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Vesicles are simple structures, but display complex, non-linear dynamics in fluid flow. I investigate the deformation of nanometer-sized vesicles, both fully-inflated and those with excess area, as they travel in tightly confined capillaries. By varying both channel size and flow strength, I simulate vesicles as they transition from steady-state to unstable shapes, and then rupture in strong flow fields. By employing a molecular dynamics model of the vesicle, fluid, and capillary system one is able to rupture the lipid bilayer of these vesicles. This is unique in that most other numerical methods for modelling vesicles are unable to show rupture. The rupture of fully-inflated vesicles is applicable to drug delivery in which the release of the encapsulated medicine needs to be controlled. The deformation and rupture of vesicles with excess area could be applicable to red blood cells which have similar rheological properties.

Vesicles are simple structures, but display complex, non-linear dynamics in fluid flow. I investigate the deformation of nanometer-sized vesicles, both fully-inflated and those with excess area, as they travel in tightly confined capillaries. By varying both channel size and flow strength, I simulate vesicles as they transition from steady-state to unstable shapes, and then rupture in strong flow fields. By employing a molecular dynamics model of the vesicle, fluid, and capillary system one is able to rupture the lipid bilayer of these vesicles. This is unique in that most other numerical methods for modelling vesicles are unable to show rupture. The rupture of fully-inflated vesicles is applicable to drug delivery in which the release of the encapsulated medicine needs to be controlled. The deformation and rupture of vesicles with excess area could be applicable to red blood cells which have similar rheological properties.

The lymphatic system is an extensive vascular network responsible for the transport of fluid, immune cells, proteins and lipids. It is composed of thin-walled vessels, valves, nodes and ducts, which work together to collect fluid, approximately 4 L/day, from the interstitium transporting it back to the systemic network via the great veins. The failure to transport lymph fluid results in a number of disorders and diseases. Lymphedema, for example, is a pathology characterized by the retention of fluid in limbs creating extreme discomfort, reduced mobility and impaired immunity. In general, there are two types of edema: primary edema, being those cases that are inherited (i.e. genetic predisposition), and secondary edema, which develop post-trauma or injury of the lymphatic vessels. With the onset of breast cancer and radiation therapies, the prevalence of secondary edema is on the rise. Clinical studies have shown that up to 80% of women who undergo nodal-dissection surgery develop lymphedema in their arms within 3-5 years of the surgery. Unfortunately, there is no cure or remedy for lymphedema stemming from our lack of understanding of the lymphatic system. The goal of this study was to evaluate lymph flow both experimentally and analytically to better understand the mechanisms regulating lymph transport. In particular we investigated the effects of pressure, volume loads and valve resistance on lymphatic function in the rat mesentery. Our experimental results were then used to develop computational and constitutive models to emulate the dynamic behavior of lymph transport. Collectively, the data illustrate the mechanics of lymphatic contractility and lymph flow. In particular, lymph flow and pumping significantly increased post edemagenic stress in the rat model. Furthermore, lymphangions exhibited highly nonlinear pressure-diameter responses at low pressures between 3-5 cmH2O. These experimental results strongly suggest the regulation of lymph flow via changes in pressure, shear stress and vessel diameter. Furthermore, the computational and constitutive models from this study provide great insight into lymphatic function characterizing the mechanical properties of a single pumping unit (i.e. lymphangion). These models will serve as valuable tools to further lymphatic research.

This thesis concerns the stability of plane Couette flow and pipe Poiseuille flow in three space dimensions. The mathematical model for both flows is the incompressible Navier--Stokes equations. Both analytical and numerical techniques are used. We present new results for the resolvent corresponding to both flows. For plane Couette flow, analytical bounds on the resolvent have previously been derived in parts of the unstable half-plane. In the remaining part, only bounds based on numerical computations in an infinite parameter domain are available. Due to the need for truncation of this infinite parameter domain, these results are mathematically insufficient. We obtain a new analytical bound on the resolvent at s=0 in all but a compact subset of the parameter domain. This is done by deriving approximate solutions of the Orr--Sommerfeld equation and bounding the errors made by the approximations. In the remaining compact set, we use standard numerical techniques to obtain a bound. Hence, this part of the proof is not rigorous in the mathematical sense. In the thesis, we present a way of making also the numerical part of the proof rigorous. By using analytical techniques, we reduce the remaining compact subset of the parameter domain to a finite set of parameter values. In this set, we need to compute bounds on the solution of a boundary value problem. By using a validated numerical method, such bounds can be obtained. In the thesis, we investigate a validated numerical method for enclosing the solutions of boundary value problems. For pipe Poiseuille flow, only numerical bounds on the resolvent have previously been derived. We present analytical bounds in parts of the unstable half-plane. Also, we derive a bound on the resolvent for certain perturbations. Especially, the bound is valid for the perturbation which numerical computations indicate to be the perturbation which exhibits largest transient growth. The bound is valid in the entire unstable half-plane. We also investigate the stability of pipe Poiseuille flow by direct numerical simulations. Especially, we consider a disturbance which experiments have shown is efficient in triggering turbulence. The disturbance is in the form of blowing and suction in two small holes. Our results show the formation of hairpin vortices shortly after the disturbance. Initially, the hairpins form a localized packet of hairpins as they are advected downstream. After approximately $10$ pipe diameters from the disturbance origin, the flow becomes severely disordered. Our results show good agreement with the experimental results. In order to perform direct numerical simulations of disturbances which are highly localized in space, parallel computers must be used. Also, direct numerical simulations require the use of numerical methods of high order of accuracy. Many such methods have a global data dependency, making parallelization difficult. In this thesis, we also present the process of parallelizing a code for direct numerical simulations of pipe Poiseuille flow for a distributed memory computer. / QC 20100825

