This diploma thesis is focused on combination of experimental study and computer modelling of diffusion processes in gel phases. The aim of experimental part of the diploma thesis was to test and optimize the setting of the diffusion coefficient in gel medium by using the method of horizontal diffusion cells, commonly used for study of diffusion processes through membranes. Specific description of experiments was to determinate the impact of presence of reactive component in inert hydro-gel carrier on final value of diffusion coefficient of low-molecular model diffusion probe. The defined dependencies were subsequently combined with computer simulation of diffusion process in a properly designed model in order to determinate the experimentally unavailable system parameters. The stated combination of both approaches was proved to be an appropriate instrument for studying of hydro-gels with a wide potential especially in the field of preparation of hydro-gel carriers with controlled release of active substances.

Radioactive isotopes enable advanced medical treatments and the study of nuclear structure, nuclear astrophysics, and fundamental symmetries. TRIUMF, Canada’s Particle Accelerator Centre, generates radioactive isotope beams using the Isotope Separation On-Line method. At TRIUMF, the Forced Electron Beam Induced Arc Discharge (FEBIAD) ion source is used to ionize specific isotopes but often presents limited performance and lower efficiencies compared to other facilities. To investigate the source limitation, elucidate the ionization mechanism, and propose improved and highly efficient sources for upcoming facilities, a combined numerical and experimental campaign has been undertaken. The developed numerical ionization model is able to describe the source as an electron impact ion source that is governed by strong space charge effects. The spatially distributed ionization rate is higher at specific locations of the anode volume, and this has been confirmed experimentally. The validated numerical model has been further used to propose simulation-based optimizations. With the overall optimization, the ionization efficiency for the TRIUMF FEBIAD is expected to increase ten-fold. / Graduate

A fluidização é uma operação unitária presente nas indústrias química, farmacêutica e alimentícia. Durante a fluidização, o leito de partículas sólidas é suspenso por um fluxo ascendente de gás. A velocidade mínima de fluidização indica a menor velocidade do gás em que as partículas iniciam a agitação, enquanto a velocidade terminal é caracterizada pela elutriação, ou arraste de partículas juntamente com o gás. Portanto, um leito fluidizado deve operar em uma velocidade de gás que esteja entre a velocidade mínima de fluidização e a velocidade terminal de arraste. No entanto, os sólidos particulados coesivos, caracterizadas pelo grupo de Geldart C, são difíceis de serem fluidizados, devido à formação de canais preferenciais, e são facilmente elutriados. Neste trabalho estudou-se a fluidização de partículas de amido de milho pela passagem de ar a 27 °C. O amido de milho obteve diâmetro médio mássico e densidade do sólido iguais a 30,3 µm e 1446,7 kg/m3, e pôde ser caracterizado como um sólido particulado coesivo, em que a velocidade efetiva de fluidização e velocidade terminal foram iguais a (0,66 e 0,68) m/s, respectivamente. A qualidade da fluidização foi aprimorada pelo uso da pulsação do gás, que possibilitou reduzir a velocidade mínima de fluidização e ampliar a faixa de velocidade de fluidização, de forma a minimizar o arraste de sólidos por elutriação. As frequências de pulsação estudadas foram (0, 5, 10 e 15) Hz. Em uma primeira etapa, foram obtidos os perfis de velocidade queda de pressão a partir de ensaios experimentais. Posteriormente, os perfis experimentais foram utilizados para validação dos modelos de escoamento bifásico Euler-Euler, em simulações realizadas pelo software COMSOL. Dentre os principais resultados, destaca-se que os modelos numéricos puderem descrever com boa aproximação os perfis fluidodinâmicos do sistema binário amido e ar. A aproximação numérica somente foi obtida ao estabelecer um diâmetro equivalente com tamanho de 100 µm, que foi superior ao diâmetro médio mássico. Este resultado evidenciou que a fluidização ocorreu na forma de agregados de partículas, que é característico de sistemas coesivos. O uso da pulsação do ar também resultou ruptura de canais preferenciais, e permitiu o início da fluidização em menores velocidades do ar. / Fluidization is a unit operation in the chemical, pharmaceutical and food industries. During the fluidization, the solid particles is suspended by a stream air flow. The minimum fluidization velocity indicates the lowest gas velocity in which the particles begin agitation while the terminal velocity is characterized by elutriation, or drag the particles along with gas. Therefore, a fluidized bed must be operated at a gas velocity which is between the minimum fluidization velocity and the terminal velocity. However, cohesive solid particles, characterized by Geldart Group C, are difficult to be fluidized due to the formation of cracks and channeling and areeasily elutriated from chamber. In this work, the fluidization of cornstarch particles occurred by anair flow at 27 °C. Cornstarch showed a mean diameter and solid density equal to 30.3 µm and 1446.7 kg/m3 and could be characterized as a cohesive particulate solid. The effective fluidization velocity and the terminal velocity were equal to (0.66 and 0.68) m/s respectively. The fluidization quality was improved by the use of pulsation air flow. The minimum fluidization velocity was reduced, increasing the fluidization velocity operational range. The air pulsation frequency were studied at (0, 5, 10 and 15) Hz. In a first step, the experimental tests obtained the fluidynamics profiles of pressure drop versus air velocity. Subsequently, the experimental profiles were used to validate the Euler-Euler model in simulations by COMSOL software. The main results emphasized that the numerical models described the fluid dynamic profiles with good approximation. The numerical approach established an equivalent diameter of 100 µm, which was greater than the mass median diameter. This result showed that the fluidization occurred in the form of aggregates of particles, which is a characteristic of cohesive systems. The use of air pulsation also resulted in the rupture of channeling and allowed the fluidization at lower air velocities.

