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 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.

Plant derived natural products represent some of the most effective anti-cancer and anti-infectious disease pharmaceuticals available today. However, uncertainty regarding the feasibility of commercial supply due to the limited availability of many plants in nature has resulted in a dramatic reduction in the use of natural products as leads in modern drug discovery. Plant cell suspension culture, consisting of dedifferentiated plant cells grown in vitro and amenable to large scale industrial biotechnology processes, is a production alternative which promises renewable and economical supply of these important drugs. The widespread application of this technology is limited by low product yields, slow growth rates, challenges in scale-up, and above all, variability in these properties, which is poorly understood. Plant cells grow as aggregates in suspension cultures ranging from two to thousands of cells (less than 100 micron to well over 2 mm). Aggregates have long been identified as an important feature of plant cell culture systems, as they create microenvironments for individual cells with respect to nutrient limitations, cell-cell signaling, and applied shear in the in vitro environment. Despite its purported significance, a rigorous engineering analysis of aggregation has remained elusive. In this thesis, aggregation was characterized, analyzed, and modeled in Taxus suspension cultures, which produce the anti-cancer drug paclitaxel. A technique was developed to reliably and routinely measure aggregate size using a Coulter counter. The analysis of aggregate size as a process variable was then used to evaluate the effect of aggregation on process performance, and the analysis of single cells isolated from different sized aggregates was used to understand the effect of aggregation on cellular metabolism and heterogeneity. Process characterization studies indicated that aggregate size changed over a batch cycle as well as from batch to batch, so a population balance equation model was developed to describe and predict these changes in the aggregate size distribution. This multi-scale engineering approach towards understanding plant cell aggregation serves as an important step in the development of rational strategies aimed at controlling the process variability which has heretofore limited the application of plant cell culture technology.

Master of Science / Department of Mechanical and Nuclear Engineering / Xiao J. Xin / Energy consumption due to dairy production constitutes 10% of all energy usage in the U.S. Food Industry. Improving energy efficiency in food refrigeration and freezing plays an important role in meeting the energy challenges of today. Freezing and hardening are important but energy-intensive steps in ice cream manufacturing. This thesis presents a series of models to address these issues. The first step taken to model energy consumption was to create a temperature-dependent ice cream material using empirical properties available in the literature. The homogeneous ice cream material is validated using finite element analysis (FEA) and previously published experimental findings. The validated model is then used to study the efficiency of various package configurations in the ice cream hardening process. The next step taken is to consider product quality by modeling the ice crystal size distribution (CSD) throughout the hardening process. This is achieved through the use of population balance equations (PBE). Crystal size and corresponding hardened ice cream coarseness can be predicted through the PBE model presented in this thesis. The crystallization results are validated through previous experimental study. After the hardening studies are presented, the topic of continuous freezing is discussed. The actual ice cream continuous freezing process is inherently complex, and therefore simplifying assumptions are utilized in this work. Simulation is achieved through combined computational fluid dynamics (CFD) and PBE modeling of a sucrose solution. By assuming constant fluid viscosity, a two-dimensional cross section is able to be employed by the model. The results from this thesis provide a practical advancement of previous ice cream simulations and lay the groundwork for future studies.

