<div>This thesis examines the problem of low Reynolds number viscous fluid–structure interactions (FSIs) at the microscale. A myriad of examples of such phenomena exist, both in nature (blood flow in arteries, air flow in lungs), as well as in the laboratory (microfluidics devices, soft robotics). For this thesis, we restrict to internal flows in conduits with deformable walls. Specifically, two types of conduits of different cross-sectional shapes are considered: microchannels and microtubes. Both of these geometries are slender and thin.</div><div>Different types of material behavior are considered, via constitutive laws, in the solid domain, namely linearly elastic, hyperelastic and viscoelastic; and in the fluid domain, namely Newtonian and power-law fluids with shear-dependent viscosity. Similarly, the geometry and dimensions of the structures allow us to use shell and plate theories in the solid domain, and the lubrication approximation of low Reynolds number flow in the fluid domain.</div><div>First, we study a rectangular microchannel with a deformable top wall of moderate thickness, conveying a power-law fluid at steady conditions. We obtain a nonlinear differential equation for pressure as a function of imposed steady flow rate, consisting of infinite expansions of hypergeometric functions. We also conduct simulations of FSI using the commercial computer-aided engineering (CAE) software ANSYS, to both benchmark our perturbative theory and to establish the limits of its applicability.</div><div>Next, we study fluid–structure interactions in a thin microtube constituted of a linearly elastic material conveying a generalized Newtonian fluid. Here, we employ the Donnell shell theory to model the deformation field in the structure of the tube. As a novel contribution, we formulate an analytical expression for the (radial) deformation of the tube using the method of matched asymptotic expansions, taking into account the bending boundary layers near the clamped ends. Using our perturbative theory, we also improve certain classical but partial results, like Fung’s model and the law of Laplace, to match with direct numerical simulations in ANSYS.</div><div>Subsequently, we explore FSI in hyperelastic tubes via the Mooney–Rivlin model. In a thin-walled vessel, we formulate a novel nonlinear relationship between (local) deformation and (local) pressure A similar approach for the thick-walled tube, yields a nonlinear ODE to be solved numerically. Due to strain hardening, the hyperelastic tube appears stiffer and supports higher pressure drops than a linearly elastic tube.</div><div>Finally, we study transient compressible flow being conveyed in a linearly viscoelastic tube. By employing a double perturbation expansion (for weak compressibility and weak FSI), a predictive relationship between the deformed radius, the flow rate and the (local) pressure is obtained. We find that, due to FSI, the Stokes flow takes a finite time to adjust to any changes emanating from the boundary motion. In the case of oscillatory pressure imposed at the inlet, acoustic streaming is shown to arise due to FSI in this compressible flow. Fundamentally, the goal of the research in this thesis is to generate a catalog of flow rate–pressure drop relationships for different types of fluid–structure interactions, depending on the combinations of fluid mechanics and structural mechanics models (behaviors). These relationships can then be used to solve practical problems. We formulate a theory of hydrodynamic bulge testing, through which the elastic modulus is estimated from the pressure drop and flow rate measurements in a microchannel with a (thick and pre-stressed) compliant top wall, without measuring the deformation. A sensitivity analysis, via Monte Carlo simulation, shows that the hydrodynamic bulge test is only a slightly less accurate</div><div>than the traditional bulge test, but is less susceptible to uncertainty emanating from the noise in measurements.</div>

<div>The atomization of jets and droplets undergoing breakup in high-speed flows has been experimentally measured and theoretically modeled. Systems for producing individual droplet breakup and full jet breakup were designed, and a wide range of diagnostics were developed and adapted to measure the results with reduced uncertainty.</div><div><br></div><div>A detailed methodology for investigating high-speed sprays in the Purdue Experimental Turbine Aerothermal Lab is presented. Optical diagnostic techniques were carefully selected and optimized for the test section geometries and flow features, such that images could be collected at high frequencies of 20 kHz with high resolutions. Developed image processing routines are outlined to demonstrate how backlit imaging with specialized lenses allowed for more accurate spray depth measurements in supersonic conditions, which were then used in regression modeling routines to derive empirical correlations that factored in test section geometry, flow conditions, and injector design. A Mie scattering imaging technique was used for quantitative analysis of the supersonic spray plume profile and measurement of the spray width. 20 kHz shadowgraphy provided sufficient gradients for analysis of the unsteadiness of the spray and surrounding supersonic flow at the point of injection. Droplet sizes and velocities were measured in subsonic conditions using digital in-line holography, in which recent advancements to the reconstruction algorithm were implemented to reduce out-of-plane measurement uncertainty, and phase Doppler particle analysis.</div><div><br></div><div>The breakup of a single drop undergoing multi-mode breakup was analytically characterized, with the proposal of a new breakup criterion in the Taylor analogy breakup model. Hill vortices within the drop were proposed as a new flow mechanism promoting multi-mode breakup. Product drop sizes from the ring breakup were predicted and compared with experimental results.</div>

