Three different models, relating to the study of microswimmers immersed in a low Reynolds number fluid, are presented. The underlying, mathematical concepts employed in each are developed using singularity methods of Stokes flow. The first topic concerns the motility of an artificial, three-sphere microswimmer with prescribed, non-reciprocal, internal forces. The swimmer progresses through a low Reynolds number, nonlinear, viscoelastic medium. The model developed illustrates that the presence of the viscoelastic rheology, when compared to a Newtonian environment, increases both the net displacement and swimming efficiency of the microswimmer. The second area concerns biological microswimming, modelling a sperm cell with a hyperactive waveform (vigorous, asymmetric beating), bound to the epithelial walls of the female, reproductive tract. Using resistive-force theory, the model concludes that, for certain regions in parameter space, hyperactivated sperm cells can induce mechanical forces that pull the cell away from the wall binding. This appears to occur via the regulation of the beat amplitude, wavenumber and beat asymmetry. The next topic presents a novel generalisation of slender-body theory that is capable of calculating the approximate flow field around a long, thin, slender body with circular cross sections that vary arbitrarily in radius along a curvilinear centre-line. New, permissible, slender-body shapes include a tapered flagellum and those with ribbed, wave-like structures. Finally, the detailed analytics of the generalised, slender-body theory are exploited to develop a numerical implementation capable of simulating a wider range of slender-body geometries compared to previous studies in the field.

La propagation d’une onde ultrasonore de compression au travers d’une distribution de particules solides identiques localisées aléatoirement dans un liquide visqueux est étudiée. La longueur d’onde de l’onde de compression est supposée grande devant le rayon des particules, et les propriétés effectives dynamiques du milieu sont recherchées.Les coefficients de diffusion d’une sphère solide isolée sont étudiés pour différentes polarisations des ondes partielles de mode n incidentes et diffusées. Des expressions approchées en sont données pour tout n dans le régime de diffusion de Rayleigh.Dans le cas de particules sphériques, le milieu est modélisé par un noyau élastique, de même matériau et rayon que les particules, et entouré d’une coque emplie du fluide hôte. L’ensemble est insoné, dans le milieu effectif, par une onde de compression partielle de mode n. Les propriétés effectives sont recherchées par minimisation de la diffusion pour différentes valeurs de n. Le module d’élasticité volumique effectif et la masse volumique effective sont obtenus respectivement à partir des modes n=0 et n=1. Comparée à la formule d’Ament, fondée sur l’équilibre des forces hydrodynamiques et inertielle au niveau de chaque particule supposée rigide, celle obtenue ici fait apparaître un effet de la concentration sur la dépendance fréquentielle de la masse volumique similaire à celui observé, expérimentalement et dans des modèles de diffusion multiple, sur les propriétés effectives des ondes de compression. La méthode d’Ament est ensuite appliquée pour obtenir la masse volumique effective dans le cas de sphéroïdes rigides alignés. / A random dispersion of identical elastic solid particles in a viscous fluid is considered and effective properties, appropriate to the propagation through the medium of an ultrasonic compressional wave of large wavelength compared to the radius of the particles, is investigated.The scattering coefficients of a single spherical particle in a viscous medium are investigated for all combinations of incident and scattered wave types for use in multiple scattering models. Approximate formulae are obtained for the coefficients at n’th partial wave order in the Rayleigh limit. For spherical particles, a core-shell self-consistent model is used, in which the medium is modelled by an elastic core of the same material and radius as the particles, surrounded by a shell of the host fluid, and placed in the effective medium. The radius of the shell is such that the ratio of the core/shell volume is equal to the particle concentration. The dynamic properties of the effective medium are sought by minimising the scattering of the shell for different incident compressional partial wave orders (n).The effective bulk modulus is found from the monopole mode n=0 and the effective mass density from the dipole mode n=1. When compared to Ament’s formula based on local force balance at the particles (assumed rigid), the effective mass density obtained from the core-shell model shows a frequency-dependent effect of concentration similar to that observed in multiple scattering models and experimentally. Ament’s method is then applied to obtain the effective mass density in case of aligned rigid spheroids.

