Thermal degradation of linear thermoplastics is modeled at several scales. High-density polyethylene (HDPE) is chosen as an example material. The relevant experimental data is surveyed. At the molecular scale, pyrolysis chemistry is studied with reactive molecular dynamics. Optimization is used to calibrate several pyrolysis mechanisms with thermogravimetric analysis (TGA) data. It is shown that molecular scale physics may be coupled to continuum scale transport equations through a population balance equation (PBE). A PBE solution method is presented and tested. This method has the advantage of preserving detailed information for the small species in the molecular weight distribution with minimal computational expense. The mass transport of these small species is modeled at the continuum scale with a bubble loss mechanism. This mechanism includes bubble nucleation, growth, and migration to the surface of the condensed phase. The bubble loss mechanism is combined with a random scission model of pyrolysis to predict TGA data for HDPE. The modeling techniques developed at these three scales are used to model two applications of engineering interest with a combined pyrolysis and devolatilization PBE. The model assumes a chemically consistent form of the random scission pyrolysis mechanism and an average, parameterized form of the bubble loss mechanism. This model is used to predict the piloted ignition of HDPE. Predictions of the ignition times are reasonable but the model over predicts the ignition temperature. This discrepancy between model and data is attributed to surface oxidation reactions. The second application is the prediction of differential scanning calorimetry (DSC) data for HDPE. The model provides detailed information on the energy absorption of the thermally degrading sample, but the literature data is too variable to validate the model. / text

ALVES, C. A. A study concerning homeostasis and population development of collagen fibers. 2017. 88 f. Tese (Doutorado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Pós-Graduação em Física (posgrad@fisica.ufc.br) on 2017-11-21T16:35:18Z No. of bitstreams: 1 2017_tese_caalves.pdf: 8939939 bytes, checksum: 5cbf75fd845e26cdee776ee15fc2cfbf (MD5) / Approved for entry into archive by Giordana Silva (giordana.nascimento@gmail.com) on 2017-11-22T18:55:25Z (GMT) No. of bitstreams: 1 2017_tese_caalves.pdf: 8939939 bytes, checksum: 5cbf75fd845e26cdee776ee15fc2cfbf (MD5) / Made available in DSpace on 2017-11-22T18:55:25Z (GMT). No. of bitstreams: 1 2017_tese_caalves.pdf: 8939939 bytes, checksum: 5cbf75fd845e26cdee776ee15fc2cfbf (MD5) Previous issue date: 2017 / Collagen is a generic name for the group of the most common proteins in mammals. It confers mechanical stability, strength and toughness to the tissues, in a large number of species. In this work we investigate two properties of collagen that explain in part the choice by natural selection of this substance as an essential building material. In the first study the property under investigation is the homeostasis of a single fiber, i.e., the maintenance of its elastic properties under the action of collagen monomers that contribute to its stiffening and enzymes that digest it. The model used for this purpose is a onedimensional chain of linearly elastic springs in series coupled with layers of sites. Particles representing monomers and enzymes can diffuse along these layers and interact with the springs according to specified rules. The predicted lognormal distribution for the local stiffness is compared to experimental data from electronic microscopy images and a good concordance is found. The second part of this work deals with the distribution of sizes among multiple collagen fibers, which is found to be bimodal, hypothetically because it leads to a compromise between stiffness and toughness of the bundle of fibers. We propose a mechanism for the evolution of the fiber population which includes growth, fusion and birth of fibers and write a Population Balance Equation for that. By performing a parameter estimation over a set of Monte Carlo simulations, we determine the parameters that best fit the available data. / Collagen is a generic name for the group of the most common proteins in mammals. It confers mechanical stability, strength and toughness to the tissues, in a large number of species. In this work we investigate two properties of collagen that explain in part the choice by natural selection of this substance as an essential building material. In the first study the property under investigation is the homeostasis of a single fiber, i.e., the maintenance of its elastic properties under the action of collagen monomers that contribute to its stiffening and enzymes that digest it. The model used for this purpose is a onedimensional chain of linearly elastic springs in series coupled with layers of sites. Particles representing monomers and enzymes can diffuse along these layers and interact with the springs according to specified rules. The predicted lognormal distribution for the local stiffness is compared to experimental data from electronic microscopy images and a good concordance is found. The second part of this work deals with the distribution of sizes among multiple collagen fibers, which is found to be bimodal, hypothetically because it leads to a compromise between stiffness and toughness of the bundle of fibers. We propose a mechanism for the evolution of the fiber population which includes growth, fusion and birth of fibers and write a Population Balance Equation for that. By performing a parameter estimation over a set of Monte Carlo simulations, we determine the parameters that best fit the available data.

