We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice $Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)$. In a first part, these processes are characterized as Gibbs states on path spaces of the form $C([0, T],R)Z^{d}$. In a second part, we study the Gibbsian character on $R^{Z}^{d}$ of $v^{t}$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law $v = v^{0}$ is Gibbsian.

We study the (strong-)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion / when the initial distribution is Gibbsian.

The authors analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the d-dimensional lattice. In the first part of the paper, these processes are characterized as Gibbs states on path spaces. In the second part of the paper, they study the Gibbsian character on R^{Z^d} of the law at time t of the infinite-dimensional diffusion X(t), when the initial law is Gibbsian. <br><br> AMS Classifications: 60G15 / 60G60 / 60H10 / 60J60

We study the (strong-)Gibbsian character on R Z d of the law at time t of an infinitedimensional gradient Brownian diffusion / when the initial distribution is Gibbsian.

We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter.

Present day water spray based dust removal technologies do not effectively remove respirable submicron coal and silica dust particles in the underground coal mines causing Coal worker’s pneumoconiosis (CWP). The objective of this research was to study the electrostatic charges present in the airborne coal dust in order to develop efficient water spraying based dust removal technology where water drops charged using ionic compounds and surfactants would be used to capture the oppositely charged coal particles. In an experimental scrubbing column, coal particles dispersed in an air stream by a Fluidized Bed Aerosol Generator were captured by water drops sprayed by an atomizer. Characterization studies performed using an Aerodynamic Particle Sizer and Aerosol Electrometer showed that airborne coal particles have a significant amount of positive charge with an average of 140 elementary units of charge. The capture efficiencies of the water drops evaluated were found to be higher than those predicted by previously determined mathematical models. It was predicted that apart from the effects of Brownian diffusion, interception and impaction, the effect of Coulombic attraction was present and the charge of the water drops was predicted to be between - 2 x 10-6 C and -2 x 10-4 C.

Après le génome, le nouveau défi est celui du protéome. Nous avons progressé vers la mise au point de la séparation électrophorétique des protéines membranaires dans un milieu qui leur conviendrait, type bicouche lipidique supportée. La grandeur principale, mesurée par FRAPP, a été le coefficient de diffusion de lipides ainsi que des protéines. L'étude du comportement de la bicouche supportée a permis de mettre en évidence, pour certains supports et dans certaines conditions de température, la formation d'une phase ondulée (ou ripple) malgré la proximité du support. La diminution de la portée des interactions coulombiennes par adjonction de sel se traduit par une augmentation de plusieurs ordres de grandeur du coefficient de diffusion, approchant au final le comportement d'une bicouche libre, tout en conservant les étapes caractéristiques de la transition gel/fluide. L'ordre de grandeur de ces énergies d'interactions a été estimé à partir des courbes D= f(T) et validé par une étude préliminaire originale de DSC sur des bicouches lipidiques supportées. L'&#945;-Hémolysine s'insère spontanément sous forme d'un pore heptamérique dans nos bicouches supportées et diffuse librement. En l'incubant en phase mixte (zones gel+ zones fluide), nous observons la formation de complexes de protéines. La dépendance du coefficient de diffusion avec la taille de l'objet est en 1/R2, R étant le rayon équivalent de la partie insérée de l'objet. L'application d'un champ électrique montre un transport électrophorétique dont la direction et l'importance sont modulées par la charge de l'objet. La mobilité électrophorétique varie également en 1/R2. / After the genome, the new challenge is the proteome. We have progressed toward electrophoretic separation of membrane proteins in a medium that they love, a supported lipid bilayer. The main parameter, measured by FRAPP, was the diffusion coefficient of different objects (lipids, proteins). Studying bilayer behaviour has showed that, on particular supports and in a given temperature range, ripple phase can exist, despite the proximity of the support. Adding salt decreases coulombic interactions which turns to increase the diffusion coefficient over several orders of magnitude, reaching the value for a free-standing bilayer in the fluid phase, meanwhile the main characteristic steps of the global gel/fluid transition are still observed. Estimation of the value of the interaction energy has been made and compared to results of a preliminary DSC study. &#945;-Hémolysin self-inserts spontaneously as an heptameric pore in supported bilayers and diffuses freely. Incubating in a gel/fluid mixture leads to protein complex formation. Diffusion varies with size as 1/R2, R being the equivalent radius of the inserted part of the object. Applying an electric field results in an electrophoretic motion where direction and magnitude are modulated by the charge of the object. Electrophoretic mobility varies also as 1/R2. Size dependence, magnitude of mobilities and a simple building protocol allow to hope carrying out soon a real electrophoretic separation of a protein mixture.