[pt] Experimentos referentes ao movimento relativo entre partículas sólidas e um fluido viscoso confinado no interior de cilindros de seção reta arbitrária (circular, quadrangular) foram realizados. Para todos os casos experimentalmente investigados e, para escoamentos variando desde regimes de muito baixo Números de Reynolds (Re menor que 0,1) até um regime bem além do regime de Oseen, constatou-se que a razão entre a força de pressão e a força de arrasto viscoso (Delta P mais A/D) pode ser diretamente medida através de parâmetros do escoamento não perturbado (escoamento em ausência da partícula). De acordo com uma recente teoria (Brenner, 1962) a afirmativa acima que se baseia em uma linearização do tipo Oseen das equações de movimento, deveria apenas ser esperada para regimes de baixos Números de Reynolds (Re menor que 2). Brenner (1962), utilizando-se dos teoremas de momentum e energia, aplicados ao movimento relativo de uma partícula sólida e um fluido viscoso confinado por paredes sólidas, mostrou que, devido ao movimento relativo, uma força de cisalhamento atuando nas paredes do cilindro deve necessariamente existir, ainda que estas paredes estejam infinitamente distantes da perturbação induzida pela partícula. A generalidade da Teoria de Brenner, relativa à geometria da seção reta do cilindro, foi também verificada nos regimes de Stokes e de Oseen. Experimentos realizados em uma coluna curta (1 m) de seção reta circular forneceram um conjunto de dados que foram utilizados para se qualificar, a um baixo nível de incerteza experimental, a técnica experimental utilizada. Experimentos realizados em uma coluna longa (3 m) de seção reta quadrangular permitiram a verificação da teoria em regimes distantes do regime teórico. Medidas da diferença de pressão adicional induzida pelo movimento relativo entre a partícula e o líquido viscoso confinado no duto de seção quadrangular, claramente definiram três diferentes regiões: i) até Re~50, verificou-se que a razão Delta P+A/D aproximadamente 2,093, resultado este que deveria ser esperado apenas para Re < 2,0. Por consideração elementares de momentum aplicáveis a um volume de controle constituído do fluido viscoso no entorno da partícula, pode-se facilmente mostrar que o valor Delta P+A/D diferente de 1,0 confirma a existência de uma força de cisalhamento finita atuando nas paredes do duto infinitamente distantes da partícula; ii) além de Re ~ 50, uma transição abrupta se inicia forçando o valor Delta P+A/D a decrescer. A razão de força Delta P+A/D decresce assintoticamente para o valor 1,0, valor este que corresponde à situação de um fluido ilimitado (meio contínuo fluido sem fronteiras) conforme prescrito pelo Princípio de Momentum; iii) para Re > 2500, a razão Delta P+A/D fortemente aproxima-se do valor 1,0. O maior regime investigado foi Re ~ 36000 mas, fisicamente, não parece existir nenhum argumento que possa contradizer a permanência do comportamento acima descrito. Este trabalho discute também um método bastante preciso conduzindo à medição do arrasto viscoso sobre a partícula e também uma técnica para se medir as pequenas quedas de pressão(~ 1 a 10 elevado à -3 mm Hg) induzidas pelo movimento da partícula. / [en] Experiments concerning the relative motion of solid particles and viscous fluids, confined within cylinders of arbitrary cross-section (circular and quadrangular) have been conducted. For all cases experimentally investigated and for a flow regime extending from a very low particle Reynolds Number (Re less than 0.1) up to far beyond the Oseen s Regime, it has been shown that the additional pressure force to viscous drag ratio (Delta plus A/D) can be directly evaluated by means of parameters of the unperturbed flow. Accordingly to a recent theory (Brenner, 1962) the above statement which uses a Oseen s type linearization of the equation of motion, should only be expected for the very low particle Reynolds Number regime (Re < 2). Brenner (1962), using momentum and energy theorems applied to the relative motion of a particle and a confined viscous fluid has shown that, as a result of the relative motion, a finete shearing force acting on the cylinder walls must existis, even if the walls are infinitely distant from the particle perturbation. The generality of Brenner s theory concerning the cylinder geometry was also verified in the Stokes and in the Oseen s regimes. Experiments conducted in a short (1 m) circular cylinder, filled with a Newtonian fluid, provided the base line data set used to qualify the experimental technique used, within very low experimental uncertainties. Experiments conducted in a long square cylinder (3 m), allowed verification of the theory far beyond the theorectical regime. Measurements of the additional pressure drop created by the relative motion between a solid particle and the viscous fluid, confined in the square cylinder, cleary defined three regions: i) up to about Re ~ 50 it was found that the pressure force to Viscous drag ratio Delta P+A/D approximately 2.093 which should be expected only for Re < 2. By elementary momentum considerations, applied to the fluid control volume around the particle present in the flow, it can easily be show that this value of Delta P+A/D diferente than 1 confirms the existence of a finete shearing force on the far walls of the cylinder; ii) beyond Re = 50 and up to Re ~ 2500 a very complex and not completely understood transition occurs. At about Re ~ 50 an abrupt transition takes place forcing the value of Delta P+A/D to decrease. The ratio Delta P+A/D decreases asymptotically towards the value 1.0 wich corresponds to the situation of an unbounded fluid as can be predicted by the Momentum Principle; iii) for particle Reynolds Number Re > 2500, the Delta P+A/D approaches very closely the value 1.0. The largest flow regime investigated was Re ~ 36000 but, physically, there seems to be no reason to expect any change in the described behaviour. This work also discusses an accurate method for directly measuring the viscous drag force and the diminute dynamic pressure (~ 1 to 10 (-3) mm Hg) created by the motion of the particle.

