Dissertations / Theses: 'Population balance modelling'

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Grancic, Peter. "Population balance modelling of non-native protein aggregation." Thesis, University of Strathclyde, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.510725.

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Sweetman, Stephen John. "Population balance modelling and experimental studies of emulsion polymerisation." Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/7430.

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Emulsion polymerisation is a process of considerable technological and industrial significance. The process presents many challenges in respect to design, optimisation and multi-objective distribution control. The quality of latex is determined by the final product properties, Le. viscosity, mechanical strength and film-forming ability, which are in turn a function of the latex attributes of PSD and MWD. This motivates an inferential control scheme utilising these distributions. This research addresses model development and controllability analysis towards model-based control. A population balance model for PSD and MWD is developed. The PSD information is incorporated via a one-dimensional population distribution of the polymer particles with respect to their size, in conjunction with a population distribution of the total live polymer radicals/particle. MWD information is incorporated via one-dimensional population distributions of the live radicals and dead polymer chains with respect to their length (in different sized particles). The model solution is facilitated by a number of algorithmic developments, including a decomposition algorithm coupled with a multi-level discretisation for PSD and the application of the method of moments for MWD. This model is compared to extensive experimental data for its validation. Improvements in the form of a twodimensional version of this model enable better prediction of compartmentalisation and hence the growth rates, thereby improving model match with experiments. This work presents a study into the simultaneous controllability of PSD and MWD, assessed through an experimental sensitivity analysis on the main process manipulations: initiator, eTA, monomer and surfactant. The work analyses the practical limitations on the attainability of PSD and MWD. The range of experiments carried out clearly indicates the operation of individual mechanisms in the simultaneous formation of PSD and MWD.

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Ramachandran, Rohit. "Multi-scale population balance modelling and controllability of granulation processes." Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/7213.

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Many continuous granulation plants operate below their design capacity, suffering from high recycle rates and instabilities. Thus, there is an immediate economic incentive for effective operation and control of granulation units. The overall granulation process is integrated and interacting, with limited manipulated variables available (e. g. binder addition, nozzle locations and mixing rate). Hence. the complex process dynamics and operational challenges presented warrant a fundamental model-based strategy for design, operation, control and scale-up that is well supported by experimental analyses. A realistic model of the granulation process has to account for the granule size, the binder content, and the porosity (or related parameter bulk density), thereby necessitating a three-dimensional population balance model to yield a good representation of the process. While this multidimensional population balance model is warranted by the physics of the problem. it is a bigger challenge to derive kernels (rate laws) for the key granulation mechanisms. Most kernels in the literature are empirical and/or semi-empirical and provide little insight into the intricacies of the granulation mechanisms. This effectively results in an inability to make the necessary engineering decisions to improve control of the granulation process. Hence, this thesis is concerned with a more systems-centric approach to enhance the design, control and scale-up of granulation processes. Experimental studies on a lab-scale batch drum granulator for a Calcite/PVOH-H20 system were performed to assess granulation kinetics and model development of the granulation process. Effects of process /material properties and liquid binder distribution on granule properties, illustrating the non-homogeneity of key particle attributes and which justify the need for multi-dimensional population balances, were studied. Process sensitivities, manipulations and potential disturbances were identified, formulating a comprehensive control configuration for granulation processes, with application seen in a continuous drum granulation of limestone. While carrying out experiments, multiple granule attributes were characterised and this presents a challenge, which this research addresses accordingly. A population balance model incorporating nucleation, aggregation, breakage and consolidation was developed in this research. Novel aspects are the mechanistic formulations of the nucleation, aggregation and breakage kernels which are derived from first-principles. Such mechanistic descriptions of the rate processes lend themselves to a more in-depth understanding of the granulation process, contributing fundamental knowledge to the design, control and scale-up of these processes. A sensitivity analysis of the model was then performed to ascertain the influence of model parameters on the particle density distribution. Continuing from this, a compartmentalised version of the combined population balance model was developed, for the purpose of controllability analysis. Results obtained were used to identify suitable control-loop pairings to facilitate enhanced control-loop performance. Experimental validation of the population balance model is an integral part of this research. The model was quantitatively validated using lab-scale experimental data for granule size, binder content and porosity. The tuned model was then able to predict evolutions and distributions of granule attributes for different operating conditions and formulations. The model was also validated for different granulation systems. This illustrates the robustness and flexibility of the model and these results are promising toward the longer-term step of a first-principles based predictive model for the granulation process that can help alleviate the need for large number of experiments. As an alternative to deriving the above-mentioned mechanistic kernels, a discrete element modelling (DEM) approach was also undertaken in this thesis. Based on a Volume of Fluid (VOF) method, the analysis carried out provided useful information to help understand the effect of primary particle morphology on granulation kinetics making it possible to establish relationships between material and process/design properties and granulation process behaviour

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Falola, Akinola Adeolu. "Online measurement and population balance modelling of stirred nano-milling." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/11860/.

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Productions of fine particles in a wet mill is important to many industries including the pharmaceutical, chemical and synthetic industry. The particle size distribution of fine particles is one of the most important properties that determine the usefulness and the quality of the final product. It is therefore important that the final suspension from the wet milling process has a narrow size distribution to meet the product specification. This requires a good real-time particle size distribution measurement system and a good process model of the manufacturing process. Particle size measurement system that can cope with all particle sizes and concentration is not yet available and population balance modelling is not well developed for the wet milling process. These issues are addressed in this thesis. Ultrasonic particle sizing techniques have the potential for real time monitoring of the particle size distribution evolution in a stirred media mill. Hardware and software for ultrasonic measurement of the real time particle size distribution were developed during this project. The particle size distribution is determined by comparing the measured attenuation spectra with the prediction from an ultrasonic wave model and the size distribution adaptively fitted by minimizing the difference between the fitted and predicted spectra. Because no single model is valid for all particle size distributions and volume concentrations, the Hybrid© model is introduced in this work to automatically pick the best model depending on the suspension’s properties. Using the Hybrid© model, the instrument was validated for several suspensions and it gave excellent particle size distributions agreement with the reference particle size distributions. All instrument functions are controlled through a graphical user interface (GUI) software developed during this project. This will make it easy to transfer the findings of this project to other workers to use in their research. The ultrasonic instrument developed was used to monitor the particle size distributions in a stirred media mills using different milling conditions. Samples were taken for offline analysis using the Malvern Mastersizer and Zetasizer instruments to validate the measured size distributions. The mill was operated in circuit mode with the suspensions continuously circulated between a 2200 ml mixing tank and the 550 ml milling chamber of the mill. The experimental results showed that generally the particle sizes decreased with time during milling. The particle sizes in the milling tank are smaller compared to the particle sizes in the mixing tank. This observation agrees with the fact that particle grinding is only done in the milling chamber; therefore it can be concluded that particle breakage took place only in the milling chamber while mixing and aggregation were the main mechanisms responsible for particle size change in the mixing tank. The results show that the smaller the grinding media size higher the particle breakage rate due to increased shear generated by smaller grinding media as well as an increase in the grinding media number density as the media size reduces for the same grinding loading. The results also show that the particle breakage rate increases with increasing mill speed but final particle size distribution is independent of the mill speed. This shows that the breakage behaviour of the particles is not a function of the mill speed. The grinding media loading however have minimal effect on both the breakage rate and the final particle size distribution. One of the main factors limiting the application of population balance modelling to wet milling is the lack of a phenomenological breakage model for wet milling. In this work, a phenomenological breakage model linking the breakage rate to the process parameters is derived. A population balance model for the circuit mode was developed and validated in this work. The parameters of the population balance model were determined by adaptively minimizing the difference between the experimental size distribution and the size distribution predicted by the population balance model. The fitted parameters show that particle breakage rate increases with increasing mill speed. The number of daughter particles produced on breakage of a single particle decreases with increasing mill speed at low mill speed before increasing with increasing mill speed at higher mill speed. The degree of attrition of particles reduces with increasing the mill speed. The particle breakage rate decreases with increasing grinding media size. However, the breakage kernel power law exponent is higher for the higher grinding media size. The higher the grinding media size, the higher the number of particles produced per breakage event and the breakage behaviour changes from attrition to something more complex with the production of high proportion of small particles and little proportion of larger particles. The breakage rate increases with the increase in the grinding media loading but the daughter distribution function is independent of the grinding media loading.