[pt] Deposição de parafinas é um dos mais críticos problemas operacionais no transporte de óleo cru, nos dutos que operam em ambientes frios. Portanto, uma predição acurada da deposição de parafinas é crucial para o projeto eficiente de linhas submarinas. Infelizmente, a deposição de parafinas é um processo complexo e os mecanismos de deposição ainda não são bem compreendidos. Visando identificar a importância relativa dos diferentes mecanismos de deposição, dois deles foram investigados: Difusão Molecular e Browniana. Para determinar a quantidade de depósito, as equações de conservação de massa, quantidade de movimento linear, energia, concentração da mistura e concentração da parafina fora da solução foram resolvidas numericamente pelo método de volumes finitos. Um sistema de coordenadas móveis não ortogonais que se adapta a interface do depósito da parafina foi empregado. Apesar da obtenção de uma concordância razoável do perfil de depósito, obtido com os mecanismos selecionados no regime laminar, com resultados disponíveis na literatura, uma discrepância significativa foi observada durante o transiente. O emprego do mecanismo de difusão browniana levou a uma pequena melhora na predição da solução nas regiões sub- resfriadas. A influência do regime turbulento como o mecanismo de difusão molecular também foi investigado, empregando o modelo de turbulência para baixo Reynolds K- (Taxa de dissipação viscosa da energia cinética turbulenta).Os resultados obtidos apresentaram coerência física, com uma taxa menor de aumento do depósito com o tempo, pois a região próxima à interface com temperatura abaixo da temperatura de aparecimento de cristais é menor no regime turbulento. / [en] Wax deposition is one of the major critical operational problems in crude oil pipelines operating in cold environments. Therefore, accurate prediction of the wax deposition is crucial for the efficient design of subsea lines. Unfortunately, wax deposition is a complex process for which the mechanisms are still not fully understood. Aiming at the identification of the relative importance of the different deposition mechanisms, two of them were investigated: Molecular and Brownian Diffusion. To determine the amount of deposit, the conservation equations of mass, momentum, energy, concentration of the mixture and wax concentration outside the solution were numerically solved with the finite volume method. A non-orthogonal moving coordinate system that adapts to the wax interface deposit geometry was employed. Although for the laminar regime, the deposition profile predicted with the selected deposition mechanisms presented a reasonable agreement with available literature results for the steady state regime, a significant discrepancy was observed during the transient. The employment of the Brownian diffusion mechanism led to only a small improvement in the transient solution prediction in sub-cooled regions. The influence of the turbulent regime with the Molecular diffusion mechanism was also investigated by employing the Low Reynolds ê&#8722;turbulence model. The results obtained were physically coherent, presenting a smaller deposit thickness, since the region with temperature below the wax appearance temperature is smaller in the turbulent regime.