Nous étudions un rideau visqueux en écoulement vertical. Un injecteur situé en haut du domaine forme un écoulement ouvert composé d'un liquide visqueux homogène qui s'écoule dans un bain et est accéléré dans son mouvement vertical par l'effet de la gravité. Des zones présentant des taux de contrainte compressifs peuvent apparaître au sein de l'écoulement. Le rideau visqueux est alors susceptible de flamber, perdant sa géométrie plane. Le flambage d'une structure fine et visqueuse a précédemment été étudié dans le contexte d'un écoulement de base présentant une direction d'invariance, ici l'état précontraint est purement bidimensionnel. La modélisation théorique de l'écoulement ouvert prend en compte les effets advectifs. Nous introduirons des outils théoriques et numériques que nous appliquons à un problème classique de la mécanique des solides. Nous utilisons ensuite ces mêmes méthodes pour le rideau tombant. Nous obtenons un modèle de plaque visqueuse dont la cinématique mélange des vitesses et un déplacement hors plan. Les termes membranaires sont inspirés de la mécanique des structures fines et obtenus par l'analogie Stokes-Rayleigh, qui transpose aux écoulements visqueux les notions d'étirement et de flexion d'une plaque. Les équations d'équilibre de flambage étant d'ordre élevé, nous aurons recours à une implémentation numérique particulière. Les effets de la capillarité peuvent être pris en compte dans le modèle et seront étudiés. Nous concluons par une approche théorique de la stabilité de l'écoulement. Nous adaptons une méthode d'analyse des écoulements ouverts instables en cisaillement à l'équilibre de flambage du rideau visqueux. / We consider a vertical sheet made up of an homogeneous viscous fluid and falling into a bath. This curtain is formed by an inlet injecting viscous fluid at the top of the domain and creating an open flow. The resulting thin structure is falling under the effect of gravity, and develops regions of compressive stress. These may lead to a mechanical instability as the sheet can buckle under compression, losing its planar geometry and deforming in the out-of-plane direction.In previous studies, buckling of a viscous sheet that leads to surface wrinkles was associated with flows having a direction of invariance. We will be considering a genuinely two-dimensional stress state.We first introduce stability methods on a simple solid mechanics problem, obtaining equations in weak form and using a finite elements solver to obtain its buckled configurations.We will then study both the modelling of the falling curtain as a viscous membrane and its numerical resolution. We will derive a model with kinematics mixing velocities and displacements and use a viscous membrane model. Inspired by the solid mechanics of thin structures it uses the Stokes-Rayleigh analogy to transpose the concepts of stretching and bending stress to viscous flows. Equations for the out-of-plane equilibrium are of high order and require a specific numerical scheme. Capillary effects can be taken into account in the model and we assess their influence.We finally present a stability analysis hoping to improve our analytical understanding of the buckling phenomenon. We adapt a framework developed for the study of open shear flows instabilities to the out-of-plane equilibrium equations.