Dry Powder Inhalers (DPIs) have great potential in pulmonary drug delivery; the granular powder, used as active ingredient in DPIs, is ozone friendly and the operation of DPIs ensures coordination between dose release and patient inhalation. However, the powder fluidisation mechanisms are poorly understood which leads to low efficiency of DPIs with 10-35 % of the dose reaching the site of action. The main aim of this thesis is to study the hydrodynamics of powder fluidisation in DPIs, using experimental and computational approaches. An experimental test rig was developed to replicate the process of transient powder fluidisation in an impinging air jet configuration. The powder fluidisation chamber was scaled up resulting in a two dimensional particle flow prototype, which encloses 3.85 mm glass beads. Using optical image processing techniques, individual particles were detected and tracked throughout the experimental time and domain. By varying the air flow rate to the test section, two particle fluidisation regimes were studied. In the first fluidisation regime, the particle bed was fully fluidised in less than 0.25 s due to the strong air jet. Particle velocity vectors showed strong convective flow with no evidence of diffusive motion triggered by inter-particle collisions. In the second fluidisation regime, the particle flow experienced two stages. The first stage showed strong convective flow similar to the first fluidisation regime, while the second stage showed more complex particle flow with collisional and convective flow taking place on the same time and length scales. The continuum Two Fluid Model (TFM) was used to solve the governing equations of the coupled granular and gas phases for the same experimental conditions. Sub-models for particle-gas and particle-particle interactions were used to complete the model description. Inter-particle interactions were resolved using models based on the kinetic theory of granular flow for the rapid flow regime and models based on soil mechanics for the frictional regime. Numerical predictions of the first fluidisation regime showed that the model should incorporate particle-wall friction and minimise diffusion, simultaneously. Ignoring friction resulted in fluidisation timing mismatch, while increasing the diffusion resulted in homogenous particle fluidisation in contrast to the aggregative convective fluidisation noticed in the experiments. Numerical predictions of the second fluidisation regime agreed well with the experiments for the convection dominated first stage of flow up to 0.3 s. However, later stages of complex particle flow showed qualitative discrepancies between the experimental and the computational approaches suggesting that current continuum granular models need further development. The findings of the present thesis have contributed towards better understanding of the mechanics of particle fluidisation and dense multiphase flow in DPI in particular, and particle bed fluidisation using impinging air jet in general. The use of TFM for predicting high speed convective granular flows, such as those in DPIs, is promising. Further studies are needed to investigate the form of particle-particle interactions within continuum granular flow models.

This thesis presents an investigation on multiphase reactor hydrodynamics using magnetic resonance imaging (MRI). The study demonstrates experimental techniques by which computational and quasi-analytical fluid models may be validated. Three types of industrially-important multiphase reaction vessels are considered: a co-current upflow gas-liquid-solid bed, a co-current downward trickle bed (gas, liquid, solid), and a gas-solid fluidised bed. These reactors were selected as they commonly demonstrate local hydrodynamic anisotropy which affects the global performance of industrial units. MRI was used to obtain 2D velocity images of the gas and liquid phases in the packed beds, and of the gas and the solid phases in the fluidised bed. This study reports the first spatially resolved velocity measurements of both the gas and liquid phases in a co-current upflow bed, and the gas and solid phases of an isolated bubble in a fluidised bed. The experimental vessels were: 52 mm in diameter using 5 mm glass spheres in the upflow bed at 8 bara, 27 mm with 5 mm glass spheres in the trickle bed at 6.75 bara, and 52 mm using 1.2 mm poppy seeds as the fluidised particles at 8.5 bara. The experiments were conducted at a laboratory temperature of 25.0 ± 3.0 °C. In the upflow bed, time-averaged velocity images were acquired over a 2.5 h experimental time. This was done to capture the steady state behaviour of the vessel operating in the pulsing flow regime. The temporally-stable trickle flow state in the trickle bed was imaged over 15-100 minutes. In both packed beds, severe spatial anisotropy in the distribution of flow between pores was revealed. Furthermore, the data were used to determine classical design features such as catalyst wetting and liquid holdup which compared well with literature models. The trickle bed data were further analysed using a morphological algorithm which unambiguously identified the gas-liquid and liquid-solid interfaces. The interfacial flow fields were found to be similar to the bulk flow, with most voxels exhibiting static behaviour. The amount of interaction between the phases was found to be minimal, which is typical of the low interaction regime. A single bubble injection system was employed in the fluidised bed which allowed the injection of isolated bubbles into the incipiently fluidised bed. It also enabled the triggered acquisition of NMR data at precise time intervals. The bubble was found to be an indented ellipsoidal shape, which rose with atypical behaviour which caused it to collapse. Rise velocity was found to be consistent with theory, and the injected bubbles were sufficiently spatially reproducible to acquire 2D velocity images using single-point imaging. These velocity images showed flow behaviour characteristic of a 'fast' rising bubble, with a gas recirculation cloud 37 mm in diameter. The particle field was shown to have very high flow in the bubble wake, revealing the mechanism of bubble collapse. The flow data were compared to classical two-phase fluidisation theory, which revealed noteworthy differences in the division of flow between the particulate and bubbling regions.