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Akridis, Petros. "Coupled CFD-population balance modelling of soot formation in laminar and turbulent flames." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/58251.

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In this thesis, a discretised Population Balance Equation (PBE) model is coupled with a detailed in-house Computational Fluid Dynamics code to study soot formation in axisymmetric diffusion flames with comprehensive gas-phase chemistries for C2H4 and CH4 fuels. The main aim of this study is to predict the complete Particle Size Distribution (PSD) of soot particles in turbulent non-premixed flames via a transported Probability Density Function approach. The PSD is obtained from the solution of the PBE without any prior assumption on its shape, using volume or diameter to describe the size of soot particles. However, due to a great number of uncertainties that appear from the turbulence interactions with chemistry, radiation and particle formation, the main objective is divided into smaller tasks where these complexities are avoided. Initially, the performance of the PBE is assessed under several numerical methods on an initial distribution-convection test, 0D reactors and 1D flamelet framework. The PBE has been originally discretised via a collocation type finite element method, and in the present work Finite Volume (FV) methods are used. The PBE with Total Variation Diminishing (TVD) scheme demonstrates better performance. The FV-TVD PBE with suitable soot kinetics is employed in 2D laminar flames where overall good agreement is achieved for the velocity, temperature, mole fraction of C2H2 and OH species and the mean properties of PSD (i.e. total number density and soot volume fraction). However, the temperature and soot volume fraction profiles on the turbulent flames do not exhibit similar accuracy as the laminar flames and there is still room for improvement. The evolution of the PSD is computed for both flames in the entire flame region exhibiting weak bimodal distribution in some points. The performance of complex coupled phenomena in PBE modelling via soot kinetics, detailed chemistry, radiation and turbulence interactions is explored.

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Di, Veroli Giovanni Yohanan. "Stochastic modelling of particle formation in turbulent flows via transported population balance-PDF method." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.515197.

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Particle formation in turbulent flows arises in a large range of industrial and environmental processes. Examples include the formation of soot particles in combustion engines, the production of nanoparticles via flame synthesis or liquid-phase reactors, or the evolution of aerosol particles in urban/non-urban environments. Simulations' can significantly improve the understanding and design/control of these processes but several difficulties arise when trying to model the underlying physics. These are mainly rooted in both the requirements of appropriate description of the particle's polydispersity and dynamics, as well as of the random fluctuations of the turbulence. In the preliminary part of this work, the turbulent effects on the particle's dynamics are discussed, showing how correlations of various orders appear in the main equation that describes them, the Population Balance Equation (PBE). The thesis elaborates a new approach for the simulation of particle formation in inhomogeneous turbulent flows, the PBE-PDF method, whose concept was recently introduced by [105]. An equation for the joint pdf of the number density and various scalars (such as the chemical species kinetically involved) is derived from fundamental equations that describe the class of considered problems. An algorithm for the numerical solution of the pdf equation is developed, based on Monte Carlo simulations. The method is discussed both at the level of the general concept of the stochastic simulations and at the level of the specific requirements of the PBE-PDF approach. The structure of the implementation is discussed in detail. Starting from empirical or theoretical kinetics, the PBE-PDF is applied to two different turbulent processes involving particle nucleation and growth. The first case considered involves the precipitation of barium sulphate crystals in a tubular reactor, while the second one involves dibutyl phthalate condensation in a free jet. For both cases the method allows for clear analysis and understanding of the particulate phase evolution, emphasis being put on the turbulent effects. Turbulence is found to have significant impact on the overall processes by spatially redistributing the intensity of the particles' mechanisms. Both processes were selected because previously studied experimentally [5][63], which allows the comparison of computed particles' size distribution with measured data. For the crystallization process the simulations' results can be directly compared, showing excellent agreements. Identified uncertainties in the experimental methods are discussed for the aerosol process, even if the computed distributions still show good agreement with the measured ones, particularly for intermediate molar fractions values.

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Menz, William Jefferson. "Stochastic modelling of silicon nanoparticle synthesis." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/245146.

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This thesis presents new methods to study the aerosol synthesis of nano-particles and a new model to simulate the formation of silicon nanoparticles. Population balance modelling is used to model nanoparticle synthesis and a stochastic numerical method is used to solve the governing equations. The population balance models are coupled to chemical kinetic models and offer insight into the fundamental physiochemical processes leading to particle formation. The first method developed in this work is a new mathematical expression for calculating the rate of Brownian coagulation with stochastic weighted algorithms (SWAs). The new expression permits the solution of the population balance equations with SWAs using a computationally-efficient technique of majorant rates and fictitious jumps. Convergence properties and efficiency of the expression are evaluated using a detailed silica particle model. A sequential-modular algorithm is subsequently presented which solves networks of perfectly stirred reactors with a population balance model using the stochastic method. The algorithm is tested in some simple network configurations, which are used to identify methods through which error in the stochastic solution may be reduced. It is observed that SWAs are useful in preventing accumulation of error in reactor networks. A new model for silicon nanoparticle synthesis is developed. The model includes gas-phase reactions describing silane decomposition, and a detailed multivariate particle model which tracks particle structure and composition. Systematic parameter estimation is used to fit the model to experimental cases. Results indicated that the key challenge in modelling silicon systems is obtaining a correct description of the particle nucleation process. Finally, the silicon model is used in conjunction with the reactor network algorithm to simulate the start-up of a plug-flow reactor. The power of stochastic methods in resolving characteristics of a particle ensemble is highlighted by investigating the number, size, degree of sintering and polydispersity along the length of the reactor.

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Gimbun, Jolius. "Scale-up of gas-liquid stirred tanks using coupled computational fluid dynamics and population balance modelling." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/11982.

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The main aim of the work was to produce scale-up methods for the design of aerated stirred tanks using a combined computational fluid dynamics (CFD) and population balance approach. First a modeling study of single phase stirred tanks was performed to evaluate the best model features (turbulence model, impeller's model, discretisation, grid etc). Good agreement was obtained between the CFD simulation and the LDA measurement on the time-averaged mean velocities and turbulence quantities. The angle-resolved mean velocities and turbulence quantities were also predicted very well as were the power number and the positions of the vortex cores. The next stage involved the development of a population balance model (PBM) which was carried out first using a well-mixed single compartment implemented in MATLAB to reduce the modeling complexity. The algorithm was validated for various mechanisms, namely breakage, aggregation, nucleation and growth which have an analytical solution available from literature. Tests using realistic models for bubble coalescence and breakage were also carried out with the results showing a reasonable agreement with the Sauter mean bubble sizes obtained from empirical correlations. The algorithm also responded well to changes in the turbulence dissipation rate, the initial bubble size distribution and the local gas hold-up, which suggest that the final bubble size is not affected by the initial bubble size. A fully predictive model must combine both the fluid mechanics and bubble dynamics models which can be performed either by a four-way or three-way coupling simulation. The disadvantage of the latter is that is does not consider the effect of the bubble dynamics in- the two-phase modelling. A four-way coupling (CFD-PBM) method was carried out by implementing the PBM within the CFD code. Various drag models which take into account the effect of distorted bubbles and dense gas dispersion are also considered. Mass transfer models are also implemented using the bubble sizes obtained from the PBM. The CFD-PBM model showed a reasonable prediction of the power number, local bubble sizes, gas hold-up, dissolved oxygen concentration and the mean velocities of the two-phase flow in comparison to experimental data taken from the literature. Finally, the CFD-PBM model was employed to evaluate the consequences of scale-up on the mass transfer rate in aerated stirred tanks agitated either by Rushton turbine or CD-6 impeller with operating volume ranged from 14L to 1500L. Three scale-up rules, namely a constant P IV combined with either constant Fig, Vg and VVM were studied. The simulation results suggest, that a successful scale-up may be achieved by keeping the P IV and VVM constant, which led to a slightly higher (kLa) representing a more conservative approach. In contrast, constant P/V and Vg led to a slight reduction in the rate of mass transfer at larger scale which is in agreement with experimental measurement . from the literature. Results from the CFD-PBM simulation also suggest a similar scale-up rule may be applicable for an advanced gas dispersion impeller such as the CD-6 which yielded a similar scale-up trend to that of a Rushton turbine.

