Cavitation is the spontaneous vaporisation of a liquid to its gaseous state due to the local absolute pressure falling to the liquid's vapour pressure (Douglas, Gasiorek et al. 1995). Cavitation is present in a wide range of mechanical systems ranging from ship screws to journal bearing. Generally, cavitation is unavoidable and may cause considerable damage and efficiency losses to these systems. This thesis considers hydraulic systems specifically, and uses a modified Greens equation to develop a boundary integral method to simulate the effect that suspended solid bodies have on a single cavitation bubble. Because of the limitations of accurately modelling cavitation bubbles beyond touchdown, results are only presented for cases up to touchdown. The aim of the model is to draw insight into the reasons there is a measurable change in cavitation erosion rate with increasing oil-in-water emulsion percentage. This principle was extended to include the effect that ingested particulates may have on cavitation in hydraulic machinery. Two particular situations are modelled; the first consists of stationary rigid particles in varying proximity to a cavitation bubble near a rigid boundary. The second case is similar; however the suspended particle is allowed to move under the influence of the pressure differential caused by the expanding/contracting cavitation bubble. Numerous characteristics of the domain are considered, including domain pressures and fluid field motion, and individual boundary surface characteristics. The conclusion of the thesis is that solid bodies, either stationary or moving, have little effect on the cavity from an energy perspective. Regardless of size or density, all energy transferred from the cavity to the solid body is returned indicating that there is no net change. As this energy is ultimately responsible for the peak pressure experienced by the domain (and hence responsible for eroding the rigid boundary) as the cavity rebounds, it then serves that a cavity with a solid body will rebound at the same pressure as a cavity without a suspended body present. If this is coupled with the observation that the cavity centroid at touchdown is largely unaffected by the presence of a suspension, then it would appear that the bubble near a solid would rebound at a very similar position as a cavity without a solid. Consequently, the damage potential of a cavity is unaffected by a suspension. However, there is one point of contention as the profile of the re-entrant jet of the cavity is altered by the presence of a suspension. As energy is radiated away from the cavity during penetration, it is possible that the shape of the jet may alter the rate that energy is radiated away during penetration. However, this requires further research to be definitive.

Les vésicules sont utilisées d'une manière extensive comme modèle pour comprendre les dynamiques et les déformations des globules rouges au niveau individuel, mais aussi concernant les phénomènes collectives et la rhéologie. La membrane de la vésicule résiste à la flexion mais pas au cisaillement, contrairement aux globules rouges, néanmoins elles partagent plusieurs propriétés dynamiques avec les globules rouges, comme le tank-treading (mouvement en chenille de char) et le tumbling (mouvement de bascule) sous écoulement de cisaillement, ou les formes parachutes et slippers (pantoufles) sous un écoulement de Poiseuille. Les globules rouges sont connus pour former des trains de cellules (clusters) dans la microcirculation attribués à la nature attractive des interactions hydrodynamiques. Nous avons étudié numériquement plusieurs types de problème comme:(i) les dynamiques de cellules isolées, (ii) le couplage hydrodynamique entre globules rouges (en utilisant les vésicules comme modèle) soumis à un écoulement de Poiseuille sous différent confinements; (iii) l'agrégation des globules rouges et la formation de rouleaux; et (iv) le rôle des macromolécules dans la formation de clusters sous écoulement. les résultats obtenus apportent un nouveau regard à la physique des objets déformables et sont transposables au cas de l'écoulement des globules rouges dans la microcirculation. / Vesicles are extensively used as a model for understanding dynamicsand deformation of red blood cells at the individual level but also regarding collective phenomena and rheology. Vesicles' membranes withstand to bending butdo not have a shear resistance, unlike red blood cells, but they still share several dynamical properties with red blood cells, like tank-treading and tumbling under linear shear flow, or parachute and slipper shapes under Poiseuille flow. The red blood cells are known to form train of cells in the microcirculation attributed to attractive hydrodynamic interactions. We investigate numerically several kind of problems such as: (i) the dynamics of isolated cells; (ii) the hydrodynamic coupling between the red blood cells (by using vesicles as a model) subject to a Poiseuille flow under different confinements; (iii) the aggregation of red blood cells and formation of rouleaux; and (iv) the contribution of macromolecules in the formation of clusters under flow condition. The obtained results give a new insight into thephysics of deformable objects under confinement that are transposable to the flow of red blood cells in the microcirculation.