La poudre de silicium métallurgique (MG-Si, pureté 99 %) ont été étudiées, en se focalisant particulièrement sur les particules fines (taille comprise entre 1 et 10 μm) Ce matériau est utilisé dans l’industrie siliconière pour la synthèse directe du diméthyldichlorosilane et est obtenu par broyage de blocs de silicium. Les propriétés de cette poudre sont cruciales pour le procédé industriel, à la fois en termes de surface spécifique, composition chimique et coulabilité. Comprendre l’influence des particules fines, qui dégradent la coulabilité, et leur origine au cours du broyage est donc d’une importance cruciale. Une nouvelle caractérisation, chimique et cristallographique, des poudres de MG-Si montre que les particules fines sont en moyennes moins chargées en éléments d’alliage que les particules plus grosses. La structure cristalline du silicium est inchangée au cours du broyage, sauf pour les particules superfines (taille inférieure à 1 μm). Celles-ci présentent des zones amorphes : cela montre qu’elles sont soumises à des contraintes plus importantes au cours du broyage, comme cette transformation étant obtenue au-delà d’un seuil de pression. Le comportement du MG-Si en broyage a été étudié pour la première fois. A l’échelle de la particule unique, il est confirmé que les fissures suivent une propagation transgranulaire. De plus, des particules fines peuvent être produites au cours d’un unique événement de broyage, en raison de l’activation simultanée de multiples systèmes de fissures qui peuvent brancher entre elles. La taille critique en-deçà de laquelle la déformation plastique est énergétiquement plus favorable que la propagation de fissure a été estimée à environ 1 μm par une méthode basée sur l’indentation. Ces deux résultats sont cohérents avec la répartition des éléments d’alliages en fonction de la taille de particule. A l’échelle multiparticulaire, une étude pilote en broyeur à tambour tournant a été menée. Les résultats de cette étude ne sont pas disponibles dans cette version publique du manuscrit. Veuillez vous reporter au manuscrit complet. Les conséquences sur la coulabilité de la présence de particules fines dans la poudre de MG-Si produite par broyage ont été caractérisées par mesures d’angle de repos, de dynamique de compaction et en fluidisation. En particulier, un nouveau comportement d’élutriation a été identifié et décrit : l’élutriation séquentielle se produit lorsque des particules fines sont initialement présentes dans le lit fluidisé et se caractérise par l’envolement d’abord des inférieures à environ 30 μm puis seulement des particules de taille supérieure. Ce comportement n’est pas observé en l’absence de fines dans le lit initial. L’explication de ce phénomène pourrait se trouver dans la formation de clusters polydisperses, formés seulement en présence de particules fines. En parallèle de l’élutriation séquentielle, des mesures électrostatiques avec un électromètre externe à la colonne ont montré la présence de potentiels très importants (10 kV), dont le signe correspond à la gamme de taille de particules envolées. Ceci suggère que l’adhésion au sein des clusters pourrait être électrostatique. / Metallurgical-grade silicon (MG-Si, 99 %) powders were extensively investigated, particularly focusing on the fine particles (whose size is between 1 and 10 μm) comprised in these powders. This material is a reactant widely used in the silicones industry for the Direct Synthesis and is obtained by size reduction of millimetric silicon lumps. Powder properties are major stakes of the industrial process. Smaller sizes favor high specific surfaces and high rates of production, but can decrease the lowability, thus inducing poor heat evacuation resulting in hot spots and a decrease in selectivity. Such lowability issues are particularly associated with fine particles, hence understand the generation of these particles during grinding is of critical importance. New chemical and crystallographic characterization of MG-Si is presented, showing that fine particles contain on average less alloying elements than larger particles, yet their crystallographic structure is preserved through grinding. On the contrary, superfine particles (smaller than 1 μm) exhibit amorphous zones: this transformation is pressure induced, showing that these particles experience larger stresses during the grinding step. The behavior of MG-Si in grinding mills has been studied for the first time. At the single particle level, it has been confirmed that transgranular fracture is preferred in MG-Si. Moreover, fine particles can be produced from a single fracture event, due to multiple crack propagation and branching. The critical size under which plastic deformation preferentially occurs over fracture has been evaluated to be approximately 1 μm. These two facts are consistent with a lower level of impurities in fines, yet remaining crystalline, and with superfines exhibiting amorphous areas. At the multiple particle level, pilot scale batch milling experiments have been performed. The results are not included in this public version of the manuscript, please refer to the full manuscript. The consequences of the presence of fine particles in ground MG-Si powder on lowability has been assessed by means of angle of repose, compaction tests and fluidization experiments. A new elutriation behavior has been observed and characterized: for naturally ground MS-Si powders (including fine particles), particles smaller than 30 μm are entrained first, then only larger particles. This was not the case in absence of fine particles. The explanation may probably lie within the presence of polydisperse clusters, formed only in presence of fine particles. Parallel to this elutriation behavior, electrostatic measurements with an external electrometer showed that high potential with sign correlated with the type of particle elutriated are attained during elutriation. This may suggest that electrostatics is responsible for cluster formation.