Quantifying the velocity field near the wall in microfluidic devices is important because surface effects become significant at micro- to nanometer scales. Recent studies have suggested that the "no-slip" boundary condition breaks down in microscale flows of Newtonian liquids, where the amount of slip is usually extrapolated from velocity components measured far from the wall. This doctoral thesis presents a new technique, multilayer nano-particle image velocimetry (MnPIV), for measuring the tangential velocity components at different distances from and within about 500 nm of the wall and its application to measuring slip. The feasibility of MnPIV was demonstrated using synthetic images of plane Couette flow incorporating Brownian diffusion and imaging noise. The errors in MnPIV data were then quantified with Brownian dynamics simulations. Calibration experiments were used to correlate the image intensity of the tracer to its distance from the wall z. Multilayer nPIV was then used to determine the z-positions and distribution of the particles for z < 500 nm in experimental studies of microscale Poiseuille flow. The tracers were divided into three distinct layers based on their image intensities, and the average velocity of each layer was placed at the average z-position sampled by the particles in that layer. The resultant velocity gradients were within 6% on average of analytical predictions for 2D Poiseuille flow. Finally, the results of MnPIV studies of aqueous solutions flowing through microchannels with hydrophilic and hydrophobically-coated fused silica surfaces suggest that if the slip lengths are nonzero for both of these surfaces, they are less than the uncertainty in these results, or 27 nm and 31 nm for the hydrophilic and hydrophobic channels, respectively.

Cette étude vise à une meilleure compréhension des phénomènes rencontrés en filtration des aérosols nanométriques, c’est-à-dire inférieurs à 100 nm, neutres et/ou chargés. Pour ce faire, trois différents types de média ont été étudiés : des grilles, en acier et matières synthétiques, des filtres non tissés, en fibres de verre ou polymériques, et des lits granulaires, constitués de billes d’acier ou de zéolithe. Il ressort des résultats expérimentaux obtenus que quel que soit le média testé, l’efficacité de collecte des particules augmente lorsque le diamètre de l’aérosol diminue, et ce jusque 4 nm. Ceci entre en contradiction avec l’approche théorique dite du rebond thermique, développée par Wang et Kasper en 1991, selon laquelle l’efficacité de collecte serait susceptible de diminuer en-dessous de 10 nm. La vérification des calculs de Wang et Kasper permet d’expliquer cette incohérence, et montre, à partir de valeurs plus réalistes de l’énergie d’adhésion particule-fibre, que si le rebond thermique existe, celui-ci ne pourra se manifester qu’en-dessous de 1 nm, au mieux. Ainsi, les perméances expérimentales des différents médias testés ont pu être modélisées en tenant compte des mécanismes de collecte par diffusion et/ou par effets électrostatiques. Une étude originale sur les performances, dans le domaine nanométrique, de filtres en fibres de verre intentionnellement percés complète ce travail. Pour un même média fibreux, la perméance augmente avec le diamètre de perforation réalisée. Par ailleurs, pour une taille de perforation donnée, la perméance devient indépendante du diamètre des particules en-dessous d’une taille limite, fonction de la dimension de la perforation. Il a enfin été mis en évidence que la baisse d’efficacité est d’autant plus importante que la résistance à l’écoulement de l’air du filtre est importante. Un modèle semi-empirique, fondé sur la différenciation du flux d’aérosol traversant la fuite du flux traversant le matelas fibreux résiduel du filtre, permet de bien représenter ces états de fait / This study aims to better understand the mechanisms encountered in nanoparticles aerosol filtration, the particles being charged or not. Three different types of media were studied: stainless steel or synthetics wire screens, unwoven filters in glass or polymer fibres, and at last, granular beds made from steel or zeolite balls. Experimental results show that, whatever the media, collection efficiency increases as the particle diameter decreases down to 4 nm. This point conflicts with the so-called thermal rebound effect developed by Wang and Kasper in 1991, according to which collection efficiency could decrease below 10 nm. The checking of Wang and Kasper’s calculations enables to explain this discrepancy and shows from more probable particle-to-fibre adhesion energy values that if thermal rebound phenomenon exists, it would only be measurable below 1 nm. Then, experimental points can be modelled from both diffusion and electrostatic forces collection mechanisms. An investigation on the filtration behaviour of fibreglass filters in the nanometric domain when intentionally-pierced with calibrated needles completes the above-mentioned works. For a same media, penetration increases as the leak diameter does. On the other hand, for a given hole size, penetration becomes independent of the particle diameter below a critical scale, which is a function of the leak diameter. It was lastly shown that the efficiency of a pierced media decreases all the more that its air flow resistance is higher. A semi-empirical model based on the differentiation between the aerosol flow across the leak and the one through the residual fibrous bed of the filter enables to well represent these points