The modelling of transport processes in biological systems is one of the main theoretical challenges in physics, chemistry and biology. This is motivated by their essential role in the emergence of diseases, like tumour metastases, which originate from the spontaneous migration of cancer cells. Thus, improvements in their understanding could potentially pave the way for an outstanding innovation of present-day techniques in medicine. These processes often exhibit anomalous properties, which are qualitatively described by the power-law scaling of their mean square displacement, compared to the linear one of normal diffusion. Such behaviour has been often successfully explained by the celebrated continuous-time random walk model. However, recent experimental studies revealed the existence of both more complicated mean square displacement behaviour and anomalous features in other characteristic observables, e.g. the position-velocity statistics or the two point correlation functions of either the velocity or the position. Thus, in order to understand the anomalous diffusion recorded in these experiments and assess the microscopic processes underlying the observed macroscopic dynamics, one needs to have a complete tool-kit of techniques and models that can be readily compared with the experimental datasets. In this Thesis, we contribute to the construction of such a complete framework by fully characterising anomalous processes, which are described by means of a continuoustime random walk with general waiting time distributions and/or external forces that are exerted both during the jumps (as in the original model) and the waiting times. In the first case we derive both the joint statistics of these processes and their observables, specifically by obtaining a generalised fractional Feynman-Kac formula, and their multipoint correlation functions and employ them to fit the mean square displacement data of diffusing mitochondria. This result supports the experimental relevance of our formalism, which comprises general formulas for several quantities that can provide readily predictable tests to be checked in experiments. In the second case, we characterise the new anomalous processes by means of Langevin equations driven by a novel type of non Gaussian noise, which reproduces the typical fluctuations of a free diffusive continuous-time random walk. For a constant external force, we also obtain the fractional evolution equations of their position probability density function and show that, contrarily to continuous-time random walks, they are weak Galilean invariant, i.e., their position distribution in different Galilean frames is obtained by shifting the sample variable according to the relative motion of the frames. Thus, these processes provide a suitable frame-invariant framework, that could be employed to investigate the stochastic thermodynamics of anomalous diffusive processes.

This thesis examines transport phenomena of cupric chloride (CuCI2) hydrolysis within a fluidized bed. Conversions of CuCi2 and steam as a fluidizing gas are numerically investigated using a new non-catalytic gas-solid reaction model, proposed in the literature but here updated for the purposes of the present study. The results are illustrated considering two cases of kinetics for the consumption of particles: Volumetric Model and Shrinking Core Model. Consistent results in terms of the conversion of reactants versus superficial velocity, bed inventory and bed temperature are obtained by developing new solution algorithms abased on each of the above kinetic models. / UOIT

This thesis looks at the transport phenomena in indium arsenide at low temperatures.

Current chemotherapeutic treatment schedule prediction methods rely heavily on PK/PD-based models and overlook the important contribution of tissue-level transport and binding. Tissue-level transport and binding phenomena are essential to understanding drug delivery and efficacy in tumors. Drugs with desirable PK/PD properties often fail in vivo due to poor tissue-level transport. We developed an in silico method to predict the effect of treatment schedule on efficacy that couples PK/PD with tissue-level transport. Treatment schedules were implemented on theoretical drugs with different PK/PD and transport properties. For each drug with a given clearance rate, diffusivity, and binding, treatment schedules consisting of one to 20 doses were simulated. Results show that at binding constants around one, high diffusivities, and high clearance rates, implementation of a treatment schedule becomes more significant. At low clearance rates, regardless of tissue-level transport and binding, one dose was predicted to be most efficacious. Tissue Drug Exposure (TDE) was shown to be to a crucial factor for treatment schedule efficacy. Efficacy was improved by increasing TDE. Implementation of a treatment schedule with more doses than one curbed the effect of poor retention with drugs. This model investigates the effect of treatment schedule on a tissue transport model and shows implementation of a proper dosing regimen is crucial to maximize TDE and chemotherapeutic efficacy.

No description available.

