Diffusivity of nonreactive gases in liquids provides a means of interpreting structure in the liquid state. Structural models of the liquid state include Hildebrand's condensed gas model and Eyring's pseudo-lattice model. The former model predicts a linear dependence of diffusivity with temperature while the latter model predicts linear dependence of log(D) versus 1/T. The limited temperature dependent diffusivity data to date with a typical precision of ± 5% do not permit distinguishing which temperature dependence is more linear. However, the present investigation shows that diffusivities of one gas solute in two nonpolar liquids indirectly supports a linear diffusivity temperature dependence by a Graham's law like relation. At a fixed temperature this relation equates relative diffusivities to the square root of the inverse molecular weights of the respective liquids. Diffusion of gases into nonpolar liquids have previously been measured by two techniques: (1) a pseudo-steady state technique developed by Hildebrand with diffusion through multiple capillaries and (2) a method by Walkley with diffusion through an open tube. Each of these methods requires prior knowledge of solubility of the gas in the liquid. An apparatus is constructed which combines these methods into a single experiment. Simultaneous solution of the two equations which describe the combined experiment yields both the solubility and diffusion coefficient. Diffusivities and solubilities of nitrogen, argon and oxygen into liquids of carbon tetrachloride and benzene as well as oxygen into water have been studied. The results compare favorably with the Literature. The diffusion cell for this technique consists of a capillary disk, which is flooded with liquid. Gas is admitted into the space over the open solvent. With temperature and pressure constant, volume uptake of the gas in the solvent is monitored. Time-volume uptake data is evaluated by the two diffusion equations. Although the experiment is conceptually easy, a small gas volume change over a prolonged period of time poses problems in data collection and experiment control. The data collection and control is simplified by dedicating a Microcomputer Interfaced Data Acquisition System (MIDAS) to the experiment. / Ph. D.

A gas-diffusion tracer experiment was conducted at the ChemNuclear, Inc., nuclear waste burial site near Barnwell, South Carolina, on June 1-10; 1981, testing a new methodology to measure the in situ gaseous diffusion characteristics of unsaturated porous media for the purpose of estimating the diffusive flux of volatile contaminants from the burial ground. The tracers used were CClBrF₂ and SF₆. They were released in the subsurface from permeation devices that closely approximate an ideal point-diffusion source. The permeation devices contain the tracer in liquid form and allow the tracer to escape at a constant rate by diffusion through a Teflon membrane. The release rates for CClBrF₂ and SF6 during the test were 105 and 3.3 nanograms/second, respectively. These compounds were selected on the basis of their compatabi1ity with the permeation-release device, their absence in the subsurface, and detectability in the part-per-tri11ion range in soil gas. Analyses were made in the field on a Varian 3700 series gas chromatograph equipped with an electron-capture detector. The instrument was modified to introduce soil gas through sampling valves and a Nafion tube desiccant. The diffusion sources were placed in the unsaturated soil at depths of 2 meters and 13 meters below land surface. Diffusive movements of tracer were monitored for a period of 7 days and tracer breakthrough was observed at points up to 3.5 meters away. Diffusion was modeled using a three-dimensional, continuous point source, transient-state, analytical model which allowed estimation of the effective diffusion coefficient of the porous media, and an independent assessment of the media's sorptive effects on the tracer gas. The model was calibrated using least squares and curve matching techniques, the latter of which enables a field technician to quickly interpret observed field data. Field values obtained for effective diffusion coefficient ranged from 0.026 to 0.037 cm²/sec. The average tortuosity factor observed for test site was 0.705.

Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.

We study systems of n dimensional diffusions whose drift and dispersion coefficients depend only on the relative ranking of the processes. We consider the question of how long it takes for a particle to go from one rank to another. It is argued that as n gets large, the distribution of particles satisfies a Porous Medium Equation. Using this, we derive a deterministic limit for the system of particles. This limit allows for direct calculation of the properties of the rank traversal time. The results are extended to the case of asymmetrically colliding particles. These models are of interest in the study of financial markets and economic inequality. In particular, we derive limits for the performance of some Functionally Generated Portfolios originating from Stochastic Portfolio Theory.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No abstract available. / Thesis (Ph.D.)-University of Natal, Durban, 1986.

