Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Flows of fluids and solid particles through microchannels have a very wide range of applications in biological and medical science and engineering. Understanding the mechanism of microflows will help to improve the development of the devices and systems in those applications. The aim of this study is to develop a sophisticated simulation and analysis technique for the study of fluid-particle flow through microchannels. This work involves construction of mathematical models, development of analytical methods and numerical algorithms, and numerical investigation and analysis. / The study consists of three parts. The first part of the research focuses on the transient flow of an incompressible Newtonian fluid through a micro-annual with a slip boundary. The flow of the fluid is governed by the continuity equation and the Navier-Stokes equations, and is driven by the pressure field with a timevarying pressure gradient. By using the Fourier series expansion in time and Bessel functions in space, an exact solution is derived for the velocity field. The velocity solution is then used to obtain the exact solutions for the flow rate and the stress field. Based on the exact solutions, the influence of the slip parameter on the flow behaviour is then investigated. / The second part of the research focuses on the particle-fluid flow in microchannels. The transport of fluid in the vessel is governed by the continuity equation and the transient Navier-Stokes equations, while the motion of the particles is governed by Newton’s laws. The particle-wall and particle-particle interactions are modelled by the interacting forces, while the particle-fluid interaction is described by the fluid drag force. A numerical scheme based on the finite element method and the Arbitary Lagrangian-Eulerian method is developed to simulate the motion of the particles and the fluid flow in the vessels. The influence of boundary slip on the velocity field in the fluid is also investigated numerically. / Based on the work in the second part, the third part of the research focuses onthe control of the movement of particles in the fluid by applying an external magneticfield to the system. Maxwell’s equations are used to model the magnetic fieldgenerated by the external magnetic source, and a finite element based numericalscheme is developed to solve the underlying boundary value problem for the magneticflux density generated. From the computed flux density and magnetic vectorpotential, the magnetic forces acting on the particles are determined. These magneticforces together with the drag force and the particle-particle interacting forcesdominate the behaviour of the particle motion. A numerical scheme, similar to thatfor the second part of the research, is then developed to study the fluid-particle flowin microchannels under magnetic forces, followed by a numerical investigation onthe influence of the magnetic forces on the particle flow behaviour.

Nous présentons dans cette thèse une adaptation de la technique de vélocimétrie par marquage moléculaire (MTV) aux micro-écoulements gazeux. Les effets de luminescence de l’acétone gazeuse excitée par un rayonnement UV, mis en jeu dans la MTV, ont été analysés en vue d’une application en vélocimétrie à basse pression. La phosphorescence de l’acétone diminue fortement avec la pression, pour devenir non détectable à des pressions de l’ordre du kPa. En revanche, la fluorescence reste détectable à des pressions de l’ordre de la dizaine de Pa. L’analyse des déplacements de molécules luminescentes au sein de l’écoulement porteur a montré que les effets de la diffusion moléculaire sont importants et augmentent avec la raréfaction du gaz. Une méthode de reconstruction, basée sur l’équation d’advection diffusion, a été développée. Elle permet d’extraire le profil de vitesse à partir de l’analyse du déplacement et de la déformation de la zone marquée, en prenant en compte la diffusion des molécules luminescentes. L’analyse d’un écoulement de Poiseuille dans un canal de section rectangulaire et de dimensions millimétriques, sous des pressions de l’ordre de 100 kPa, a montré la capacité de la MTV à extraire avec précision la vitesse locale en écoulements confinés, lorsque la méthode de reconstruction est appliquée. Une feuille de route pour l’analyse future par MTV des écoulements raréfiés, notamment dans le régime glissant, est finalement proposée. / In the present thesis we present an adaptation of Molecular Tagging Velocimetry (MTV) to gas microflows. The photo-luminescence effects of gaseous acetone excited by UV light, implemented in MTV, have been analyzed in various pressure conditions. The acetone phosphorescence shows a drastic decrease with pressure and becomes non measurable for pressures lower than 1 kPa. On the other hand, fluorescence shows a slower decrease and remains clearly detectible at pressures as low as 10 Pa. The motion of tracer molecules within the carrier flow has been studied. The analysis of the displacement of the tagged molecules has shown the strong influence of molecular diffusion, this influence being increased with the gas rarefaction. A reconstruction method based on the advection-diffusion equation has been developed. It allows to extract the velocity profile from the analysis of the displacement and deformation of the tagged region, taking into account the diffusion of tracer molecules. This reconstruction method has been successfully implemented to analyse a Poiseuille flow in a rectangular millimetric channel, under atmospheric pressure conditions, and the capability of MTV to accurately extract the local velocity in confined gas flows has been demonstrated. Finally, some short term perspectives have been proposed with the aim to help achieving rarefied flows analysis by MTV.