This thesis concerns the construction of a detailed, compartmental population balance model for twin-screw granulation using the stochastic weighted particle method. A number of new particle mechanisms are introduced and existing mechanisms augmented including immersion nucleation, coagulation, breakage, consolidation, liquid penetration, primary particle layering and transport. The model’s predictive power is assessed over a range of liquid-solid mass feed ratios using existing experimental data and is demonstrated to qualitatively capture key experimental trends in the physical characteristic of the granular product. As part of the model development process, a number of numerical techniques for the stochastic weighed method are constructed in order to efficiently solve the population balance model. This includes a new stochastic implementation of the immersion nucleation mechanism and a variable weighted inception algorithm that dramatically reduces the number of computational particles (and hence computational power) required to solve the model. Optimum operating values for free numerical parameters and the general convergence properties of the complete simulation algorithm are investigated in depth. The model is further refined though the use of distinct primary particle and aggregate population balances, which are coupled to simulate the complete granular system. The nature of this coupling permits the inclusion of otherwise computational prohibitive mechanisms, such as primary particle layering, into the process description. A new methodology for assigning representative residence times to simulation compartments, based on screw geometry, is presented. This residence time methodology is used in conjunction with the coupled population balance framework to model twin-screw systems with a number of different screw configurations. The refined model is shown to capture key trends attributed to screw element geometry, in particular, the ability of kneading elements to distribute liquid across the granular mass.

Emulsions constitute a wide range of natural as well as processed products. Pharmaceutical applications of emulsions include oral administration, parenteral delivery, ophthalmic medicine, topical and transdermal creams, and fluorocarbon-in-water emulsions for blood oxygenation. In the foods area many of the products like mayonnaise, margarine, ice-creams are emulsions by nature and some products can also be used for delivery of active ingredients (e.g. nutraceuticals) with potential health benefits. Emulsions are also encountered at many stages of petroleum recovery, transportation, and processing. Typically, emulsions are manufactured in a two-step process. First a coarse emulsion called a premix is made which is passed through a high-pressure homogenizer. Intense energy supplied in the high pressure homogenizer causes breakage of the coarse emulsion to a fine one with a tighter distribution. Population balance equation (PBE) models are useful for emulsions since they allow prediction of the evolution of the drop size distribution on specification of the two rate processes i.e., breakage of drops due to the flow field and coalescence of colliding drops. In our work, we developed a PBE model to describe emulsion breakage in a high pressure homogenizer. The focus of the work was breakage and conditions to keep coalescence to minimum were implemented. Two breakage rates representing two mechanisms i.e., turbulent inertial and turbulent viscous breakage were necessary for reproducing the bimodal nature of the distributions. We used mechanistic functions in the PBE model to develop a predictive model which could be extended to changes in formulation variables as well as process variables. Starting with the assumption of binary breakage, the model was refined to include multiple drop breakage. The developed model was found to be extensible to reasonable changes in oil concentration, surfactant concentration, continuous phase viscosity and constant ratio of oil to surfactant. Anomalies in pressure prediction encountered earlier were also corrected for by including some additional features like heating, maximum stable diameter, and number of daughter drops. A preliminary attempt was also made to use the developed model for designing experiments for making target emulsions with pre-specified properties.

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In this thesis, a thorough study of the batch top-spray fluidized bed granulation was carried out including experimental study, population balance model (PBM), computational fluid dynamic (CFD) study and control strategy development. For the experimental study, the influence variables of pulsed frequency, binder spray rate and atomization pressure of a batch top-spray fluidized bed granulation process were studied using the Box-Behnken experimental design method. Different mathematical models were developed to predict the mean size of granules, yield, relative width of granule distribution, Hausner ratio and final granule moisture content. Validation experiments have shown the reliability and effectiveness of using the Box-Behnken experimental design method to study a fluidized bed granulation process. The one-dimensional population balance models (ODPBMs) have been developed to model a pulsed top-spray fluidized bed granulation, linking the operating factors of the pulsed frequency, the binder spray rate, and atomization air pressure with the granule properties to predict granule growth behavior at different operating conditions. A multi-stage open optimal control strategy based on the developed ODPBMs was proposed to reduce the model and process mismatch through adjusting the trajectory of the evolution of the granule size distribution at predefined sample intervals. The effectiveness of the proposed modeling and multi-stage open optimal control strategy has been validated by experimental and simulation tests. In addition, an Eulerian-Eulerian two-fluid model (EETFM) was developed to describe the gas-particle two-phase flow in the fluidized bed granulator. By computational fluid dynamic analysis, it has been proven that the fluidized bed granulation system is not homogeneous, based on which a two-compartmental population balance model (TCPBM) was developed to describe the particle growth in the fluidized bed granulation. Validation experiments have shown the effectiveness and superior accuracy of the TCPBM comparing with the ODPBM in predicting the final particle size distribution.