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GEMELLO, LUCA. "Modelling of the hydrodynamics of bubble columns using a two-fluid model coupled with a population balance approach." Doctoral thesis, Politecnico di Torino, 2018. http://hdl.handle.net/11583/2725552.

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La simulazione di colonne a bolle in condizioni industriali è un problema di grande rilevanza. L’obiettivo principale di questo lavoro è prevedere con modelli computazionali la dimensione delle bolle, legata alla fluidodinamica dei reattori, considerando i fenomeni di rottura e di coalescenza. La validazione del modello è effettuata tramite il confronto con dati sperimentali appositamente raccolti, tra cui la dimensione delle bolle, ottenuta con un’innovativa tecnica di cross-correlazione. Gli esperimenti effettuati con acqua parzialmente contaminata e con acqua demineralizzata con l’eventuale aggiunta di etanolo, mostrano che gli additivi riducono la coalescenza e diminuiscono la dimensione media delle bolle. Sono stati inoltre utilizzati negli esperimenti con due sparger diversi, per disaccoppiare lo studio di rottura e coalescenza. I dati sperimentali sono stati utilizzati per convalidare simulazioni CFD 3D transitorie Euleriane-Euleriane. Il modello per la forza di trascinamento è corretto da un fattore di swarm per considerare l’effetto delle interazioni tra le bolle. Sono stati testati diversi modelli di turbolenza, nonché il contributo delle bolle sulla miscelazione degli scalari. Per prevedere la dimensione delle bolle, è stato utilizzato un bilancio di popolazione risolto con il metodo di quadratura dei momenti. Nella presente tesi viene proposto un set di kernel di rottura e coalescenza per prevedere le dimensioni delle bolle in diverse condizioni operative, considerando anche gli effetti dello scale-up.
The simulation of bubble column reactors under industrial operating conditions is an exciting challenge. The main objective of this work is to predict the bubble size, in turn interconnected to the reactor hydrodynamic conditions, with computational models, by modelling bubble breakage and coalescence. Experimental data is collected for model validation, including bubble size measurements with an innovative cross-correlation technique. Experiments are carried out with tap water and demineralized water, with or without the addition of ethanol, and gathered results show that additives reduce coalescence and lower the mean bubble size. Two different spargers are used, in order to decouple the investigation of breakage and coalescence. The experimental data set is used to validate out unsteady three-dimensional Eulerian-Eulerian CFD simulations. A drag law for oblate bubbles is considered, together with a swarm factor, that accounts for the swarm effect. Several turbulence models are tested. The contribution of bubble induced turbulence (BIT) to scalar mixing is assessed. To predict bubble size, a population balance model is coupled to the hydrodynamic model and is solved with the quadrature method of moments. A set of breakage and coalescence kernels is proposed, capable of predicting the bubble size for different operating conditions. Scale-up effects are also investigated.
La simulation de réacteurs à bulles en régime industriel est un grand défi. L'objectif principal de ce travail est la prédiction de la taille des bulles à l’aide d’un modèle numérique de bilan de population, basé sur la modélisation des phénomènes de brisure et de coalescence, et pouvant être couplé aux conditions hydrodynamiques présentes dans les réacteurs. Différentes données expérimentales sont obtenues pour valider le modèle. La taille des bulles est mesurée à l'aide d'une technique innovante de corrélation croisée. Les essais, réalisés en eau du réseau (partiellement contaminée) et en eau déminéralisée avec ajout éventuel d'éthanol, montrent que les additifs réduisent la coalescence et diminuent la taille moyenne des bulles. Deux distributeurs du gaz différents sont utilisés pour découpler l'étude de la brisure et de la coalescence. Les données expérimentales sont utilisées initialement pour valider des simulations CFD 3D transitoires Eulériennes-Eulériennes. La loi de traînée est corrigée par un facteur de swarm pour intégrer l’effet d’une fraction de gaz élevée. Différents modèles de turbulence sont testés. La contribution de la turbulence induite par les sillages de bulles au mélange de scalaires est évaluée. Enfin, pour prédire la taille des bulles, un bilan de population est couplé au modèle hydrodynamique préalablement validé et est résolu par la méthode de quadrature des moments (QMOM). Un set original de kernels de brisure et coalescence est proposé, capable de prédire la taille des bulles pour différentes conditions opératoires. Le comportement du modèle lors de l’extrapolation des réacteurs est également examiné.

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Borsos, Akos. "Modelling and control of crystal purity, size and shape distributions in crystallization processes." Thesis, Loughborough University, 2017. https://dspace.lboro.ac.uk/2134/25478.

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Crystallization is a key unit operation used for obtaining purified products by many process industries. The key properties of the crystalline products, such as size and shape distribution, purity and polymorphic form are controlled by the crystallization process. All these properties impact significantly the downstream operations such as drying or filtration. Therefore, monitoring and controlling this process is fundamental to ensure the quality of the final product. Process analytical technology (PAT) brings numerous new methods and opportunities in the process analytics and real time process monitoring systems, which can be integrated into the control algorithm and provide high level optimal control strategies as well as deeper understanding of the process. Process monitoring helps develop mathematical models which can, in one hand, help in better understanding the processes and consecvently the development and application of advanced control methods in order to achieve better product quality. In this work, image processing and image analysis based direct nucleation control (IA-DNC) is developed in order to investigate the evolution of the crystal properties, such as crystal size, and crystal shape distribution. The IA-DNC approach is also compared to alternative DNC techniques, in which particle number were measured by Focused Beam Reflectance Measurement (FBRM) in order to control crystal size. A control approach is introduced that control the nucleation and disappearance of crystals during cooling and heating segments related to the changes of the number of counts (measured by Particle Vision Measurment, so called PVM or combination of FBRM and PVM). The approach was applied to investigate crystallization of compounds with different behavior: potassium dihydrogen phosphate (KDP) water, contaminated KDP -water and Ascorbic acid water systems. The results demonstrate the application of imaging technique for model-free feedback control for tailoring crystal product properties. The second main aim of the thesis is to investigate and control crystallization processes in impure media in the presence of multiple impurities, with an impact on the crystal shape via growth kinetics. The broad impact of the crystal growth modifiers (impurities) on the growth kinetics is observed in real time by using in situ video imaging probe and real-time image analysis. A morphological population balance model is developed, which incorporates a multi-site, competitive adsorption mechanism of the impurities on the crystal faces. The kinetic parameters of primary nucleation, growth and impurity adsorption for a model system of potassium dihydrogen phosphate crystallization in water in the presence of two impurities, were estimated and validated with experimental results. It was demonstrated that the model can be used to describe the dynamic evolution of crystal properties, such as size and aspect ratio during crystallization for different impurity profiles in the system. Manual, feedback and hybrid feedback-feedforward control techniques are developed and investigated numerically for continuous processes, while model-based and model-free control approach for crystal shape are developed for batch processes. The developed morphological population balance model is implemented and applied in the model-based control approaches, which are suitable to describe multicomponent adsorption processes and their influence on the crystal shape. Case studies show the effectiveness of crystal growth modifiers based shape control techniques. Comparison of different control approaches shows the effectiveness of the techniques. The third part of the thesis deals with purification of crystals when adsorption of impurities on crystal surfaces and its incorporation into crystals are considered. A purification method, called competitive purity control (CPC) is proposed and investigated. A morphological population balance model, including nucleation, growth and competitive impurity adsorption kinetics is developed to describe the case when multiple impurities can adsorb competitively on the crystal surface. The model is also combined with liquid phase chemical reaction model, in order to investigate the purity control case when an additive is introduced in the system that reacts with the impurity forming a non-adsorbing reaction product. Both competitive purity control approaches proposed: the adsorption based competitive purity control (A-CPC) and the reaction based competitive purity control (R-CPC); are investigated using detailed numerical simulations then compared with the alternative widely used purification method, called recrystallization. In the last contribution chapter, an integrated process optimization of a continuous chemical reactor and crystallizer is performed and studied numerically. The purpose of this study is to show the way in which the byproduct produced in the chemical reactor may affect the crystallization process and how its negative effect can be reduced by applying integrated process optimization. Sensitivity analysis of the system was performed by considering the flow rate and the concentration of substances in the input stream of the chemical reactor as manipulated process variables. Model based integrated process optimization and the sensitivity analysis in order to obtain improved quality product in terms of crystal size, shape and purity.