Cette thèse présente une étude numérique et expérimentale d’écoulements gazeux raréfiés confinés, induits par gradients thermiques. L’écoulement d’un gaz raréfié peut en effet être généré en appliquant uniquement un gradient tangentiel de température le long d'une paroi. Ainsi, sans gradient initial de pression, le gaz peut se déplacer de la région froide vers la région chaude. Ce phénomène, appelé transpiration thermique, est à la base du fonctionnement des pompes dites de Knudsen, capables de générer un pompage du gaz sans utiliser de pièces mécaniques mobiles. L’apport principal de ce travail est relatif à l’investigation numérique de l’écoulement de transpiration thermique dans trois nouvelles configurations de pompe Knudsen. Dans ce but, une méthode numérique de simulation d’écoulements dans le régime de glissement a été développée ; elle implémente des conditions aux limites de saut de vitesse et de température spécifiques dans un code CFD commercial. Parallèlement, un code DSMC a été mis en œuvre pour étudier des écoulements plus fortement raréfiés dans les géométries les plus complexes. Des écoulements de transpiration thermique générés dans des canaux courbés, dans des canaux convergents/divergents ou entre deux surfaces spécialement micro-texturées ont ainsi été étudiés. D’autre part, l’analyse expérimentale d’un écoulement de transpiration thermique dans un microtube de section circulaire a été réalisée sur un nouveau banc d’essais conçu pour être adaptable à diverses géométries de canaux ou de pompes Knudsen. / This thesis presents a numerical and experimental analysis of internal rarefied gas flows induced by temperature fields. In rarefied gases, a flow can be generated by solely applying a tangential temperature gradient along a wall: without any initial pressure gradient, the gas macroscopically moves from the cold toward the hot region. This phenomenon is the so-called thermal creep or thermal transpiration effect. It is the main operating principle of the Knudsen pump, which can generate gas pumping without the need of any moving parts. The main aspect of this work is centered on numerical investigations of thermal transpiration flows in three new possible configurations of Knudsen pumps. For that goal, a numerical model for slip flows has been developed in which the appropriate slip boundary conditions are implemented in a commercial CFD code and a DSMC code has been adapted for studying transition flows in complex geometries. The pumping effect of curved-channel Knudsen pumps, the thermal transpiration flows through tapered channels and between two ratchets surfaces at different uniform temperatures have been investigated. In addition, an experimental study of thermal transpiration flow through a single micro-tube has been carried out on a new experimental set-up designed to be adaptable for testing thermally driven flows through various kinds of microchannels or generated by autonomous Knudsen compressors

Ce mémoire traite de la mise au point et des applications d’un fluxmètre gazeux à pression constante, instrument de référence primaire pour la mesure de très faibles débits gazeux, couramment utilisé par les Laboratoires nationaux de métrologie. Il intervient dans la traçabilité des basses pressions absolues, via la méthode d’expansion continue, et celle des fuites d’hélium, liées aux applications dans le domaine du vide. De plus, nous avons montré que le fluxmètre à pression constante du Laboratoire commun de métrologie (LCM) permettait le raccordement des mesures de micro-débits, sous-domaine de la débitmétrie. Outre les points clés de la conception et la caractérisation métrologique, ce mémoire décrit l’étude de l’expansion continue ainsi que les travaux de comparaison du fluxmètre gazeux à pression constante avec les méthodes de référence employées au LCM, en particulier la méthode de gravimétrie dynamique. / This dissertation concerns the development and applications of a constant pressure gas flowmeter, the primary reference instrument used by National metrology laboratories to measure very low gas flows. It guarantees the traceability of low absolute pressures, via the continuous expansion method, and that of helium leaks, both related to applications in the field of vacuum. In addition, we have shown that the Laboratoire commun de métrologie (LCM) constant pressure flowmeter is well suited to micro-flow measurements, a sub-field of flow metering. Besides key points of the design and metrological characterization, this document describes the study of the continuous expansion method and work on comparisons of the constant pressure gas flowmeter with reference methods used at LCM, in particular the dynamic gravimetric method.