De nombreux systèmes fluides dans les domaines de la biologie ou encore de la cosmétique sont limités par une interface dont les propriétés mécaniques régissent la stabilité. En particulier, les objets tels que des gouttes, vésicules ou polymersomes se déforment dans un écoulement simple et mènent à une grande richesse de dynamiques spatio-temporelles contrôlées par la nature des matériaux qui composent l'interface. Les travaux présentés concernent l'étude numérique de la déformation de ces objets dans un écoulement de Stokes, en particulier dans des situations où les viscosités de l'interface jouent un rôle important. Un code de calcul couplant intégrales de frontières et éléments finis a été utilisé afin de décrire la physique interfaciale et étudier leur comportement une fois plongés dans un écoulement. Ces travaux ont permis d'étudier l'influence des viscosités interfaciales sur la dynamique d'une goutte dans un écoulement extensionnel plan, leur influence sur sa dynamique de déformation et sur les conditions de rupture de celle-ci. Les études réalisées sur une vésicule fortement dégonflée et plongée dans un écoulement cisaillé ont caractérisé la bifurcation entre les deux familles de forme existantes dans ces conditions. Ces formes ayant une influence sur la dynamique de la vésicule dans l'écoulement, celle-ci a été étudiée dans le cadre d'un écoulement infini puis proche d'une paroi parallèle à l'écoulement. Enfin, de premiers résultats sur la dynamique d'un polymersome dans un écoulement cisaillé permettent de construire un diagramme de phase illustrant les différents comportement de cet objet en fonction de la viscosité de la membrane et du taux de cisaillement / There are many fluid systems in the biology, food industry, pharmacology or cosmestics fields that are bound by an interface which mechanical properties rule the system stability. Objects like droplets, vesicles or polymersomes change their shape in a simple flow which lead to a wealth of space and time dynamics. These properties are controlled by the nature of the interface material. The aim of this work is the numerical study of the deformation of droplets, vesicles and polymersomes in a Stokes flow, especially when the interfacial viscosities play an important role. A numerical computation code coupling boundary integrals and finite elements was used to describe the interfacial physics of these objects and study their behaviour when immerged in a flow. Multiple resolution strategies where developped to this end in order to optimize the numerical computation in the cas of an interface with viscosities.Using this work, the influence of interfacial viscosities on the dynamics of a droplet in an extensional flow is studied : in particular, their influence on the stretching dynamics of a droplet and its break up conditions was characterized. The study of a vesicle, droplet bounded by a lipid bilayer, strongly deflated and immerged in a shear flow detailed the bifurcation between two shape types existing for this system. These shapes have an influence on the vesicle dynamics under flow, which is studied for an unbounded flow and a near-wall flow. Finally, we show first results about the dynamics of a polymersome in a shear flow. We used them to build a phase diagram for the behaviour of this object depending on the membrane viscosity and the shear rate

In this thesis, simulations are performed to study the motion ofindividual cells in flow, focusing on the hydrodynamics of actively swimming cells likethe self-propelling microorganisms, and of passively advected objects like the red bloodcells. In particular, we develop numerical tools to address the locomotion ofmicroswimmers in viscoelastic fluids and complex geometries, as well as the motion ofdeformable capsules in micro-fluidic flows. For the active movement, the squirmer is used as our model microswimmer. The finiteelement method is employed to study the influence of the viscoelasticity of fluid on theperformance of locomotion. A boundary element method is implemented to study swimmingcells inside a tube. For the passive counterpart, the deformable capsule is chosen as the modelcell. An accelerated boundary integral method code is developed to solve thefluid-structure interaction, and a global spectral method is incorporated to handle theevolving cell surface and its corresponding membrane dynamics. We study the locomotion of a neutral squirmer with anemphasis on the change of swimming kinematics, energetics, and flowdisturbance from Newtonian to viscoelastic fluid. We also examine the dynamics of differentswimming gaits resulting in different patterns of polymer deformation, as well as theirinfluence on the swimming performance. We correlate the change of swimming speed withthe extensional viscosity and that of power consumption with the phase delay of viscoelasticfluids. Moreover, we utilise the boundary element method to simulate the swimming cells in astraight and torus-like bent tube, where the tube radius is a few times the cell radius. Weinvestigate the effect of tube confinement to the swimming speed and power consumption. Weanalyse the motions of squirmers with different gaits, which significantly affect thestability of the motion. Helical trajectories are produced for a neutralsquirmer swimming, in qualitative agreement with experimental observations, which can beexplained by hydrodynamic interactions alone. We perform simulations of a deformable capsule in micro-fluidic flows. We look atthe trajectory and deformation of a capsule through a channel/duct with a corner. Thevelocity of capsule displays an overshoot as passing around the corner, indicating apparentviscoelasticity induced by the interaction between the deformable membrane and viscousflow. A curved corner is found to deform the capsule less than the straight one. In addition, we propose a new cell sorting device based on the deformability of cells. Weintroduce carefully-designed geometric features into the flow to excite thehydrodynamic interactions between the cell and device. This interaction varies andclosely depends on the cell deformability, the resultant difference scatters the cellsonto different trajectories. Our high-fidelity computations show that the new strategy achievesa clear and robust separation of cells. We finally investigate the motion of capsule in awall-bounded oscillating shear flow, to understand the effect of physiological pulsation to thedeformation and lateral migration of cells. We observe the lateral migration velocity of a cellvaries non-monotonically with its deformability. / <p>QC 20140313</p>

Three-dimensional mathematical problems of the interaction between thermoelastic and scalar oscillation fields are considered in a general anisotropic case. An elastic structure is assumed to be a bounded homogeneous anisortopic body occupying domain $\Omega^+\sub\R^3$ , where the thermoelastic field is defined, while in the physically anisotropic unbounded exterior domain $\Omega^-=\R^3\\ \overline{\Omega^+}$ there is defined the scalar field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface $\delta\Omega^{+-}$. Uniqueness and existence theorems, for the non-resonance case, are proved by the reduction of the original interface problems to equivalent systems of boundary pseudodifferential equations ($\Psi DEs$) . The invertibility of the corresponding matrix pseudodifferential operators ($\Psi DO$) in appropriate functional spaces is shown on the basis of generalized Sommerfeld-Kupradze type thermoradiation conditions for anisotropic bodies. In the resonance case, the co-kernels of the $\Psi DOs$ are analysed and the efficent conditions of solvability of the transmission problems are established.

The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.