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Lebaz, Noureddine. "Modélisation de l’hydrolyse enzymatique de substrats lignocellulosiques par bilan de population." Thesis, Toulouse, INSA, 2015. http://www.theses.fr/2015ISAT0030/document.

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L’hydrolyse enzymatique de la biomasse lignocellulosique est une voie prometteuse pour la bioconversion des matières végétales en sucres fermentescibles en vue de la production du bioéthanol de seconde génération. En général, des cocktails enzymatiques contenant différentes familles d’activités, caractérisées par des modes d’action différents, sont utilisés comme biocatalyseurs. L’essentiel des travaux de modélisation de ce procédé abordent la question via des approches cinétiques où les aspects particulaires et dynamique d’évolution des propriétés du substrat/biocatalyseur/système ne sont pas pris en compte. De plus, ce type de modèles, visant à reproduire les cinétiques de production des sucres simples, traite uniquement le cas de la mise en contact simultanée des enzymes et de la matière à hydrolyser (substrat). Dès lors, les questions relatives au design/optimisation du procédé telles que le mode d’alimentation (batch/continu) ou l’ajout séquencé des enzymes et/ou du substrat ne peuvent pas être abordées avec ces modèles. Dans ce travail, une approche de modélisation par le formalisme du bilan de population est proposée. Le modèle est basé sur une hétérogénéité structurale du substrat à savoir la distribution de taille des chaines/particules. Comme première approche numérique, la méthode des classes est utilisée dans le cas de l’hydrolyse de chaines polymères subissant des attaques endoglucanases (rupture aléatoire) et exoglucanases (coupure d’un dimère en bout de chaine). En deuxième lieu, la méthode des moments a été adoptée pour traiter du cas d’un substrat particulaire. Ici la rupture s’opère sous l’effet des contraintes hydrodynamiques tandis que l’hydrolyse enzymatique modifie la cohésion des particules. Par ailleurs, la nécessité de confronter les résultats numériques issus de la méthode des moments avec les distributions expérimentales a motivé un travail sur les méthodes de reconstruction des distributions à partir de leurs moments. Parallèlement à ce travail de modélisation, plusieurs métrologies nécessaires à la caractérisation de ces systèmes ont été mises en oeuvre. Trois techniques granulométriques (Morpho-granulométrie, Focused Beam Reflectance Measurement Technique (FBRM) et Granulométrie laser) ont été utilisées pour accéder à l’évolution de la distribution de taille des particules au cours de l’hydrolyse d’une cellulose microcristalline (Avicel). De plus, les concentrations en sucres réducteurs et en sucres simples (glucose et cellobiose) ont été mesurées. Les modélisations proposées combinent ainsi les aspects de cinétique homogène et de catalyse hétérogène. Intégrées dans une approche de type bilan de population multivariable, elles permettent d’accéder à l’évolution de la distribution de taille des chaines/particules du substrat ainsi qu’aux cinétiques de conversion en sucres simples
The enzymatic hydrolysis of lignocellulosic biomass is a promising approach for the bioconversion of organic matter into fermentable sugars aiming ultimately to produce second generation biofuel. Globally, enzymatic cocktails, containing different activities which are characterized by their specific mechanisms, are used as biocatalysts. Most of the studies devoted to the modelling of this process address the problem via kinetic approaches in which the particulate aspects and the dynamic evolution of the properties of the substrate/biocatalyst/system are not taken into account. Moreover, such models aim to reproduce the kinetics of release of simple sugars and treat only the case where the enzymes and the substrate are simultaneously mixed at the beginning of the hydrolysis reaction. Therefore, issues related to the design/optimization of the process such as the supplying mode (batch/continuous) and the sequential adding of the enzymes/substrate cannot be addressed with these models. In this work, a population balance formalism is proposed as modelling approach. The model is based on a structural heterogeneity of the substrate namely the chain/particle size distribution. As a first numerical approach, the method of classes is used in the case of polymer chains undergoing endoglucanase (random breakage) and exoglucanase (chain-end scission) attacks. Secondly, the method of moments is adopted to solve the same problem and then adapted to the case of a particulate substrate by introducing the particle cohesion effect which depends on the enzymatic attacks as well as on the hydrodynamic shear stress. Finally, the confrontation of the numerical results from the method of moments to the experimental distributions motivated the development of reconstruction methods in order to restore distributions from a finite sequence of their moments. Alongside this modelling work, the suitable metrology has been developed for the characterization of these systems. Three different granulometric techniques (Morphogranulometry, Focused Beam Reflectance Measurement (FBRM) technique and Laser Diffraction Particle Size Analysis) are used to reach the time-evolution of the particle size distribution of microcrystalline cellulose (Avicel). In this context, numerical tools used for the analysis and the comparison of the different experimental distributions are proposed. In addition, the concentrations of reducing and simple sugars (glucose and cellobiose) are measured all along the hydrolysis reactions. The modeling of enzymatic hydrolysis developed here combines the concepts of homogeneous and heterogeneous catalysis. Integrated into the framework of multivariable population balance model, these allow the chain/particle size distribution evolution during the reaction and the kinetics of simple sugars release to be predicted

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Rynhart, Patrick Reuben. "Mathematical modelling of granulation processes : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematical Physics at Massey University, Palmerston North, New Zealand." Massey University. Institute of Fundamental Sciences, 2004. http://hdl.handle.net/10179/242.

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Granulation is an industrial process where fine particles are bound together into larger granules. The process has numerous applications including the manufacture of pharmaceuticals and the production of cosmetics, chemicals, detergents and fertilisers. This thesis studies aspects of wet granulation which involves the application of a viscous binder, usually in the form of a spray, to an agitated bed of powder particles. Individual powder particles may adhere together, joined by small quantities of binder fluid called liquid bridges. By a process of collision and adherence additional particles may join the newly formed agglomerates. Agglomerates may also coalesce together which is a process that leads to granule formation. On the completion of this process, granules are typically dried.This thesis studies wet granulation on three different levels. First, micro-level investigations of liquid bridges between two and three particles are performed. For the two-particle case, the fluid profile of static (stationary) and dynamic (moving) liquid bridges is investigated. For the static case, a numerical solution to the Young-Laplace equation is obtained; this relates the volume of binder fluid to liquid bridge properties such as the inter-particle force. An analytic solution is also obtained, providing the liquid bridge profile in terms of known mathematical functions. For both solutions, the radii of the (spherical) primary particles may be different. The dynamic case is then studied using the Navier-Stokes equations with the low Reynolds number approximation. The motion of the approaching particles is shown to be damped by the viscosity of the liquid bridge. Static liquid bridges between three equally sized primary particles are then studied. Symmetry of the problem is used to obtain a numerical solution to the Young-Laplace equation. Liquid bridge properties are calculated in terms of the binder fluid volume. Experimental agreement is provided.Secondly, a model to estimate the stickiness (fractional wet surface area) of agglomerates is proposed. Primary particles are approximated as spheres and are added one at a time in a closely packed arrangement. The model includes parameters to control the inter-particle separation distance and the fluid saturation state. Computational geometry is used to obtain results which relate the number of particles and the volume of binder fluid to the stickiness of the agglomerates.Finally, a population balance model for wet granulation is developed by extending an earlier model to incorporate the effects of binder fluid. Functions for the inter-particle collision rate and drying rate are proposed, including functions which are derived from the geometric model, described above, for the case of maximum particle consolidation. The model is solved numerically for a range of coalescence kernels and results are presented which show the effect of binder volume and the drying rate.