<p>This work utilized Pointwise and Fluent to generate a two-dimensional axisymmetric model a Mk 48 torpedo, with the intention of informing methods to reduce the turbulence, and therefore hydrodynamic noise, of the torpedo’s wake. However, this work was unable to gather data on the unsteady nature of the turbulence expected around the torpedo due to Fluent providing unrealistic results when run using a transient solver. This work shows that the transient solver computed boundary layers greater than one order of magnitude smaller than expected, and in some cases there was no change in boundary layer thickness over the torpedo’s body. The work does contain steady state solutions that were validated by first performing a grid convergence study for a flat plate. The steady state results for the flat plate and torpedo both showed the expected growth for a turbulent boundary layer. Additionally, there was a high level of convergence with the Log-Law showing that the steady state data is valid. Future work should use a transient solver to determine the characteristics of the turbulence to resolve unsteady flow from vortex shedding, wake characteristics, and any broadband or narrowband noise to develop solutions to reduce the noise made by the Mk 48.</p>

<div>Advances in modern research have unveiled numerous fundamental and practical benefits of studying the hydrodynamics of microorganisms. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. In this thesis, we investigate the interplay between hydrodynamics and chemotaxis toward dictating bacterial distribution around fluid-fluid interfaces, which often act as a source of nutrition. We approach our problem statements using mathematical models and numerical and/or semi-analytical tools. Our studies are particularly relevant in the context of hydrocarbon degradation after oil-spills.</div><div><br></div><div>We begin by showing that the flow generated by rising oil drops delocalizes dissolved nutrient patches in the ocean, and aids chemotactic bacteria in improving their nutrition (over non-chemotactic bacteria) by 45%. We then move from studying colonization of soluble nutrient patches to colonization around nutrient sources, e.g., oil drops, marine snow. Towards this, we first demonstrate the phenomenon of hydrodynamics-mediated 'trapping' of bacteria around oil drops and show that a surfactant-laden drop can retain an approaching bacterium on its surface for approximately 35% longer times than a clean drop. We also analyze hydrodynamic trapping of bacteria around settling marine snow particles and show how bacteria can collide with and colonize the marine snow, even when the latter moves 10 times faster than the former. In all the cases above, we show how the hydrodynamic interactions are complemented by chemotaxis to enable extremely effective bacterial foraging. We next explore how propulsion mechanisms of microorganisms affect their ability to form biofilms on fluid-fluid interfaces and unveil the hydrodynamic origins behind the tendency of flagellated bacteria to swim parallel to plane surfactant-laden interfaces. Finally, we summarize our results, identify further avenues of research and propose problem statements related to them.</div>