Au cours de cette étude du procédé de granulation humide, nous avons mis l’accent sur l’intérêt que présente la distribution du liquide de mouillage dans la définition des propriétés finales de grains. Dans ce cadre, une méthode utilisant un traceur a été développée pour le suivi cinétique de la répartition du liquide de mouillage au cours de la granulation. Une formulation à base d’excipent pharmaceutique a été granulée dans un mélangeur-granulateur à haut cisaillement Mi-Pro. On a pu ainsi montrer que le début du procédé est caractérisé par l’hétérogénéité de la distribution du liquide de mouillage qui se redistribue ensuite selon une loi cinétique d’ordre un. Les propriétés des grains (taille, porosité et observation microscopique) ne deviennent uniformes qu’après une répartition homogène du liquide de mouillage entre les différentes classes de grains. L’étude de l’influence de certaines variables opératoires (vitesse d’agitation, débit et critère de mouillabilité) sur le phénomène de redistribution a été également menée. Par ailleurs, les bilans de population ont été utilisés comme outil de modélisation. Des écritures du noyau d’agglomération ont été proposées en se basant sur la taille des particules et leur teneur en liquide de mouillage. Bien que reproduisant les résultats expérimentaux, les bilans de population présentent certaines limites liées à la difficulté d’intégrer toutes les données de l’étude / In this study of wet granulation process, we are especially interested in binder liquid distribution as a mean to deduce final granule properties. Then, a tracer method is developed to study binder liquid distribution kinetics during granulation process. Granulation experiments are carried out in high shear mixer Mi-Pro using pharmaceutical excipients. The beginning of the process is characterized by heterogeneous binder liquid distribution. Then, liquid redistribution phenomenon is observed according to a first order model. Granule properties (size, porosity, microscopic observation) are found to be similar when binder liquid is homogeneously distributed among different granule classes. Finally operating conditions influence (speed rate, flow rate and wetting criterion) are discussed. In addition, population balances are used as a tool to model experimental results. Agglomeration kernels are presented depending on particle size and binder liquid ratio. Although experimental results could be satisfactorily modelled, population balances show some limitations related to the difficulty of integrating all the study data

ABSTRACT This work applies the concepts of the attainable region for process synthesis in comminution. The attainable region analysis has been successfully applied for process synthesis of reactor networks. The Attainable Region is defined as the set of all possible output states for a constrained or unconstrained system of fundamental processes (Horn, 1964). A basic procedure for constructing the attainable region for the fundamental processes of reaction and mixing has been postulated in reaction engineering (Glasser et al., 1987). This procedure has been followed in this work to construct the candidate attainable region for size reduction processes as found in a size reduction environment. A population balance model has been used to characterise the evolution of particle size distributions from a comminution event. Herbst and Fuerstenau (1973) postulated the dependency of grinding on the specific energy. A specific energy dependent population balance model was used for the theoretical simulations and for the fitting of experimental data. A new method of presenting particle size distributions as points in the Euclidian space was postulated in place of the traditional cumulative distribution. This allows successive product particle size distributions to be connected forming a trajectory over which the objective function can be evaluated. The curve connects products from successive batch grinding stages forming a pseudo-continuous process. Breakage, mixing and classification were identified as the fundamental processes of interest for comminution. Agglomeration was not considered in any of the examples. Mathematical models were used to describe each fundamental process, i.e. breakage, mixing and classification, and an The application of the attainable region analysis in comminution Abstract algorithm developed that could calculate the evolution of product particle size distributions. A convex candidate attainable region was found from which process synthesis and optimisation solutions could be drawn in two dimensional Euclidian space. As required from Attainable Region Theory, the interior of the bounded region is filled by trajectories of higher energy requirements or mixing between two boundary optimal points. Experimental validation of the proposed application of the attainable region analysis results in comminution was performed. Mono-sized feed particles were broken in a laboratory ball mill and the products were successfully fitted using a population balance model. It was shown that the breakage process trajectories were convex and they follow first order grinding kinetics at long grind times. The candidate attainable region was determined for an objective function to maximise the mass fraction in the median size class 2. It was proved that the same specific energy input produces identical products. The kinematic and loading conditions are supposed to be chosen as a subsequent event after the required specific energy is identified. Finally the fundamental process of classification was added to the system of breakage and mixing. The attainable regions analysis affords the opportunity to quantify exactly the reduction in energy consumption due to classification in a comminution circuit, thus giving optimal targets. Classification showed the potential to extend the candidate attainable region for a fixed specific energy input. The boundary of the attainable region is interpreted as pieces of equipment and optimum process conditions. This solves both the original process synthesis and successive optimisation problems.