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Jaradat, Moutasem [Verfasser], and Han-Jörg [Akademischer Betreuer] Bart. "Dynamic Modelling and Simulation of (Pulsed and Stirred) Liquid-Liquid Extraction Columns using the Population Balance Equation / Moutasem Jaradat. Betreuer: Han-Jörg Bart." Kaiserslautern : Technische Universität Kaiserslautern, 2012. http://d-nb.info/1027622186/34.

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Alzyod, Samer [Verfasser], Hans-Jörg [Akademischer Betreuer] Bart, and Menwer [Akademischer Betreuer] Attarakih. "A Coupled SQMOM-CFD Population Balance Framework for Modelling and Simulation of Liquid-liquid Extraction Equipment / Samer Alzyod ; Hans-Jörg Bart, Menwer Attarakih." Kaiserslautern : Technische Universität Kaiserslautern, 2018. http://d-nb.info/1174205245/34.

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Utomo, Johan. "Experimental kinetics studies and wavelet-based modelling of a reactive crystallisation system." Thesis, Curtin University, 2009. http://hdl.handle.net/20.500.11937/1375.

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This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation.Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques.The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape.A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained.In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering.

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LAVINO, ALESSIO DOMENICO. "Multiscale Modelling of Polymer Self-Assembly in Binary Solvent Mixtures." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2732328.

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17

Utomo, Johan. "Experimental kinetics studies and wavelet-based modelling of a reactive crystallisation system." Curtin University of Technology, Department of Chemical Engineering, 2009. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=128195.

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This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation.
Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques.
The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape.
A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained.
In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering.

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DROGHETTI, HERMES. "Multiscale Modelling of Flowing Soft Matter: Copolymers and Emulsions." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2744936.

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Gemello, Luca. "Modélisation de l'hydrodynamique des colonnes à bulles selon une approche couplant modèle à deux fluides et bilan de population." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1245/document.

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La simulation de réacteurs à bulles en régime industriel est un grand défi. L'objectif principal de ce travail est la prédiction de la taille des bulles à l’aide d’un modèle numérique de bilan de population, basé sur la modélisation des phénomènes de brisure et de coalescence, et pouvant être couplé aux conditions hydrodynamiques présentes dans les réacteurs. Différentes données expérimentales sont obtenues pour valider le modèle. La taille des bulles est mesurée à l'aide d'une technique innovante de corrélation croisée. Les essais, réalisés en eau du réseau (partiellement contaminée) et en eau déminéralisée avec ajout éventuel d'éthanol, montrent que les additifs réduisent la coalescence et diminuent la taille moyenne des bulles. Deux distributeurs du gaz différents sont utilisés pour découpler l'étude de la brisure et de la coalescence. Les données expérimentales sont utilisées initialement pour valider des simulations CFD 3D transitoires Eulériennes-Eulériennes. La loi de traînée est corrigée par un facteur de swarm pour intégrer l’effet d’une fraction de gaz élevée. Différents modèles de turbulence sont testés. La contribution de la turbulence induite par les sillages de bulles au mélange de scalaires est évaluée. Enfin, pour prédire la taille des bulles, un bilan de population est couplé au modèle hydrodynamique préalablement validé et est résolu par la méthode de quadrature des moments (QMOM). Un set original de kernels de brisure et coalescence est proposé, capable de prédire la taille des bulles pour différentes conditions opératoires. Le comportement du modèle lors de l’extrapolation des réacteurs est également examiné
The simulation of bubble column reactors under industrial operating conditions is an exciting challenge. The main objective of this work is to predict the bubble size, in turn interconnected to the reactor hydrodynamic conditions, with computational models, by modelling bubble breakage and coalescence. Experimental data is collected for model validation, including bubble size measurements with an innovative cross-correlation technique. Experiments are carried out with tap water and demineralized water, with or without the addition of ethanol, and gathered results show that additives reduce coalescence and lower the mean bubble size. Two different spargers are used, in order to decouple the investigation of breakage and coalescence. The experimental data set is used to validate out unsteady three-dimensional Eulerian-Eulerian CFD simulations. A drag law for oblate bubbles is considered, together with a swarm factor, that accounts for the swarm effect. Several turbulence models are tested. The contribution of bubble induced turbulence (BIT) to scalar mixing is assessed. To predict bubble size, a population balance model is coupled to the hydrodynamic model and is solved with the quadrature method of moments. A set of breakage and coalescence kernels is proposed, capable of predicting the bubble size for different operating conditions. Scale-up effects are also investigated

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Hanhoun, Mary. "Analyse et modélisation de la précipitation de struvite : vers le traitement d'effluents aqueux industriels." Thesis, Toulouse, INPT, 2011. http://www.theses.fr/2011INPT0037/document.

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La réduction des apports phosphorés des eaux usées régie par la Directive Européenne de 1991 (91/271/EEC) est considérée comme le facteur clé de la lutte contre la pollution des rivières et des lacs. Ces travaux concernent exclusivement l'étude de la formation maîtrisée de struvite (MgNH4PO4.6H2O) par précipitation comme alternative originale de récupération du phosphore et, par voie de conséquence, de l'ammonium à partir d'eaux usées. Un atout de ce procédé concerne la valorisation du précipité en tant que fertilisant. Dans ce contexte général, l'objectif consiste à développer une démarche combinant des aspects expérimentaux et de modélisation de la précipitation de la struvite. Un effluent synthétique contenant du phosphore, du magnésium et de l'ammonium a servi de solution modèle pour étudier le rôle de la température, de la concentration en réactifs, et du pH sur l'efficacité de la précipitation de la struvite ainsi que sur la distribution de la taille des cristaux obtenus. Les essais expérimentaux ont été réalisés par précipitation en cuve agitée. Diverses méthodes d'analyse des phases solide et liquide (spectrophotométrie, absorption atomique, granulométrie laser, MEB et Morphométrie) ont été utilisées. Le dosage du magnésium, ainsi que celui d'ammonium et du phosphore permet de déterminer le taux de conversion de ces composés et d'étudier une éventuelle formation d'un sous-produit. L'approche développée dans ce mémoire permet de déterminer les conditions de pH et de température favorisant l'efficacité maximale pour la récupération de la struvite. Deux voies complémentaires ont été proposées. La première étape concerne la modélisation des équilibres chimiques, d'une part, pour calculer le taux de conversion du phosphate final en fonction du pH à l'équilibre pour plusieurs températures et, d'autre part, pour évaluer l'impact de la température sur la constante de solubilité de la struvite. La stratégie numérique implique un algorithme génétique (NSGA II) pour initialiser efficacement un algorithme de résolution classique (Newton Raphson) et garantir la robustesse de la procédure. Dans la seconde étape, un modèle numérique basé sur un bilan de population couplé avec le modèle thermodynamique prédit la distribution de taille des particules,. Cette approche s'est avérée particulièrement stable d'un point de vue numérique lors du calcul des paramètres des vitesses de nucléation et de croissance, utilisés ensuite pour prédire la distribution de taille à l'aide d'une méthode de reconstruction. La forme de la distribution de taille des cristaux obtenue est typique d'un modèle nucléation – croissance. La méthodologie proposée trouve tout son intérêt pour traiter des effluents de qualité variable et prédire l'efficacité du procédé dans lequel le contrôle du pH et de la sursaturation constituent des paramètres clés
The reduction of phosphorus contribution in wastewater, governed by the European directive of 1991 (91/271/EEC) is regarded as the key factor of the fight against pollution of rivers and lakes. This work concerns exclusively the study of the controlled struvite formation (MgNH4PO4.6H2O) by precipitation as an alternative removal of phosphorus and, consequently, of ammonium from waste-water discharges. The valorization of the precipitate as a fertilizer constitutes an asset of the process. In this general context, the objective consists in developing a methodology combining an experimental approach with struvite precipitation modelling. A synthetic effluent containing phosphorus, magnesium and ammonium was used as a model solution to study the role of temperature, concentration in reagents and pH on struvite precipitation efficiency as well as on particle size distribution in a stirred tank reactor. Various analysis methods of both solid and liquid phases (spectrophotometry, atomic absorption, laser granulometry, MEB and Morphology) were used. The residual concentration of magnesium, ammonium and phosphorus allows to determine the conversion rate of these compounds and to study a likely formation of a co-product. The proposed framework is based on a two-level modelling approach. The former level, based on an equilibrium prediction of the study system Mg-PO4-NH4, involves, on the one hand, the computation of the final conversion rate of phosphate as a function of equilibrium pH at different temperatures and, on the other hand, the temperature impact assessment on struvite solubility product. The numerical strategy implies a genetic algorithm (NSGA II) to initialize a traditional algorithm of resolution (Raphson Newton) and to guarantee the robustness of the process. In the second stage, a population balance-based model coupled with the thermodynamic one predicts the particle size distribution. This approach turns out to be particularly numerically stable for the identification of nucleation and particle growth kinetics parameters that are then used to predict the size distribution, typical of a nucleation - growth model, using a method of reconstruction. The proposed methodology is particularly interesting for the treatment of industrial waste-water discharges that may be of variable quality as well as for the prediction of the process efficiency for which pH control and supersaturation constitute key parameters