Os biopolímeros comestíveis, tais como amido e alginato, podem ser utilizados na formulação de géis com elevada capacidade de retenção de água. A secagem convectiva pode ser utilizada para a remoção da umidade em géis. Os parâmetros da secagem (temperatura, velocidade do ar e umidade de equilíbrio) necessitam ser monitorados para a produção de um sólido seco e sem degradação de compostos ativos. A modelagem matemática da secagem pelo método numérico de elementos finitos em COMSOL Multiphysics tem sido utilizada para simular a secagem, usando um número reduzido de ensaios experimentais. Este trabalho teve como objetivo o desenvolvimento de modelos analíticos e numéricos para predizer a umidade e tamanho de fatias de géis de amido de milho e alginato de cálcio durante a secagem convectiva. O acoplamento entre a transferência de massa e encolhimento das fatias durante a secagem foi simulado e a difusividade mássica efetiva foi obtida pelo ajuste não linear aos dados experimentais. Três modelos foram utilizados como estudos de caso: A secagem de géis contendo 60% de água e 5.4% de amido gelatinizados (GC90), foram descritas pela solução analítica da segunda lei de Fick (R2 = 0.997-0.998); A secagem de géis contendo 60% de água e 5.4% de amido nativo (RC90), foram mais bem explicadas pelo modelo analítico com inclusão do termo de encolhimento (R2 = 0.992); O modelo numérico desenvolvido em COMSOL Multiphysics descreveu adequadamente a secagem de géis formulados com 86% de água e 34% amido gelatinizado e não-gelatinizado (GC50 e RC90), dando um R2 de 0.983-0.992. O encolhimento foi estimado a partir do fluxo molar de água, enquanto a deformação da geometria foi simulada pelo método arbitrário Lagrangian-Eulerian (ALE). A inclusão do termo de encolhimento modificou o perfil de taxa de secagem e o período de pseudo-taxa constante foi observado. O modelo desenvolvido neste trabalho pode ser aplicado em estudos de secagem de géis, alimentos e outros materiais que apresentam elevada razão de encolhimento. / Biopolymers, such as starch and alginate, can be used in the formulation of gels with high water retention. The convective drying can be applied to gel moisture removing. Drying parameters (temperature, air velocity and equilibrium moisture) should be monitored in view of producing a dry solid without degradation of active compounds. The mathematical modeling by the finite element method in COMSOL Multiphysics has been used to simulate drying profiles, with reduced experimental runs. This work aimed at developing of analytical and numerical models to predict the moisture and size of slices of gels containing cornstarch and calcium alginate, during convective drying. The coupling between mass transfer and shrinkage of slices during drying was simulated and the effective mass diffusivity was obtained by non-linear adjustment to the experimental data. Three models have been used as case studies obtained the effective mass diffusivity. Drying of gels containing 60% water and 5.4% gelatinized cornstarch (GC90 samples) as well fitted by the analytical solution of Fick\'s second law (R2 = 0.997-0.998). Drying of gels containing 60% water and 5.4% native starch (RC90 samples) as explained by Fick\'s analytical model while inclusion of the shrinkage term (R2 = 0.992). The numerical model developed in COMSOL Multiphysics adequately described the drying of gels formulated with 86% water and 34% of starch, gelatinized or non-gelatinized, (GC50 and RC90 samples), giving a R2 of 0.983-0.992. The shrinkage was estimated by the molar flux of water, while the geometry shrinkage was simulated by the Arbitrary Lagrangian-Eulerian (ALE) method. The inclusion of the shrinkage modified the drying rate profiles and a pseudo-constant rate period was observed. The model developed in this work can be applied to drying studies of gels, food and other materials that have a high shrinkage ratio.