This thesis aims to improve the understanding of transport and critical layer mixing in the troposphere and stratosphere. A dynamical approach is taken based on potential vorticity which has long been recognised as the essential field inducing the flow and thermodynamic structure of the atmosphere. Within the dynamical framework of critical layer mixing of potential vorticity, three main topics are addressed. First, an idealised model of critical layer mixing in the stratospheric surf zone is examined. The effect of the shear across the critical layer on the critical layer evolution itself is investigated. In particular it is found that at small shear barotropic instability occurs and the mixing efficiency of the critical layer increases due to the instability. The effect of finite deformation length is also considered which extends previous work. Secondly, the dynamical coupling between the stratosphere and troposphere is examined by considering the effect of direct perturbations to stratospheric potential vorticity on the evolution of midlatitude baroclinic instability. Both zonally symmetric and asymmetric perturbations to the stratospheric potential vorticity are considered, the former representative of a strong polar vortex, the latter representative of the stratospheric state following a major sudden warming. A comparison of these perturbations gives some insight into the possible influence of pre or post-sudden warming conditions on the tropospheric evolution. Finally, the influence of the stratospheric potential vorticity distribution on lateral mixing and transport into and out of the tropical pipe, the low latitude ascending branch of the Brewer-Dobson circulation, is investigated. The stratospheric potential vorticity distribution in the tropical stratosphere is found to have a clear pattern according to the phase of the quasi-biennial oscillation (QBO). The extent of the QBO influence is quantified, by analysing trajectories of Lagrangian particles using an online trajectory code recently implemented in the Met Office's Unified Model.

Orientador: Adalberto Bono Maurizio Sacchi Bassi / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-25T02:48:09Z (GMT). No. of bitstreams: 1 Reis_MartinaCosta_D.pdf: 1200753 bytes, checksum: 9318dbbd02e3d4660c4a6806e68dad7d (MD5) Previous issue date: 2014 / Resumo: Este trabalho descreve a termodinâmica de sistemas eletroquímicos. Explorando os princípios da teoria constitutiva, algumas hipóteses ad hoc e, em especial, o princípio de entropia Müller-Liu, modelos termo-eletroquímicos são propostos para soluções eletrolíticas e para as regiões de bulk e dupla camada de um sistema eletroquímico. A influência das interações íon-íon e íon-solvente sobre a dinâmica da mistura é considerada através da termodinâmica de contínuos polares e as equações de balanço são apropriadamente postuladas. Além disso, equações fenomenológicas são apresentadas para uma solução eletrolítica diluída e isotrópica e as condições para o equilíbrio termodinâmico local do bulk e da dupla camada são investigadas. Comparando-se as desigualdades residuais de entropia obtidas para cada região, foi demonstrado que alguns processos, tais como os fenômenos de difusão térmica, termoeletricidade e eletroforese, desenvolvem-se somente na dupla camada. Consequentemente, o estado de equilíbrio termodinâmico local na dupla camada requer condições termodinâmicas mais severas do que no bulk. Apesar das equações constitutivas serem as mais simples possíveis, os modelos constitutivos propostos para as regiões de dupla camada e bulk são fisicamente consistentes e mais abrangentes do que os modelos eletroquímicos usuais, visto que as equações e relações termodinâmicas obtidas não se limitam às condições limites e nem de equilíbrio. Portanto, a descrição termodinâmica mostrada neste trabalho pode estimular químicos e engenheiros químicos a usar a abordagem contínua no estudo da mobilidade iônica em meios bio e geológicos, fluxos de íons e de outras espécies químicas através de membranas e processos cujas transferências de calor e massa são intensificadas por campos eletromagnéticos / Abstract: This work concerns the thermodynamics of electrochemical systems. Exploiting the principles of constitutive theory, few expedient assumptions, and, in special, the Müller-Liu entropy principle, a thermo-electrochemical continuum model is proposed for electrolyte solutions as well as for the bulk and double layer regions of an electrochemical system. The influence of ion-ion and ion-solvent interactions on the mixture dynamics is taken into account through the thermodynamics of polar materials and balance laws for an electrochemical system are accordingly stated. In addition, phenomenological equations are schemed for a dilute and isotropic electrolyte solution, and the conditions for local thermodynamic equilibrium of bulk and double layer regions are investigated. Comparing the residual entropy inequalities obtained for each region of an electrochemical system, it is shown that some mechanisms develop only in the double layer, such as the thermal diffusion, thermoelectricity and electrophoresis phenomena. As a consequence, the local thermodynamic equilibrium state in the double layer requires stricter conditions than in the bulk. Although the constitutive equations are the simplest possible, the constitutive models proposed for the double layer and bulk regions are physically consistent and more comprehensive than the usual models since the emerging equations do not constrain themselves to equilibrium neither limiting conditions. Therefore, the thermodynamic description provided in this work may stimulate chemists and chemical engineers to take advantage of it to study the flow of ions and other chemical species across cell membranes, ionic mobility in bio and geological media, and processes whose heat and mass transfers are enhanced by electromagnetic fields / Doutorado / Físico-Química / Doutora em Ciências