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Niazi, Erfan. "A Mesoscopic Model for Blood Flow Prediction Based on Experimental Observation of Red Blood Cell Interaction." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/38078.

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In some species, including humans, red blood cells (RBCs) under low shear stress tend to clump together and form into regular stacks called rouleaux. These stacks are not static, and constantly move and break apart. This phenomenon is referred to as red blood cell aggregation and disaggregation. When modelled as a single liquid, blood behaves as a non-Newtonian fluid. Its viscosity varies, mainly due to the aggregation of RBCs. The aim of this research is to develop a mesoscale computational model for the simulation of RBCs in plasma. This model considers RBC interaction and aggregation to predict blood-flow characteristics such as viscosity, rouleaux size and velocity distribution. In this work, the population-balance modelling (PBM) approach is utilized to model the RBC aggregation process. The PBM approach is a known method that is used for modelling agglomeration and breakage in two-phase flow fluid mechanics to find aggregate size. The PBM model is coupled to the incompressible Navier-Stokes equations for the plasma. Both models are numerically solved simultaneously. The population-balance equation has been used previously in a more restricted form, the Smoluchowski equation, to model blood viscosity, but it has never been fully coupled with the Navier-Stokes equation directly for the numerical modelling of blood flow. This approach results in a comprehensive model which aims to predict RBC aggregate size and their velocities for different flow configurations, as well as their effects on the apparent macro-scale viscosity. The PBM approach does not treat the microscopic physics of aggregation directly but rather uses experimental correlations for aggregation and disaggregation rates to account for the effects of aggregation on the bulk. To find the aggregation rate, a series of experiments on RBC sedimentation due to gravity is designed. In these tests, aggregated RBCs (rouleaux) tend to settle faster than single RBCs and, due to low shear stresses, disaggregation is very low and can be neglected. A high-speed camera is used to acquire video-microscopic pictures of the process. The size of the aggregates and their velocities are extracted using image processing techniques. For image processing, a general Matlab program is developed which can analyze all the images and report the velocity and size distribution of rouleaux. An experimental correlation for disaggregation rate is found using results from a previous steady-state Couette flow experiment. Aggregation and disaggregation rates from these experiments are used to complete the PBM model. Pressure-driven channel flow experiments are then used for the final validation of the model. Comparisons of the apparent viscosity of whole blood in previous experiments show reasonable agreement with the developed model. This model fills a gap between micro-scale and macro-scale treatments and should be more accurate than traditional macro-scale models while being cheaper than direct treatment of RBCs at the micro-scale.

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Wang, Li Ge. "Particle breakage mechanics in milling operation." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28950.

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Milling is a common unit operation in industry for the purpose of intentional size reduction. Considerable amount of energy is consumed during a grinding process and much of the energy is dissipated as heat and sound, which often makes grinding into an energy-intensive and highly inefficient operation. Despite many attempts to interpret particle breakage during a milling process, the grindability of a material in a milling operation remains aloof and the mechanisms of particle breakage are still poorly understood. Hence the optimisation and refinement in the design and operation of milling are in great need of an improved scientific understanding of the complex failure mechanisms. This thesis aims to provide an in-depth understanding of particle breakage associated with stressing events that occur during milling. A hybrid of experimental, theoretical and numerical methods has been adopted to elucidate the particle breakage mechanics. This study covers from single particle damage at micro-scale to bulk comminution during the whole milling process. The mechanical properties of two selected materials, i.e. alumina and zeolite were measured by indentation techniques. The breakage test of zeolite granules subjected to impact loading was carried out and it was found that tangential component velocity plays an increasingly important role in particle breakage with increasing impact velocity. Besides, single particle breakage via in-situ loading was conducted under X-ray microcomputed tomography (μCT) to study the microstructure of selected particles, visualize the progressive failure process and evaluate the progressive failure using the technique of digital image correlation (DIC). A new particle breakage model was proposed deploying a mechanical approach assuming that the subsurface lateral crack accounts for chipping mechanism. Considering the limitation of existing models in predicting breakage under oblique impact and the significance of tangential component velocity identified from experiment, the effect of impact angle is considered in the developed breakage model, which enables the contribution of the normal and tangential velocity component to be rationalized. The assessment of breakage models including chipping and fragmentation under oblique impact suggests that the equivalent normal velocity proposed in the new model is able to give close prediction with experimental results sourced from the public literature. Milling experiments were performed using the UPZ100 impact pin mill (courtesy by Hosokawa Micron Ltd. UK) to measure the comminution characteristics of the test solids. Several parameters were used to evaluate the milling performance including product size distribution, relative size span, grinding energy and size reduction ratio etc. The collective data from impact pin mill provides the basis for the validation of numerical simulation results. The Discrete Element Method (DEM) is first used to model single particle breakage subject to normal impact loading using a bonded contact model. A validation of the bonded contact model was conducted where the disparity with the experimental results is discussed. A parametric study of the most significant parameters e.g. bond Young’s modulus, the mean tensile bond strength, the coefficient of variation of the strength and particle & particle restitution coefficient in the DEM contact model was carried out to gain a further understanding of the effect of input parameters on the single particle breakage behavior. The upscaling from laboratory scale (single particle impact test) to industrial process scale (impact pin mill) is achieved using Population Balance Modelling (PBM). Two important functions in PBM, the selection function and breakage function are discussed based on the single particle impact from both experimental and numerical methods. An example of predicting product size reduction via PBM was given and compared to the milling results from impact pin mill. Finally, the DEM simulation of particle dynamics with emphasis on the impact energy distribution was presented and discussed, which sheds further insights into the coupling of PBM and DEM.

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Pinto, Mark Alexander. "Modelling of biological systems using multidimensional population balances." Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/8502.