Šiame darbe buvo analizuojama programinė įranga skirta diskretizuoti sritį į baigtinius elementus. Analizuotos MATLAB sistemos ir COMSOL programos diskretzavimo galimybės. Sukurta programa sujungianti COMSOL ir MATLAB, kuri leidžia diskretizuoti sritį į baigtinius elementus. / In this work was done study of software for domain discretization by finite elements. Created program that connects MATLAB and COMSOL, which allows domain discretization by finite elements.

This work is dealing with issues concerning mathematical and computer modeling of events describable with help of rst and second order differential equations. First part contains summary of basic procedures for searching differential equations using analythical methods, next chapter is focused on software used to solve chosen tasks and demonstration of speci c physics problems.

Os biopolímeros comestíveis, tais como amido e alginato, podem ser utilizados na formulação de géis com elevada capacidade de retenção de água. A secagem convectiva pode ser utilizada para a remoção da umidade em géis. Os parâmetros da secagem (temperatura, velocidade do ar e umidade de equilíbrio) necessitam ser monitorados para a produção de um sólido seco e sem degradação de compostos ativos. A modelagem matemática da secagem pelo método numérico de elementos finitos em COMSOL Multiphysics tem sido utilizada para simular a secagem, usando um número reduzido de ensaios experimentais. Este trabalho teve como objetivo o desenvolvimento de modelos analíticos e numéricos para predizer a umidade e tamanho de fatias de géis de amido de milho e alginato de cálcio durante a secagem convectiva. O acoplamento entre a transferência de massa e encolhimento das fatias durante a secagem foi simulado e a difusividade mássica efetiva foi obtida pelo ajuste não linear aos dados experimentais. Três modelos foram utilizados como estudos de caso: A secagem de géis contendo 60% de água e 5.4% de amido gelatinizados (GC90), foram descritas pela solução analítica da segunda lei de Fick (R2 = 0.997-0.998); A secagem de géis contendo 60% de água e 5.4% de amido nativo (RC90), foram mais bem explicadas pelo modelo analítico com inclusão do termo de encolhimento (R2 = 0.992); O modelo numérico desenvolvido em COMSOL Multiphysics descreveu adequadamente a secagem de géis formulados com 86% de água e 34% amido gelatinizado e não-gelatinizado (GC50 e RC90), dando um R2 de 0.983-0.992. O encolhimento foi estimado a partir do fluxo molar de água, enquanto a deformação da geometria foi simulada pelo método arbitrário Lagrangian-Eulerian (ALE). A inclusão do termo de encolhimento modificou o perfil de taxa de secagem e o período de pseudo-taxa constante foi observado. O modelo desenvolvido neste trabalho pode ser aplicado em estudos de secagem de géis, alimentos e outros materiais que apresentam elevada razão de encolhimento. / Biopolymers, such as starch and alginate, can be used in the formulation of gels with high water retention. The convective drying can be applied to gel moisture removing. Drying parameters (temperature, air velocity and equilibrium moisture) should be monitored in view of producing a dry solid without degradation of active compounds. The mathematical modeling by the finite element method in COMSOL Multiphysics has been used to simulate drying profiles, with reduced experimental runs. This work aimed at developing of analytical and numerical models to predict the moisture and size of slices of gels containing cornstarch and calcium alginate, during convective drying. The coupling between mass transfer and shrinkage of slices during drying was simulated and the effective mass diffusivity was obtained by non-linear adjustment to the experimental data. Three models have been used as case studies obtained the effective mass diffusivity. Drying of gels containing 60% water and 5.4% gelatinized cornstarch (GC90 samples) as well fitted by the analytical solution of Fick\'s second law (R2 = 0.997-0.998). Drying of gels containing 60% water and 5.4% native starch (RC90 samples) as explained by Fick\'s analytical model while inclusion of the shrinkage term (R2 = 0.992). The numerical model developed in COMSOL Multiphysics adequately described the drying of gels formulated with 86% water and 34% of starch, gelatinized or non-gelatinized, (GC50 and RC90 samples), giving a R2 of 0.983-0.992. The shrinkage was estimated by the molar flux of water, while the geometry shrinkage was simulated by the Arbitrary Lagrangian-Eulerian (ALE) method. The inclusion of the shrinkage modified the drying rate profiles and a pseudo-constant rate period was observed. The model developed in this work can be applied to drying studies of gels, food and other materials that have a high shrinkage ratio.

