served as a platform for generating operating strategies that optimise antibody titre and increase cost-efficiency while minimising impurity levels.

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Ismail, Hamza Y., Mehakpreet Singh, Ahmad B. Albadarin, and Gavin M. Walker. "Complete two dimensional population balance modelling of wet granulation in twin screw." International Journal of Pharmaceutics 591 (December 2020): 120018. http://dx.doi.org/10.1016/j.ijpharm.2020.120018.

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41

Monnier, O., G. Févotte, C. Hoff, and J. P. Klein. "An advanced calorimetric approach for population balance modelling in batch crystallization processes." Thermochimica Acta 289, no. 2 (December 1996): 327–41. http://dx.doi.org/10.1016/s0040-6031(96)03010-9.

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42

Boje, Astrid, Jethro Akroyd, Stephen Sutcliffe, John Edwards, and Markus Kraft. "Detailed population balance modelling of TiO 2 synthesis in an industrial reactor." Chemical Engineering Science 164 (June 2017): 219–31. http://dx.doi.org/10.1016/j.ces.2017.02.019.

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43

Muralidhar, R., S. Gustafson, and D. Ramkrishna. "Population balance modelling of bubbling fluidized beds. II. Axially dispersed dense phase." Sadhana 10, no. 1-2 (April 1987): 69–86. http://dx.doi.org/10.1007/bf02816198.

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44

Adetayo, A. A., J. D. Litster, S. E. Pratsinis, and B. J. Ennis. "Population balance modelling of drum granulation of materials with wide size distribution." Powder Technology 82, no. 1 (January 1995): 37–49. http://dx.doi.org/10.1016/0032-5910(94)02896-v.

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45

Grancic, Peter, Viera Illeova, Milan Polakovic, and Jan Sefcik. "Thermally induced inactivation and aggregation of urease: Experiments and population balance modelling." Chemical Engineering Science 70 (March 2012): 14–21. http://dx.doi.org/10.1016/j.ces.2011.07.050.

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46

Bari, Atul H., and Aniruddha B. Pandit. "Ultrasound-facilitated particle breakage: Estimation of kinetic parameters using population balance modelling." Canadian Journal of Chemical Engineering 92, no. 12 (October 8, 2014): 2046–52. http://dx.doi.org/10.1002/cjce.22072.

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47

Zhou, Kun, Xiao Jiang, and Tat Leung Chan. "Error analysis in stochastic solutions of population balance equations." Applied Mathematical Modelling 80 (April 2020): 531–52. http://dx.doi.org/10.1016/j.apm.2019.11.045.

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48

Salehi, F., M. J. Cleary, and A. R. Masri. "Population balance equation for turbulent polydispersed inertial droplets and particles." Journal of Fluid Mechanics 831 (October 17, 2017): 719–42. http://dx.doi.org/10.1017/jfm.2017.653.

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This paper presents a probability density function (PDF) form of the population balance equation (PBE) for polysized and polyshaped droplets and solid particles in turbulent flows. A key contribution of this paper lies in the inclusion of an explicit consideration of the inertial effects and the shape of particles in the PDF-PBE formulation. The number density is taken as a function of droplet or particle size (volume) and shape as well as space and time. Potentially, other particle properties could also be included in the formulation. Inertial effects are quantified through the Stokes number, leading to accurate modelling of the different trajectories that are followed by droplets and/or particles with different sizes and shapes. To treat these effects, a new affordable approach is proposed and referred to as the method of Stokes binning. Here, the inertial dispersed elements are accelerated due to fluid dynamic forces associated with an averaged Stokes number in each bin. The model is validated against two data sets. The first data set includes a series of numerical test cases involving the injection of polyshaped droplets ranging in size from 1 to 50 $\unicode[STIX]{x03BC}\text{m}$ into a turbulent jet resulting in inlet Stokes numbers ranging from 0.03 to 75.2. The second data set consists of an experimental case focusing on the dispersion of 60 and 90 $\unicode[STIX]{x03BC}\text{m}$ spherical droplets in a turbulent round jet, resulting in inlet Stokes numbers of 53 and 122, respectively. The results confirm the ability of the approach to accurately model the polysized and polyshaped droplet dispersion using as few as eight Stokes bins. This approach has the potential to greatly reduce the computational cost of modelling the evolution of inertial droplets and particles in turbulent flows.

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49

Nopens, I., C. A. Biggs, B. De Clercq, R. Govoreanu, B. M. Wilén, P. Lant, and P. A. Vanrolleghem. "Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)." Water Science and Technology 45, no. 6 (March 1, 2002): 41–49. http://dx.doi.org/10.2166/wst.2002.0092.

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A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data. This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.

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50

Krzosa, Radosław, Łukasz Makowski, Wojciech Orciuch, and Radosław Adamek. "Population Balance Application in TiO2 Particle Deagglomeration Process Modeling." Energies 14, no. 12 (June 13, 2021): 3523. http://dx.doi.org/10.3390/en14123523.

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The deagglomeration of titanium-dioxide powder in water suspension performed in a stirring tank was investigated. Owing to the widespread applications of the deagglomeration process and titanium dioxide powder, new, more efficient devices and methods of predicting the process result are highly needed. A brief literature review of the application process, the device used, and process mechanism is presented herein. In the experiments, deagglomeration of the titanium dioxide suspension was performed. The change in particle size distribution in time was investigated for different impeller geometries and rotational speeds. The modification of impeller geometry allowed the improvement of the process of solid particle breakage. In the modelling part, numerical simulations of the chosen impeller geometries were performed using computational-fluid-dynamics (CFD) methods whereby the flow field, hydrodynamic stresses, and other useful parameters were calculated. Finally, based on the simulation results, the population-balance with a mechanistic model of suspension flow was developed. Model predictions of the change in particle size showed good agreement with the experimental data. Using the presented method in the process design allowed the prediction of the product size and the comparison of the efficiency of different impeller geometries.

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Journal articles on the topic 'Population balance modelling'

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