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Biological systems are intrinsically heterogeneous and, consequently, their mathematical descriptions should account for this heterogeneity as it often influences the dynamic behaviour of the individual cells. For example, in the cell cycle dependent production ofproteins, it is necessary to account for the distribution of the individual cells with respect to their position in the cell cycle as this has a strong influence on protein production. A second notable example is the formation of cancerous cells. In this case, the failure of regulatory mechanisms results in the transition of somatic cells to their cancerous state. Therefore, in developing the corresponding mathematical model, it is necessary to consider both the different states of the cells as well as their regulation. In this regard, the population balance equation is the ideal mathematical framework to capture cell population heterogeneity as it elegantly takes into account the distribution of cell populations with respect to their intracellular state together with the phenomena of cell birth, division, differentiation and recombination. Recent developments in solution algorithms together with the exponential increase in computational abilities now permit the efficient solution of one-dimensional population balance models which attribute the heterogeneity of cell populations to differences in the age or mass of individual cells. The inherent complexity of biological systems implies that the differentiation of cells based on a single characteristic alone may not be sufficient to capture the underlying biological phenomena. Therefore, current research is focussing on the development of multi-dimensional population balances that consider the differentiation of cells based on multiple characteristics, most notably, the state of cells with respect to key intracellular metabolites. However, conventional numerical techniques are inefficient for the solution of the formulated population balance models and this warrants the development of novel, tailor-made algorithms. This thesis presents one such solution algorithm and demonstrates its application to the study of several biological systems. The algorithm developed herein employs a finite-volume technique to convert the partial-differential equation comprising the population balance model into a set of ordinary differential equations. A two-tier technique based on the solution technique for inhomogeneous differential equations is then developed to solve the system of ordinary differential equations. This approach has two main advantages: (a) the decomposition technique considerably reduces the stiffness of the system of equations enabling more efficient solution, and (b) semianalytical solutions for the integrals employed in the modelling of cell division and differentiation can be obtained further reducing computation times. Further improvements in solution efficiency are obtained by the formulation of a two-level discretisation algorithm. In this approach, processes such as cell growth which are more sensitive to the discretisation are solved using a fine grid whereas less sensitive processes such as cell' division - which are usually more computationally expensive - are solved using a coarse grid at a higher level. Thus, further improvements are obtained in the efficiency of the technique. The solution algorithm is applied to various multi-dimensional population balance models of biological systems. The technique is first demonstrated on models of oscillatory dynamics in yeast glycolysis, cell-cycle related oscillations in eukaryotes, and circadian oscillations in crayfish. A model of cell division and proliferation control in eukaryotes is an example of a second class of problems where extracellular phenomena influence the behaviour of cells. As a third case for demonstration, a hybrid model of biopolymer accumulation in bacteria is formulated. In this case, cybernetic modelling principles are used to account for intracellular competitions while the population balance framework takes into consideration the heterogeneity of the cell population. Another important aspect in the formulation ofmulti-dimensional population balances is the development of the intracellular models themselves. While research in the biological sciences is permitting the formulation of detailed dynamic models of various bioprocesses, the accurate estimation of the kinetic parameters in these models can be difficult due to the unavailability of sufficient experimental data. This can result in considerable parametric uncertainty as is demonstrated on a simple cybernetic' model of biopolymer accumulation in bacteria. However, it is shown that, via the use of systems engineering tools, experiments can be designed that permit the accurate estimation of all model parameters even when measurements pertaining to all modelled quantities are unavailable.

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Bouaniche, Alexandre. "A hybrid stochastic-sectional method for the simulation of soot particle size distributions Vitiated high karlovitz n-decane/air turbulent flames: scaling laws and micro-mixing modeling analysis A hybrid stochastic/fixed-sectional method for solving the population balance equation." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR23.

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Les particules de suie (qui sont un type de particules ultrafines) peuvent être produites et émises dans des conditions de combustion riche. Les secteurs comme les transports (routier et aérien), où l'industrie sont des contributeurs significatifs aux émissions de particules. Celles-ci sont habituellement considérées comme des polluants dans la mesure où leur impact négatif sur la santé a été mesuré. Dans certains cas spécifiques comme la production de nanomatériaux, elles peuvent être synthétisées de manière volontaire. Dans les deux cas, une compréhension précise et une capabilité de prédiction de la distribution de tailles de particules (PSD en anglais) sont nécessaires, pour une meilleure conception des chambres de combustion. Dans cette thèse, une méthode innovante est proposée pour la prédiction de l'évolution de la distribution de tailles de particules (PSD). Elle consiste en une approche hybride composée de particules stochastiques représentant une fonction de densité de probabilité (PDF en anglais) et de sections fixes. L'objectif est de résoudre de manière précise le terme source de croissance/oxydation, en traitant le problème de diffusion numérique rencontré par des méthodes sectionnelles classiques. D'autre part, la méthode proposée est moins coûteuse qu'une méthode de Monte Carlo complète. D'abord, le contexte et les motivations de cette thèse sont expliqués. Les concepts et modèles pour les termes sources physiques de suie sont brièvement résumés. Ensuite, l'équation de bilan de population (PBE en anglais) qui pilote l'évolution de la distribution de tailles de particules (PSD), est présentée, ainsi que les différentes classes de méthodes utilisées pour sa résolution. La nouvelle méthode hybride est introduite. Sa précision et son efficacité sont démontrées sur des cas tests analytiques. Enfin, la méthode est appliquée sur une flamme prémélangée d'éthylène
Soot particles (which are one kind of ultra-fine particles) can be produced and emitted in fuel rich combustion conditions. Sectors like road and air transportation, or industry are significant contributors to soot particles emissions. Soot particles are usually considered as a pollutant as their negative impact on health has been assessed. In some specific cases like nanomaterials production, they can be synthesized on purpose. In both cases, accurate understanding and prediction capability of the Particle Size Distribution (PSD) is needed, for a better combustors design. In this thesis, a novel numerical method is proposed to predict the Particle Size Distribution (PSD) evolution. It consists in a hybrid approach featuring stochastic particles representing a Probability Density Function (PDF), and fixed sections. The objective is to solve accurately for the surface growth/oxidation term, mitigating the problem of numerical diffusion encountered in some classical sectional methods. On the other hand, the proposed method is less expensive than a full Monte Carlo method. First, the context and motivation of the thesis are explained. Concepts and models for soot physical source terms are shortly reviewed. Then, the Population Balance Equation (PBE), which drives the evolution of the Particle Size Distribution (PSD), is presented as well as the different classes of numerical methods used for its resolution. Subsequently, the novel hybrid method is introduced. Its accuracy and efficiency are demonstrated on analytical test cases. Finally, the method is applied on a premixed ethylene sooting flame

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Neumann, Luis Eduardo. "Modelling of flocculation and settling of suspended sediments using population balances /." St. Lucia, Qld, 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17750.pdf.

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Pardelha, Filipa Alexandra Guerreiro. "Constraint-based modelling of mixed microbial populations: Application to polyhydroxyalkanoates production." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2013. http://hdl.handle.net/10362/13111.

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Dissertação para obtenção do Grau de Doutor em Engenharia Química e Bioquímica
The combined use of mixed microbial cultures (MMC) and fermented feedstock as substrate may significantly decrease polyhydroxyalkanoates (PHA) production costs and make them more competitive in relation to conventional petroleum-based polymers. However, there still exists a lack of knowledge at metabolic level that limits the development of strategies to make this process more effective. In this thesis, system biology computational tools were developed and applied to PHA production by MMC from fermented sugar cane molasses, rich in volatile fatty acids (VFA). Firstly, a metabolic network able to describe the uptake of complex mixtures of VFA and PHA production was defined. This metabolic network was applied to metabolic flux analysis (MFA) to describe substrate uptake and PHA production fluxes over the enrichment time of a culture submitted to the feast and famine regimen. Then, the minimization of the tricarboxylic acid cycle (TCA) fluxes was identified as the key metabolic objective of a MMC subjected to this regimen by flux balance analysis (FBA). This model enabled to predict, with an acceptable accuracy, the PHA fluxes and biopolymer composition. Subsequently, data gathered from microautoradiography-fluorescence in situ hybridization (MAR-FISH) was used to develop a segregated FBA model able to predict the flux distribution for the three populations identified in the enriched culture. These results were slightly better than those obtained by the non-segregated FBA and were consistent with MFA results. Finally, a dynamic metabolic model was proposed based on the previous models and on a regulatory factor for VFA uptake and PHA production. This model allowed to identify the dynamics of the process and regulatory factor as well as to validate the previous results. Globally, this thesis enabled to demonstrate the potential of using computational tools to understand and optimize PHA production by MMC.

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Seltz, Andréa. "Application of deep learning to turbulent combustion modeling of real jet fuel for the numerical prediction of particulate emissions Direct mapping from LES resolved scales to filtered-flame generated manifolds using convolutional neural networks Solving the population balance equation for non-inertial particles dynamics using probability density function and neural networks: application to a sooting flame." Thesis, Normandie, 2020. http://www.theses.fr/2020NORMIR08.