Cette thèse porte sur les effets combinés de l’excentricité et du débit axial sur les propriétés de stabilité linéaire de l’écoulement de Couette circulaire avec cylindre extérieur fixe. Cet écoulement intervient, entre autres, lors du forage de puits de pétrole. Une méthode pseudospectrale est mise en oeuvre pour calculer l’écoulement de base, stationnaire et invariant suivant la direction axiale, ainsi que les modes normaux d’instabilité. L’écoulement est régi par quatre paramètres adimensionnels : rapport de rayons _ et excentricité e pour la géométrie, nombres de Reynolds azimuthal et axial, Re et Rez, pour la dynamique. La première partie de l’étude est consacrée aux propriétés de stabilité temporelle. Il apparaît que l’excentricité repousse le seuil d’instabilité convective vers de plus fortes valeurs de Re. L’effet de l’advection axiale sur le seuil est principalement stabilisant également. L’excentricité a pour conséquence de déformer la structure des modes par rapport au cas concentrique. Le mode au plus fort taux de croissance temporelle est ainsi constitué de tourbillons de Taylor « pseudo-toroïdaux » lorsque le débit axial est nul, et de structures « pseudo-hélicoïdales » d’ordre azimuthal croissant lorsque Rez augmente. Les résultats sont qualitativement similaires lorsque l’on change le rapport de rayons. Les prédictions théoriques sont en bon accord avec les quelques résultats expérimentaux disponibles. Dans une seconde partie, l’instabilité absolue est étudiée par application d’un critère de point selle à la relation de dispersion. Le débit axial a pour effet d’inhiber fortement l’instabilité absolue, d’origine centrifuge, et la valeur de Re au seuil est typiquement supérieure à celle de Rez d’un ordre de grandeur. L’effet de l’excentricité est plus complexe : légère stabilisation aux faibles valeurs de e, puis déstabilisation marquée aux excentricités modérées lorsque Rez est suffisament grand, et enfin stabilisation lorsque e croît davantage. Contrairement au cas de l’instabilité convective, le mode dominant l’instabilité absolue correspond à l’écoulement tourbillonnaire « pseudo-toroïdal » pour toute la gamme de paramètres considérée. / This work is concerned with the combined effects of eccentricity and pressure-driven axial flow on the linear stability properties of circular Couette flow with a fixed outer cylinder. An example of this flow can be found in oil-well drilling operations. A pseudospectral method is implemented to compute the basic flow, steady and homogeneous in the axial direction, as well as the normal modes of instability. There are four non-dimensional parameters: the radius ratio _ and the eccentricity e for the geometry, the azimuthal and axial Reynolds numbers, Re and Rez, for the dynamics. The first part of the study is devoted to the temporal stability properties. It is found that eccentricity pushes the convective instability threshold towards higher values of Re. The effect of axial advection on the threshold also tends to be stabilising. Eccentricity deforms the modes structure compared to the concentric case. As a result, the mode with the largest temporal growth rate takes the form of ‘pseudo-toroidal’ Taylor vortices in the absence of axial flow, and ‘pseudo-helical’ structures with increasing azimuthal order as Rez becomes larger. Results are qualitatively similar for different radius ratios. Agreement with the few available experimental data is good. In a second part, absolute instability is studied by applying the pinch-point criterion to the dispersion relation. Axial flow is found to strongly inhibit absolute instability, the mechanism of which being centrifugal, and the value of Re at the threshold is typically one order of magnitude larger than that of Rez. The effect of eccentricity is more complex: weak stabilisation for low values of e, marked destabilisation for moderate eccentricities and high enough Rez, and finally stabilisation as e is further increased. Unlike temporal instability, the dominant absolutely unstable mode is the ‘pseudo-toroidal’ Taylor vortex flow over the whole range of parameter space considered.

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Molecular dynamics (MD) and computational fluid dynamics (CFD) allowresearchers to study fluid dynamics from two very different standpoints. From a microscopic standpoint, molecular dynamics uses Newton's second law of motion to simulate the interatomic behavior of individual atoms, using statistical mechanics as a tool for analysis. In contrast, CFD describes the motion of a fluid from a macroscopic level using the transport of mass, momentum, and energy of a system as a model. This thesis investigates both MD and CFD as a viable means of studying viscous flow on a nanometer scale. Specifically, we investigate a pressure-driven Poiseuille flow. The results of the MD simulations are processed using software we created to measure velocity, density, and pressure. The CFD simulations are run on numerical software that implements the MacCormack method for the Navier-Stokes equations. Additionally, the CFD simulations incorporate a local definition of viscosity, which is usually uncharacteristic of this simulation method. Based on the results of the simulations, we point out similarities and differences in the obtained steady-state solutions. / Master of Science

This thesis focuses on the lattice-Boltzmann method (LBM) and its ability to simulate immiscible two-phase flow. We introduce the main lattice-Boltzmann-based approaches for analyzing two-phase flow: the color-fluid model by Gunstensen, the interparticle-potential model by Shan and Chen, the free-energy model by Swift and Orlandini, and the mean-field model by He. The first objective is to assess the ability of these methods to maintain continuity at the interface of two fluids, especially when the two fluids have different viscosities or densities. Continuity issues have been mentioned in the literature but have never been quantified. This study presents a critical comparison of the four lattice-Boltzmann-based approaches for analyzing two-phase flow by analyzing the results of the two-phase Poiseuille flow for different viscosity ratios and density ratios. The second objective is to present the capability of the most recent version of the color-fluid model for simulating 3D flows. This model allows direct control over the surface tension at the interface. We demonstrate the ability of this model to simulate surface tension effects at the interface (Laplace bubble test), stratified two-phase flows Poiseuille two-phase flow), and bubble dynamics (the free rise of a bubble in a quiescent viscous fluid).