Em um tratamento de águas de abastecimento ou residuárias, a coagulação/floculação é um processo de grande importância. A determinação dos agentes coagulante/floculante e a quantidade necessária de cada um deles são problemas rotineiros para os profissionais e podem influenciar na qualidade do tratamento. Determinar o tamanho dos flocos é fundamental para que a operação de floculação ocorra com melhor eficiência. Ainda, variáveis hidrodinâmicas, como a velocidade, volume das partículas e do recipiente, também têm a mesma importância nesta finalidade. No presente trabalho, a modelagem do processo de floculação via balanço populacional foi estudada com o objetivo de prever a formação de agregados/flocos em relação com o tempo até atingir o estado estacionário e em condições de operação distintas. Assim, um modelo de balanço populacional pela técnica de discretização por pivô fixo foi implementado no software EMSO. Um estudo foi realizado através de processamento/análise de imagens capturadas em um experimento de coagulação/floculação. As imagens obtidas do processo de floculação foram analisadas e foi verificado a distribuição do tamanho dos flocos. Com os dados de volume e concentração inicial de partículas foi possível a simulação no modelo matemático. Assim tornou-se possível observar o crescimento, a estabilização, o comportamento dos flocos em comparação com o modelo matemático e a frequência desses flocos em cada tamanho em diferentes condições, como o gradiente de velocidade e a concentração inicial de partículas. Os resultados obtidos em comparação com os dados experimentais e a simulação do modelo matemático foram possíveis verificar comportamento semelhante de distribuição de tamanho de flocos. A partir dessa análise, o modelo matemático mostrou-se satisfatório em prever o comportamento experimental. Em diferentes condições pode-se verificar que o gradiente de velocidade e a concentração inicial de partículas influenciam na formação e estabilização dos flocos. Este estudo teve a utilização de softwares de livre acesso para trazer a proposta de implementação a fim de trazer economia de agentes químicos utilizados e melhoria nos processos de operação da estação tratamento de efluentes. / In a wastewater treatment, coagulation / flocculation is a process of great importance. The determination of coagulant / flocculant agent and the required amount of each problems are routine for professional and can influence the quality of treatment. Determination the flocs size is essential for flocculation operation to occur with greater efficiency. Still, hydrodynamic variables, such as speed, particles volume and the container also have the same importance in this purpose. In the present work, modeling of flocculation process by population balance was studied in order to predict the formation of aggregates / flocs in relation to time to reach steady state and at different operating conditions. Thus, a population balance model by discretization technique for fixed pivot was implemented in EMSO software. A study was conducted through the processing / analysis of images captured on an experiment coagulation / flocculation. Images obtained in the flocculation process were analyzed and it was found the size distribution of flocs. With the volume and initial particle concentration values, simulation was possible in mathematical model. Thus it became possible to observe the growth, establization and behavior of flocs in comparison with the mathematical model, and the frequency of such flocs in each size in different conditions, such as the velocity gradient and the initial particle concentration. The results obtained in comparison to experimental data and simulation of the mathematical model we observed behavior flocs size distribution similar. From this analysis, mathematical model was satisfactory to predict the experimental behavior. Under different conditions can be seen that the velocity gradient and the initial concentration of particles influence the formation and stabilization of flocs. This study was the use of software-free access to bring the implementation of proposal in order to bring savings of chemicals used and improvement in operating processes of wastewater treatment station.

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.