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Face à l'urgence climatique, l’efficacité énergétique et la réduction des émissions polluantes est devenue une priorité pour l'industrie aéronautique. La précision de la modélisation des phénomènes physicochimiques joue un rôle critique dans qualité de la prédiction des émissions de suie et des gaz à effet de serre par les chambres de combustion. Dans ce contexte, des méthodes d’apprentissage profond sont utilisées pour construire des modélisations avancées des émissions de particules. Une méthode automatisée de réduction et d’optimisation de la cinétique chimique d’un combustible aéronautique réel est dans un premier temps appliquée à la simulation aux grandes échelles pour la prédiction des émissions de monoxyde de carbone. Ensuite, des réseaux de neurones sont entraînés pour simuler le comportement dynamique des suies dans la chambre de combustion et prédire la distribution de taille des particules émises
With the climate change emergency, pollutant and fuel consumption reductions are now a priority for aircraft industries. In combustion chambers, the chemistry and soot modeling are critical to correctly quantify engines soot particles and greenhouse gases emissions. This thesis aimed at improving aircraft numerical pollutant tools, in terms of computational cost and prediction level, for engines high fidelity simulations. It was achieved by enhancing chemistry reduction tools, allowing to predict CO emissions of an aircraft engines at affordable cost for the industry. Next, a novel closure model for unresolved terms in the LES filtered transport equations is developed, based on neural networks (NN), to propose a better flame modeling. Then, an original soot model for engine high fidelity simulations is presented, also based on NN. This new model is applied to a one-dimensional premixed sooted flame, and finally to an industrial combustion chamber LES with measured soot comparison

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Greenwood, Ava A. "Mathematical modelling of the dilute acid pretreatment of sugarcane bagasse." Thesis, Queensland University of Technology, 2016. https://eprints.qut.edu.au/93372/1/Ava_Greenwood_Thesis.pdf.

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Dilute acid pretreatment is a process that is used to enhance ethanol yields in biofuel manufacturing by removing hemicelluloses from plant biomass. This thesis presents a new mathematical model of dilute acid pretreatment that can be used to predict hemicellulose yield profiles at the laboratory scale and inform further investigations at the industrial reactor scale. This work provides a framework for determining the optimal reaction conditions for acid pretreatment and thus has the potential to reduce the cost of commercial bioethanol production from 2nd generation lignocellulosic biomass feedstocks.

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Krepper, Eckhard, Roland Rzehak, Frank Barthel, Ronald Franz, and Uwe Hampel. "Entwicklung von CFD-Modellen für Wandsieden und Entwicklung hochauflösender, schneller Röntgentomographie für die Analyse von Zweiphasenströmungen in Brennstabbündeln." Forschungszentrum Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-125406.

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In einem Verbundprojekt im Rahmen des Programms „Energie 2020+“ gefördert durch das BMBF koordiniert durch das HZDR arbeiteten 4 Universitäten, 2 Forschungszentren und ANSYS zusammen. Der vorliegende Bericht beschreibt die Arbeiten des HZDR, die im Zeitraum September 2009 bis Januar 2013 durchgeführt wurden. Das Vorhaben war auf die Entwicklung und Validierung von CFD-Modellen von unterkühltem Sieden bis zu Filmsieden gerichtet. Im Bericht werden die entwickelten und verwendeten Modelle dargestellt. Anhand der Nachanalyse von Experimenten wird auf die vorgeschlagene Kalibrierung der Modelle eingegangen. Wichtig ist hierbei eine genauere Beschreibung der Zwischenphasengrenzfläche, die durch Kopplung des Wandsiedemodells mit einem Populationsmodell erreicht werden kann. Anhand der Analyse von Bündelexperimenten konnte gezeigt werden, dass die gemessenen querschnittsgemittelten Messwerte mit einem Satz im Rahmen der Modellunsicherheiten kalibrierter Modellparameter reproduziert werden kann. Für die Berechnung der Verteilungsmuster des Dampfgehaltes im Kanalquerschnitt muss die Modellierung der Turbulenz beachtet werden. Die experimentellen Arbeiten waren auf die Untersuchung eines Brennelementbündels gerichtet. An einer Versuchsanordnung zu einem Brennelementbündel werden die turbulente einphasige Geschwindigkeit (PIV), der mittlere Gasgehalt (Gamma-Densitometrie) sowie der zeitlich und räumlich aufgelöste Gasgehalt (Hochgeschwindigkeits-Röntgentomographie) gemessen. Letztere Methode wurde in Rossendorf entwickelt.

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Perala, Siva Rama Krishna. "Alternative Mechanisms for Size Control in Synthesis of Nanoparticles - Population Balance Modelling and Experimental Studies." Thesis, 2013. http://etd.iisc.ernet.in/2005/3361.

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The extensive growth of nanotechnology has necessitated the development of economical and robust methods for large scale production of nanomaterials. It requires detailed quantitative understanding of lab-scale processes to enable effective scale-up and development of new contacting strategies for their controlled synthesis. In this thesis, attempts are made in both the directions using experimental and modelling approaches for synthesis of different nanoparticles. The two-phase Brust--Schiffrin protocol for the synthesis of gold nanoparticles was investigated first. The mechanism of transfer of reactants from aqueous to organic phase using phase transfer catalyst (PTC) was investigated using the measurement of interfacial tension, viscosity, SLS, SAXS, 1H NMR, DOSY-NMR, and Karl-Fischer titration. The study shows that the reactants are transferred to organic phase through the formation of hydrated complexes between reactants and PTC rather than through the solubilization of reactants in water core of inverse micelles of PTC, proposed recently in the literature. The particle synthesis reactions thus occur in the bulk organic phase. The extensive body of seemingly disparate experimental findings on Brust--Schiffrin protocol were put together next. The emerging picture ruled out both thermodynamic considerations and kinetics based arguments as exemplified by the classical LaMer's mechanism with sequential nucleation growth capping for size control in Brust--Schiffrin protocol. A new model for particle synthesis was developed. The model brought out continued nucleation--growth--capping based size control, an hitherto unknown mechanistic route for the synthesis of monodisperse particles, as the main mechanism. The model not only captured the reported features of the synthesis but also helped to improve the uniformity of the synthesized particles, validated experimentally. The two-step mechanism of Finke--Watzky---first order nucleation from precursor and autocatalytic growth of particles---proposed as an alternative to LaMer model to explain an induction period followed by a sigmoidal decrease in precursor concentration for the synthesis of iridium nanoparticles was investigated next. The mechanism is tested using an equivalent population balance model for its ability to explain the experimentally observed near constant breadth of the evolving size distribution as well. The predictions show that while it captures precursor conversion well, it fails to explain particle synthesis on account of its inability to suppress nucleation. A minimal four-step mechanism with additional steps for nucleation from reduced iridium atoms and their scavenging using particle surface is proposed. The new mechanism when combined with the first or second order nucleation, or classical nucleation with no scavenging of reduced atoms also fails to suppress nucleation. A burst like onset of nuclei formation with homogeneous nucleation and the scavenging of reduced atoms by particles are simultaneously required to explain all the reported features of the synthesis of iridium nanoparticles. A new reactor is proposed for continuous production of CaCO3 nanoparticles in gas-liquid reaction route. The key feature of the new reactor is the control of flow pattern to ensure efficient mixing of reactants. A liquidliquid reaction route for production of CaCO3 nanoparticles is also optimized to produce nanoparticles at high loading. Optimum supersaturation combined with efficient breakup of initial gel-like structure by mechanical agitation and charge control played a crucial role in producing nano sized CaCO3 particles.

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Drumm, Christian [Verfasser]. "Coupling of computational fluid dynamics and population balance modelling for liquid-liquid extraction / von Christian Drumm." 2010. http://d-nb.info/1003636101/34.

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Rao, Narni Nageswara [Verfasser]. "Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM) / Nageswara Rao Narni." 2009. http://d-nb.info/99448674X/34.

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Dissertations / Theses on the topic 'Population balance modelling'

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