Nanoparticles are used in various applications like medical diagnostics, drug delivery, energy technology, electronics, catalysis etc. Although particles of such small dimensions can be synthesized through various methods, the liquid phase synthesis methods stands out for their simplicity. Typically, these methods involve reaction of precursors to form solute. At high concentration of solute, nucleation commences and nuclei are formed. These nuclei grow in size by assimilating solute from the bulk. Stabilizers or capping agents compete with solute for adsorption on the surface of a growing particle. Two partially protected particles can form bigger particle by coagulation. Uncontrolled turbulent flow field in laboratory scale reactors combined with all the above quite fast and poorly understood steps often lead to poorly controlled synthesis of particles. In many a systems, it also leads to very poor reproducibility. Any attempt to synthesis nanoparticles at engineering scale, with good control on mean size and polydispersity, requires quantitative understanding of the synthesis process. It can then be combined with description of other transport processes in reactors to optimize synthesis protocols. Two main factors hinder progress in this direction: complex and often poorly understood chemistry, and inefficient tools to simulate particle synthesis. In the first part of the thesis, a quantitative model is developed for tannic acid method of synthesis of gold nanoparticles. It showcases the approach used to model a system with poorly understood chemistry and which defies an understanding through the widely used homogeneous nucleation based mechanism for particle synthesis. An organizer based mechanism in which tannic acid brings together nucleating species to facilitate nucleation is invoked. Simple reaction network based models however fail to explain the experimental findings. The underlying chemistry is explored to develop a comprehensive reaction network. This network is used as a guide to seek pathways which can mimic burst of nucleation, a characteristic of homogeneous nucleation based mechanism, through self-limiting nucleation, and various other features present in the experimental data. After successful prediction of all the features of the experimental data through this network, a minimal organizer based mechanism which leads to self-limiting nucleation is developed. The minimal organizer model offers itself as a competing and alternative mechanism to explain nanoparticle synthesis. A few new predictions made by the new model are verified by others in our group. Monte-Carlo (MC) simulations are used as a powerful tool to simulate stochastic processes. Their application to nanoparticle synthesis is limited by three problems: (i) zero initial rate of stochastic processes which leads to infinite time step at the beginning of the simulation, (ii) sensitively time dependent rate of stochastic processes, and (iii) computation intensive simulations. We propose a new approach to carry out MC simulations. It makes use of simulation results obtained with systems of extremely small sizes. These system size dependent predictions, obtained at substantially reduced computational cost are used to construct results for system of infinite size. The approach is based on a new power law scaling that we have found in this work. An efficient implementation of MC simulation for time dependent rate processes is also developed. In this method, an additional variable is introduced for inter-event evolution. It increases the number of differential equation by one, but significantly reduces the computational effort required to estimate the interval of quiescence for time dependent rate processes. All the above ideas are combined in the new approach to simulate complete size distribution for simultaneous nucleation and growth of nanoparticles for a system of infinite size from erroneous simulations carried out with three extremely small size systems. A new framework for solving multidimensional population balance equations (PBEs) which routinely arise in modeling of nanoparticle synthesis is also developed. The new framework advances the concept of minimal internal consistency of discretization. It suggests that an n dimensional PBE is a statement of evolution of population of particles while accounting for how n internal attributes of particles change in particulate events. Thus, a minimum of n + 1 attributes of particles, instead of 2n attributes used hitherto, need to be represented perfectly in discrete representation. This is termed as the concept of minimum internal consistency of discretization in this work. The elements used for discretization should therefore be triangles for 2-d, tetrahedrons for 3-d, and an object with n + 1 vertices in n-d space for the solution of a n-d PBE. The results presented for the solutions for 2-d and 3-d PBEs show the superiority of this framework over the earlier framework. The present work also shows that directionality of elements plays a critical role in the solution of multi-dimensional PBEs. A mere change in connectivity of pivots in space, which changes their directionality, is shown to influence numerical results. This work led to new radial discretization of space, which has been followed up by others in the group and demonstrated to be quite powerful. A physical model is developed to understand digestive ripening of nanoparticles, a technique which is in extensive use in the literature to improve monodispersity of nanoparticles. The physical model is based on critical analysis of the large body of experimental findings available in the literature on several variations of this technique. The physical model is the first one to consistently and qualitatively explain all the reported experimental findings.

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.

La congélation partielle du mix dans un échangeur de chaleur à surface raclée (ECSR)est l'étape la plus critique dans la fabrication d'un sorbet, car c'est la seule étape où de nouveaux cristaux de glace se forment; par la suite ces cristaux ne font que grossir. L'objectif principal est de produire un grand nombre de cristaux les plus petits possibles afin d'obtenir une texture onctueuse. Pendant le procédé de congélation, le produit est soumis à des interactions couplées d'écoulement du fluide, de transfert de chaleur, de changement de phase et de cisaillement. Ces interactions sont déterminées par les conditions opératoires du procédé de congélation et affectent l'évolution de la distribution de taille des cristaux de glace, ainsi que la texture finale du produit. Ce travail présente la caractérisation expérimentale et la modélisation du procédé de congélation d'un sorbet. La congélation du sorbet à été effectuée dans un ECSR à l'échelle pilote. L'objectif principal de ce travail est l'étude de l'influence des conditions opératoires du procédé de congélation sur les caractéristiques finales du produit: distribution de taille de cristaux de glace, température du produit, fraction volumique de glace et viscosité apparente. Le comportement de l'écoulement du produit dans l'ECSR a été caractérisé par une étude expérimentale et une modélisation de la distribution du temps de séjour (DTS). Une approche de modélisation de la cristallisation de la glace couplant le modèle de DTS avec des équations de transfert de chaleur et de bilan de population des différentes classes de taille de cristaux a été développée. À partir d'une première estimation des paramètres, le modèle de cristallisation prédit de façon satisfaisante les tendances expérimentales et donne un bon aperçu de l'évolution de la distribution de taille des cristaux de glace au cours du procédé de congélation dans l'ECSR. / The partial freezing of the mix inside the scraped surface heat exchanger (SSHE) is the most critical step in sorbet manufacturing, since it is the only stage where new ice crystals are produced; further in the process these ice crystals will only grow. The main objective of the freezing process is to form the smallest possible ice crystals, so as to assure a smooth texture in the final product. During the freezing process the product is subjected to coupled interactions of fluid flow, heat transfer, ice phase change and shear. These interactions are determined by the freezing operating conditions and affect the evolution of the ice crystals size distribution (CSD) and the final texture of the product. This work presents the experimental characterization and the modelling of the initial freezing process of a sorbet. The freezing of sorbet was carried out in a SSHE at the pilot scale. The main objective of this work was the study of the influence of the freezing operating conditions on the final product characteristics: ice CSD, product temperature, ice volume fraction, apparent viscosity. The product flow behaviour in the SSHE was characterized by an experimental and modelling study of the residence time distribution (RTD) of the product. An ice crystallization modelling approach, taking into account the coupling of an empirical RTD model with heat transfer equations and a population balance of the different ice crystal size classes was developed. With a first set of estimated parameters, the ice crystallization model predicts satisfactorily the experimental trends, and made it possible to have an insight on the evolution of ice CSD during the freezing process in the SSHE.