Ce travail de thèse porte sur le développement de la technique de Vélocimétrie par Marquage Moléculaire (Molecular Tagging Velocimetry - MTV) pour l’étude expérimentale des micro-écoulements gazeux internes. Les micro-écoulements gazeux sont des écoulements raréfiés, caractérisés par un nombre de Knudsen non négligeable. L’analyse de la littérature montre un besoin crucial de données expérimentales de grandeurs locales relatives aux micro-écoulements gazeux. Ces données permettraient une discussion pertinente de la précision et des limites d’applicabilité des différents modèles théoriques proposés dans la littérature pour l’étude du régime de glissement, régime raréfié le plus souvent rencontré en microfluidique gazeuse. Dans cette optique, un banc d’essais expérimental a été développé pour la mesure de champs de vitesses par MTV. La technique consiste à suivre des molécules traceuses d’acétone introduites dans le gaz en écoulement et qui deviennent phosphorescentes lorsqu’elles sont excitées par une source lumineuse UV. Les différents compromis pris en compte pour le développement de ce banc (choix du traceur et du matériau, conception du canal instrumenté,…), ainsi que les techniques d’acquisition et de traitement de signal sont détaillés dans le manuscrit. L’analyse expérimentale commence par une étude du signal de phosphorescence de l’acétone. Ensuite, la technique de vélocimétrie par marquage moléculaire est validée par la mesure de champs de vitesses dans des écoulements laminaires confinés en régime non raréfié. Les résultats obtenus sont comparés à des profils de vitesse théoriques d’un écoulement de Poiseuille à pression atmosphérique. Enfin, les premiers résultats obtenus à basse pression sont présentés et commentés. La détection du signal à un niveau de pression de 1kPa est encourageante et offre de nombreuses perspectives pour l’exploration d’écoulements en régime raréfié / This thesis focuses on the development of Molecular Tagging Velocimetry (MTV) technique for the experimental analysis of internal microflows of gases. Gaseous microflows are rarefied flows characterized by a non-negligible Knudsen number. A literature review highlights a crucial need of experimental data on velocity fields within gaseous microflows. These data are required for a relevant discussion on the validity and limits of applicability of the different boundary conditions proposed in the slip flow, which is a regime often encountered in gaseous microsystems. An experimental setup has been designed for analyzing by MTV the velocity distribution in microchannels. The technique consists in detecting the displacement of acetone molecules, introduced as tracers in a gas flow; these molecules exhibit phosphorescence once excited by a UV light source. The various compromises taken into account for the setup design (choice of tracer, laser, channel material and design, camera and intensifier…), as well as the acquisition and processing techniques are detailed in the manuscript. The experimental analysis starts with a study of the acetone phosphorescence signal. Then, the MTV technique is validated by velocity field measurements in internal laminar flows through a rectangular minichannel in non-rarefied regime. The obtained results are successfully compared to the theoretical velocity profile of a Poiseuille flow. Finally, preliminary results obtained at lower pressures are presented and commented. The signal detection at a pressure level as low as 1 kPa is encouraging and draws various perspectives for the exploration of rarefied regimes