<div>Particle Image Velocimetry (PIV) is a non-invasive measurement technique which resolves the flow velocity by taking instantaneous snapshots of tracer particle motion in the flow and uses digital image cross-correlation to estimate the particle shift up to subpixel accuracy. The measurement chain incorporates numerous sets of parameters, such as the particle displacements, the particle image size, the flow shear rate, the out-of-plane motion for planar PIV and image noise to name a few, and these parameters are interrelated and influence the final velocity estimate in a complicated way. In the last few decades, PIV has become widely popular by virtue of developments in both the hardware capabilities and correlation algorithms, especially with the scope of 3-component (3C) and 3-dimensional (3D) velocity measurements using stereo-PIV and tomographic-PIV techniques, respectively. The velocity field measurement not only leads to other quantities of interest such as Pressure, Reynold stresses, vorticity or even diffusion coefficient, but also provides a reference field for validating numerical simulations of complex flows. However, such a comparison with CFD or applicability of the measurement to industrial design requires one to quantify the uncertainty in the PIV estimated velocity field. Even though the PIV community had a strong impetus in minimizing the measurement error over the years, the problem of uncertainty estimation in local instantaneous PIV velocity vectors have been rather unnoticed. A typical norm had been to assign an uncertainty of 0.1 pixels for the whole field irrespective of local flow features and any variation in measurement noise. The first article on this subject was published in 2012 and since then there has been a concentrated effort to address this gap. The current dissertation is motivated by such a requirement and aims to compare the existing 2D PIV uncertainty methods, propose a new method to directly estimate the planar PIV uncertainty from the correlation plane and subsequently propose the first comprehensive methods to quantify the measurement uncertainty in stereo-PIV and 3D Particle Tracking Velocimetry (PTV) measurements.</div><div>The uncertainty quantification in a PIV measurement is, however, non-trivial due to the presence of multitude of error sources and their non-linear coupling through the measurement chain transfer function. In addition, the advanced algorithms apply iterative correction process to minimize the residual which increases the complexity of the process and hence, a simple data-reduction equation for uncertainty propagation does not exist. Furthermore, the calibration or a reconstruction process in a stereo or volumetric measurement makes the uncertainty estimation more challenging. Thus, current uncertainty quantification methods develop a-posterior models utilizing the evaluated displacement information and combine it with either image information, correlation plane information or even calibration “disparity map” information to find the desired uncertainties in the velocity estimates.</div><div><br></div>

Finite amplitude perturbations in compressible media are ubiquitous in scientific and engineering applications such as gas-turbine engines, rocket propulsion systems, combustion instabilities, inhomogeneous solids, and traffic flow prediction models, to name a few. Small amplitude waves in compressible fluids propagate as sound and are very well described by linear theory. On the other hand, the theory of nonlinear acoustics, concerning high-amplitude wave propagation (Mach<2) is relatively underdeveloped. Most of the theoretical development in nonlinear acoustics has focused on wave steepening and has been centered around the Burgers' equation, which can be extended to nonlinear acoustics only for purely one-way traveling waves. In this dissertation, theoretical and computational developments are discussed with the objective of advancing the multi-fidelity modeling of nonlinear acoustics, ranging from quasi one-dimensional high-amplitude waves to combustion-induced detonation waves. <br> <br> We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order in perturbation variables is derived. The exact energy corollary of such second-order system of equations is then formulated and used to elucidate the spectral energy dynamics of nonlinear acoustic waves. We then extend this analysis to thermoacoustically unstable waves -- i.e. amplified as a result of thermoacoustic instability. We drive such instability up until the generation of shock waves. We further study the nonlinear wave propagation in geometrically complex case of waves induced by the spark plasma between the electrodes. This case adds the geometrical complexity of a curved, three-dimensional shock, yielding vorticity production due to baroclinic torque. Finally, detonation waves are simulated by using a low-order approach, in a periodic setup subjected to high pressure inlet and exhaust of combustible gaseous mixture. An order adaptive fully compressible and unstructured Navier Stokes solver is currently under development to enable higher fidelity studies of both the spark plasma and detonation wave problem in the future. <br>

The study is focused on study of surface and interfacial properties of oil at high temperatures, to understand the mechanisms of heat transfer and oil absorption during frying