Indiana University-Purdue University Indianapolis (IUPUI) / Computational analysis of lithium ion batteries has been improved since Newman and et al. suggested the porous electrode theory. It assumed the electrode as a simple structure of homogeneous spherical particles. Bruggeman relationship which characterizes porous material by a simple equation was adopted in the homogeneous electrode model instead of the electrode morphology. To improve the prediction of a cell performance, the numerical analysis requires the realistic microstructure of the cell. Based on the experimentally determined microstructure of the positive and negative electrodes of a lithium ion battery (LIB) using x-ray micro/nano-CT technology, three dimensional (3D) simulations have been presented in this research. Tortuosity of the microstructures has been calculated by a linear diffusion equation to characterize the 3D morphology. The obtained tortuosity and porosity results pointed out that the Bruggeman relationship is not sufficiently estimate the tortuosity by the porosity of electrodes. We studied the diffusion-induced stress numerically based on realistic morphology of reconstructed particles during the lithium ion intercalation process. Diffusion-induced stresses were simulated at different C rates under galvonostatic conditions and compared with spherical particles. The simulation results showed that the intercalation stresses of particles depend on their geometric characteristics. The highest von Mises stress and tresca stress in a real particle are several times higher than the stresses in a spherical particle with the same volume. With the reconstructed positive electrode structure, local effects in the LIB cathode electrode during galvanostatic discharge process have been studied. The simulation results reported that large current density usually occurs at the joints between cathode active material particles and in the small channels in electrolyte, which will generate high electric joule power. By using the 3D real image of a LIB cathode electrode, numerical simulation results revealed that the spatial distribution of variable fields such as concentration, voltage, reaction rate, overpotential, and etc. in the cathode electrode are complicated and non-uniform, especially at high discharge rates.

A compreensão dos fenômenos de adsorção e difusão em superfícies é fundamental no desenvolvimento de materiais de alto rendimento utilizados em uma série de processos de grande relevância industrial. A modelagem de materiais adsorventes porosos através de modelos de rede tem seu potencial uma vez que se pode estudar os fenômenos a nível microscópico incorporando uma série de parâmetros estatísticos importantes na compreensão dos mecanismos nessa escala. Neste trabalho de dissertação de mestrado, em um primeiro momento, foram utilizadas redes bidimensionais quadradas com abordagem de percolação de sítio-sítio para modelar superfícies sujeitas às condições de adsorção em tempo infinito, com o intuito de se estudar as isotermas de adsorção em processos batelada. Numa primeira parte foi observada uma relação estatística na determinação das isotermas de adsorção, em que a probabilidade de adsorção estava condicionada ao número de moléculas na fase líquida. Na segunda parte foram incorporados diferentes tipos e tamanhos de moléculas, sendo observados diferentes comportamentos das isotermas de adsorção de acordo com a variação dessas moléculas adsorvidas. Outro fenômeno de interesse foi o estudo do Limiar de Percolação utilizando diferentes tipos e tamanhos de moléculas, sendo observados comportamentos específicos para cada caso. Desta forma, pode-se obter parâmetros das isotermas relacionados com os tipos e tamanhos moleculares estudados, sendo observado uma forte dependência daqueles com o tamanho da molécula, uma vez que a seletividade à adsorção aumenta com o tamanho da molécula. Ainda nesta primeira parte foram calculados também a probabilidade de ocupação relacionada com a entropia, observando comportamentos na probabilidade de ocupação a cada etapa de tempo. Em um segundo momento, foi estudado a dinâmica de difusão, mediante random walk ou passeadores aleatórios, em redes quadradas e cúbicas, em que foram obtidas leis de potência para cada dimensão. Aspectos como dispersão axial e porosidade foram incorporadas nas simulações, sendo abservados comportamentos específicos para cada caso.