A comprehensive, transient three-dimensional model of a single-pass laser surface alloying process has been developed and used to examine the heat, momentum and species transport phenomena. A numerical study is performed in a co-ordinate system moving with the laser at a constant scanning speed. In this model a fixed grid enthalpy-porosity approach is used, which predicts the evolutionary pool development. In this model two extreme cases of alloying element and base metal combinations are considered based on their relative melting points. One extreme case is for an alloying element with its melting point much lower than that of the base metal. In this case the alloying element melts almost instantaneously. Hence it is assumed that the alloying element introduced on the melt pool surface is in the molten state. Thus, while solving the species conservation equation a species flux condition is used on the entire melt pool surface. This case is analysed for aluminium alloying element on iron base metal. The final species distribution in the melt pool as well as in the solidified alloy is predicted. The other extreme case is studied for an alloying element with its melting point relatively higher than that of the base metal. In this case all the alloying element particles on the melt pool surface will not melt. Only those particles which fall in the region on the melt pool surface where the local temperature is higher than the melting point of the alloying element will melt. The particles which fall away from this region are advected into the melt pool, due to a strong Marangoni convection on the melt pool surface. If a particle is advected into the inner region in the melt pool (where the temperature is higher than its melting point), it starts melting and thus the molten species mass gets distributed. Hence, the species flux condition at the entire surface of the melt pool is not valid. The particles are tracked in the melt pool by assuming the alloying particles to be spherical in shape and moving without any relative velocity with the surrounding fluid. Simultaneously, the temperature field inside the spherical particle is solved by assuming its surface temperature to be the local temperature in the melt pool. The amount of particle mass that fuses as it passes through a particular control volume is noted. The same procedure is repeated for a large number of particles initiated at various locations on the pool surface, and a statistical distribution of the species mass source in the entire pool is obtained. This species mass source distribution is then used to solve the species conservation equation. Nickel alloying element on aluminium base metal is used to illustrate this case. The numerical results obtained from the two cases are compared with the available experimental results. A qualitative matching is found between the numerical and experimental results.

O balanço populacional é um método comprovado de se aumentar a previsibilidade do comportamento de um sistema multifásico, e sua utilização em conjunto de técnicas de CFD tem sido cada vez maior pelo desenvolvimento constante de ambas as tecnologias. Este trabalho apresenta o equacionamento genérico do balanço populacional para sistemas bifásicos com agregação e quebra de partículas, além de uma discussão sobre a natureza de sistemas bifásicos. Métodos numéricos específicos para a resolução deste tipo de problema são discutidos, implementados e validados. Como exemplo de aplicação do equacionamento sugerido, é obtido um modelo específico para o caso de coalescência de gotas de água salgada dispersas numa fase óleo submetidas a um campo elétrico alternado, como no processo de dessalgação de petróleo. Um algoritmo baseado em autômatos celulares é utilizado como fonte de dados para validação do modelo e técnicas de CFD produzem um perfil de escoamento da emulsão. / The population balance is a proven method for increasing a multiphase systems behavior predictability, and its employment along with CFD techniques is increasing following the constant development of both technologies. This work presents the generic Population Balance Equations for two-phase systems where its particles suffer aggregation and breakage and a discussion on the nature of two-phase systems. Specific numerical methods for the solution of such problems are discussed, implemented and validated. A specific model for the coalescence of water droplets dispersed in an oily phase under the effects of an alternated electric field is obtained as an application example of the suggested equations, mimicking the oil desalting process. A cellular automata based algorithm is used as data source for the models validation and CFD techniques are used to produce the emulsions flow profile.

While rheological and microstructural complexities have posed tremendous challenges to researchers in developing first principles models and simulation techniques that can accurately and robustly predict the dynamical behaviour of polymeric flows, the past two decades have offered several significant advances towards accomplishing this goal. These accomplishments include: (1). Stable and accurate formulation of continuum-level viscoelastic constitutive models and their efficient implementation using operator splitting methods to explore steady and transient flows in complex geometries, (2). Prediction of rheology of polymer solutions and melts based on micromechanical models as well as highly parallel self-consistent multiscale simulations of non-homogeneous flows. The main objective of this study is to leverage and build upon the aforementioned advances to develop a quantitative understanding of the flow-micro-structure coupling mechanisms in viscoelastic polymeric fluids and in turn predict, consistent with experiments, their essential macroscopic flow properties e.g. frictional drag, interface shape, etc. To this end, we have performed extensive continuum and multiscale flow simulations in several industrially relevant bulk and free surface flows. The primary motivation for the selection of the specific flow problems is based on their ability to represent different deformation types, and the ability to experimentally verify the simulation results as well as their scientific and industrial significance.