A fluidização é uma operação unitária presente nas indústrias química, farmacêutica e alimentícia. Durante a fluidização, o leito de partículas sólidas é suspenso por um fluxo ascendente de gás. A velocidade mínima de fluidização indica a menor velocidade do gás em que as partículas iniciam a agitação, enquanto a velocidade terminal é caracterizada pela elutriação, ou arraste de partículas juntamente com o gás. Portanto, um leito fluidizado deve operar em uma velocidade de gás que esteja entre a velocidade mínima de fluidização e a velocidade terminal de arraste. No entanto, os sólidos particulados coesivos, caracterizadas pelo grupo de Geldart C, são difíceis de serem fluidizados, devido à formação de canais preferenciais, e são facilmente elutriados. Neste trabalho estudou-se a fluidização de partículas de amido de milho pela passagem de ar a 27 °C. O amido de milho obteve diâmetro médio mássico e densidade do sólido iguais a 30,3 µm e 1446,7 kg/m3, e pôde ser caracterizado como um sólido particulado coesivo, em que a velocidade efetiva de fluidização e velocidade terminal foram iguais a (0,66 e 0,68) m/s, respectivamente. A qualidade da fluidização foi aprimorada pelo uso da pulsação do gás, que possibilitou reduzir a velocidade mínima de fluidização e ampliar a faixa de velocidade de fluidização, de forma a minimizar o arraste de sólidos por elutriação. As frequências de pulsação estudadas foram (0, 5, 10 e 15) Hz. Em uma primeira etapa, foram obtidos os perfis de velocidade queda de pressão a partir de ensaios experimentais. Posteriormente, os perfis experimentais foram utilizados para validação dos modelos de escoamento bifásico Euler-Euler, em simulações realizadas pelo software COMSOL. Dentre os principais resultados, destaca-se que os modelos numéricos puderem descrever com boa aproximação os perfis fluidodinâmicos do sistema binário amido e ar. A aproximação numérica somente foi obtida ao estabelecer um diâmetro equivalente com tamanho de 100 µm, que foi superior ao diâmetro médio mássico. Este resultado evidenciou que a fluidização ocorreu na forma de agregados de partículas, que é característico de sistemas coesivos. O uso da pulsação do ar também resultou ruptura de canais preferenciais, e permitiu o início da fluidização em menores velocidades do ar. / Fluidization is a unit operation in the chemical, pharmaceutical and food industries. During the fluidization, the solid particles is suspended by a stream air flow. The minimum fluidization velocity indicates the lowest gas velocity in which the particles begin agitation while the terminal velocity is characterized by elutriation, or drag the particles along with gas. Therefore, a fluidized bed must be operated at a gas velocity which is between the minimum fluidization velocity and the terminal velocity. However, cohesive solid particles, characterized by Geldart Group C, are difficult to be fluidized due to the formation of cracks and channeling and areeasily elutriated from chamber. In this work, the fluidization of cornstarch particles occurred by anair flow at 27 °C. Cornstarch showed a mean diameter and solid density equal to 30.3 µm and 1446.7 kg/m3 and could be characterized as a cohesive particulate solid. The effective fluidization velocity and the terminal velocity were equal to (0.66 and 0.68) m/s respectively. The fluidization quality was improved by the use of pulsation air flow. The minimum fluidization velocity was reduced, increasing the fluidization velocity operational range. The air pulsation frequency were studied at (0, 5, 10 and 15) Hz. In a first step, the experimental tests obtained the fluidynamics profiles of pressure drop versus air velocity. Subsequently, the experimental profiles were used to validate the Euler-Euler model in simulations by COMSOL software. The main results emphasized that the numerical models described the fluid dynamic profiles with good approximation. The numerical approach established an equivalent diameter of 100 µm, which was greater than the mass median diameter. This result showed that the fluidization occurred in the form of aggregates of particles, which is a characteristic of cohesive systems. The use of air pulsation also resulted in the rupture of channeling and allowed the fluidization at lower air velocities.