Silicon Germanium, SiGe, is an important emerging semiconductor material. In order to optimize growth techniques for SiGe production, such as Liquid Phase Diffusion, LPD, or Melt Replenishment Czochralski, a good understanding of the transport phenomena in the melt is required. In the context of the Liquid Phase Diffusion growth technique, the transport phenomena of silicon in a silicon-germanium melt has been explored. Experiments isolating the dissolution and transport of silicon into a germanium melt have been conducted under a variety of flow conditions. Preliminary modeling of these experiments has also been conducted and agreement with experiments has been shown. In addition, full LPD experiments have also been conducted under varying flow conditions. Altered flow conditions were achieved through the application of a variety of magnetic fields. Through the experimental and modeling work better understanding of the transport mechanisms at work in a silicon-germanium melt has been achieved. / Graduate

[pt] A solução numérica de problemas de escoamentos de fluidos com transferência de calor, envolve a solução de um conjunto de equações diferenciais parciais não lineares acopladas. O maior esforço computacional gasto na solução dessas equações, é devido a solução dos sistemas algébricos resultantes da discretização das equações de conservação. A taxa de convergência de varios métodos iterativos é sensível a natureza do problema que está sendo resolvido. Portanto, nenhum método pode ser aclamado como melhor para todos os problemas. Junto com o desenvolvimento de novos métodos iterativos, o desenvolvimento de técnicas de aceleração da convergência dos métodos iterativos conhecidos é de consideravel interesse de ponto de vista prático. O objetivo primário do presente trabalho consistiu em analisar uma classe de algoritmos para a solução de sistemas algébricos provenientes da discretização das equações de conservação de fenômenos de transporte. O segundo objetivo foi o de selecionar um método adequado e eficiente que produza um aumento da taxa de convergência. Para este propósito, selecionou-se e implementou-se um esquema de - multigrid - por correção aditiva. Esta é uma técnica recente na qual o mesmo problema diferencial é aproximado em diversas malhas cujos tamanhos de malha são geralmente múltiplos integrais. Investigou-se seu desempenho para melhorar a taxa de convergência junto com o método iterativo linha por linha TDMA, e comparou-se seu desempenho com o método de correção por blocos. / [en] The numerical solution of fluid flows problems with heat transfer requires the solution of a set of coupled non- linear partial differencial equations. The major computational effort in solving these equations is due to the solution of the algebraic systems resultant from the discretization of the conservation equations. The convergence rate of iterative methods is sensitive to the nature of the problem being solved. Therefore, no one method may be claimed to be the best for all problems. Along with the development of new iterative methods, the development of technics for accelerating the convergence of known iterative methods presents a considerable interest from a practical standpoint. The primary objective of the present work was to analise a class of algorithms for the solution of algebraic systems resulting from the discretization of transport phenomena conservation equations. The second objective was to select an adequate and efficient method which lead an increase of the convergence rate. For this purpose a multigrid additive correction scheme was selected and implemented. This is a novel technique in which the same differential problem is approximated on several grids whose mesh sizes are usually integral multiples. It was investigated its performance to improve the convergence rate in combination with the iterative line-by-line TDMA as well as its performance with the use of block correction algorithm. / [es] La solución numérica de problemas de flujo de fluidos con transferencia de calor, comprende la solución de un conjunto de ecuaciones diferenciales parciales no lineales acopladas. El mayor esfuerzo computacional en la solución de esas ecuaciones, se debe a la resolución de los sistemas algebraicos resultantes de la discretización de las ecuaciones de conservación. La tasa de convergencia de varios métodos iterativos es altamente sensible a la naturaleza del problema. Por lo tanto, ningún método puede ser considerado como el