La modélisation du transport réactif dans les milieux poreux implique la simulation de plusieurs processus physico-chimiques : écoulement de phases fluides, transport de chaleur, réactions chimiques entre espèces en phases identiques ou différentes. La résolution du système d'équations qui décrit le problème peut être obtenue par une approche soit totalement couplée soit découplée. Les approches découplées simplifient le système d'équations en décomposant le problème sous-parties plus faciles à gérer. Chacune de ces sous-parties peut être résolue avec des techniques d'intégration appropriées. Les techniques de découplage peuvent être non‑itératives (operator splitting methods) ou itératives (fixed‑point iteration), chacunes ayant des avantages et des inconvénients. Les approches non‑iteratives génèrent une erreur associée à la séparation des sous­-parties couplées, et les approaches itératives peuvent présenter des problèmes de convergence. Dans cette thèse, nous développons un code sous licence libre en langage MATLAB (https://github.com/TReacLab/TReacLab) dédie à la modélisation du la problématique de la carbonatation atmosphérique du béton, dans le cadre du stockage de déchets de moyenne activité et longue vie en couche géologique profonde. Le code propose un ensemble d'approche découplée : classique, comme les approches de fractionnement séquentiel, alternatif ou Strang, et moins classique, comme les approches de fractionnement additif ou par répartition symétrique. En outre, deux approches itératives basées sur une formulation spécifique (SIA CC et SIA TC) ont également été implémentées. Le code été interfacé de manière générique avec différents solveurs de transport (COMSOL, pdepe MATLAB, FVTool, FD scripts) et géochimiques (iPhreeqc, PhreeqcRM). Afin de valider l'implémentations des différentes approches, plusieurs bancs d'essais classiques dans le domaine du transport réactif ont été utilises avec succès. L'erreur associée à la combinaison du fractionnement de l'opérateur et des techniques numériques étant complexe à évaluer, nous explorons les outils mathématiques existants permettant de l'estimer. Enfin, nous structurons le problème de la carbonatation atmosphérique et présentons des simulations préliminaires, en détaillant les problèmes pertinents et les étapes futures à suivre. / Reactive transport modeling in porous media involves the simulation of several physico‑chemical processes: flow of fluid phases, transport of species, heat transport, chemical reactions between species in the same phase or in different phases. The resolution of the system of equations that describes the problem can be obtained by a fully coupled approach or by a decoupled approach. Decoupled approaches can simplify the system of equations by breaking down the problem into smaller parts that are easier to handle. Each of the smaller parts can be solved with suitable integration techniques. The decoupling techniques might be non‑iterative (operator splitting methods) or iterative (fixed‑point iteration), having each its advantages and disadvantages. Non‑iterative approaches have an error associated with the separation of the coupled effects, and iterative approaches might have problems to converge. In this thesis, we develop an open‑source code written in MATLAB (https://github.com/TReacLab/TReacLab) in order to model the problematic of concrete atmospheric carbonation for an intermediate‑level long‑lived nuclear waste package in a deep geological repository. The code uses a decoupled approach. Classical operator splitting approaches, such as sequential, alternating or Strang splitting, and less classical splitting approaches, such as additive or symmetrically weighted splitting, have been implemented. Besides, two iterative approaches based on an specific formulation (SIA CC, and SIA TC) have also been implemented. The code has been interfaced in a generic way with different transport solvers (COMSOL, pdepe MATLAB, FVTool, FD scripts) and geochemical solvers (iPhreeqc, PhreeqcRM). In order to validate the implementation of the different approaches, a series of classical benchmarks in the field of reactive transport have been solved successfully and compared with analytical and external numerical solutions. Since the associated error due to the combination of operator splitting and numerical techniques may be complex to assess, we explore the existing mathematical tools used to evaluate it. Finally, we frame the atmospheric carbonation problem and run preliminary simulations, stating the relevant problems and future steps to follow.

The aim of this thesis is measure the specimens placed in field of MR tomograph, the measured data to evaluace the process and measurement errors. The theoretical part is focused on describing basic parameters of magnetic field, commissioning some older methods of measurement and design methods for the measurement of samples not issuing MR signal. There is performed modeling for the proposed Metod and the 1D, 2D and 3D environments using COMSOL Multiphysics. The practical part is the measurements samples in the tomograph the Institute of Scientific Instruments Academy of Science in Brno. The measured data are processed in Marevisi and Matlab programs. The MATLAB program is written for processing, analysis and data evaluation, after which it is possible to determine the value of the magnetic susceptibility of the selected samples. In conclusion of the work is the quantification accuracy of measurements.