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

Peristalsis is a mechanism of pumping fluids in ducts when a progressive wave of area contraction or expansion propagates along the length of a distensible tube containing fluid. It induces in general propulsive and mixing movements and pumps the fluids against pressure rise. Physiologically, peristaltic action is an inherent property of smooth muscle contraction. It is an automatic and vital process that drives the urine from the kidney to the bladder, food through the digestive tract, bile from the gall-bladder into the duodenum, movement of ovum in the fallopian tube and many other situations. A major industrial application of this principle is in the design of roller pumps, which are used in pumping fluids without being contaminated due to the contact with the pumping machinery. Even though peristalsis is a well-known mechanism in biological system, the first theoretical and experimental analysis of its fluid dynamics aspects were given four decades ago. In reality, the peristaltic flow problems are unsteady moving free boundary value problems where the shape of the wave on flexible tube wall is not known apriori. But the mathematical models on peristaltic transport considered in the literature deal with a prescribed train of waves moving with constant speed on the flexible boundaries and they are studied in either a fixed frame or a wave frame moving with constant velocity of the wave. In a wave frame the moving walls become stationary wavy walls. Further the motion could be treated steady under the assumptions that the peristaltic wave train is periodic, the pressure difference across the length of the tube is constant and the tube length is an integral multiple of the wavelength. Some mathematical models of peristaltic flows representing some physiological situations are studied using a wave frame of reference in this thesis. The important characteristics of these flows namely pumping (variation of time averaged flux with difference in pressures across one wavelength), trapping (splitting of streamlines enclosing a bolus which moves as a whole along with the wave), reflux phenomena (the presence of some fluid particles whose mean motion over one cycle is against the net pumping direction) are discussed in detail. A brief general introduction to the peristaltic transport and their application in physiological fluid dynamics is presented in chapter one. In the second chapter, the peristaltic transport of an incompressible viscous Newtonian fluid in an asymmetric channel is studied under long wavelength and low-Reynolds number assumptions. Choosing the peristaltic wave train on the walls to have different amplitudes and phase produces the channel asymmetry. This study is motivated by the intra-uterine fluid flow induced by uterine wall contractions which represent a peristaltic flow in an asymmetric channel and this flow is responsible for embryo transport to a successful implantation site. The solution for the stream function is obtained by neglecting inertia and curvature effects. The streamlines are plotted in both fixed and wave frames. The effects of different geometric parameters causing asymmetry like phase difference; varying channel width and wave amplitudes are investigated on the pumping characteristics, streamline pat-tern, trapping and reflux phenomena. It is observed that the pumping against pressure rise, trapping and reflux layer exists only when cross-section of the channel varies along the axis. The limits on the time averaged flux for trapping and reflux are obtained. The peristaltic waves on the walls with same amplitudes propagating in phase produce zero flux rate as the channel cross-section remains the same through out. The trapping and reflux regions reduce for asymmetric channels compared to symmetric channels. The flow of an incompressible viscous fluid driven by the traveling waves along the boundaries of an asymmetric channel is studied in the chapter three, when inertia and streamline curvature effects are not negligible. It was well documented that the inertial forces cannot be ignored in the pharyngeal phase of bolus transport. Choosing the wave train on the walls to have different amplitudes and phases produces the channel asymmetry here. An asymptotic solution is obtained in powers of a geometric parameter £, the ratio of the channel width to the wavelength, giving curvature and inertia effects. A domain transformation is used to transform the channel of variable cross section to a uniform cross section, and this facilitates in easy way of finding closed form solutions at higher orders. The solutions are presented upto second order in 6. It has been found that, the relation connecting the pressure gradient and time average flux rate is a cubic leading to a non-unique of flux for a given pressure gradient. A uniqueness criterion is derived which restricts the parameters to get a unique flux for a prescribed pressure difference. The effects of inertia and curvature on peristaltic pumping, trapping and shear stress are discussed for various parameters governing the flow for symmetric and asymmetric channels and compared with the existing results in the literature. Even under a favourable pressure gradient the possibility of fluid flow in a direction opposite to the direction of the waves propagating on the walls is detected as in the case of some non-Newtonian fluids. It is noticed that the Reynolds number and asymmetry of the wall geometry may play an important role in producing mixing. The appearance of a second trapped bolus near the down streamside of the channel for some Reynolds number is a new feature. Further, the non-zero curvature produces three trapped boluses for high Reynolds number in symmetric channel as well as for inertia free flow in an asymmetric channel. Another interesting phenomena is that the shear stress distribution on the walls vanishes at some points but it does not indicate any flow separation as the MRS criteria is not satisfied. The gastrointestinal tract is surrounded by a number of muscle layers having smooth muscle. The most important smooth muscle layers in gastrointestinal tract are submucosa and a layer of epithelial cells and these- are responsible for the absorption of nutrients and water in the intestine. These layers consist of many folds and there are pores through out the tight junctions of them. Thus a study of peristaltic transport with porous peripheral layer and porous boundaries of a duct are important. Motivated by this the flow in gastrointestinal tract is mathematically modeled by a peristaltic flow of two fluid system in a two-dimensional channel with a porous peripheral layer and a Newtonian fluid core layer, in chapter four. The fluid flow is investigated under the assumptions of long wavelength and low Reynolds number in a wave frame of reference. Brinkman extended Darcy equation is utilized to model the flow in the porous peripheral layer. A shear stress jump boundary condition of Ochoa-Tapia and Whitaker is used at the interface between porous and fluid regions together with continuity of velocity and normal stress conditions. Here one needs an extra assumption that the fluid interface and the peristaltic wave on the boundary have the same period in addition to the constant pressure difference at the ends of channel and the length of the channel to be an integral multiple of the wavelength, to consider the flow to be steady. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. Matlab packages are used to solve the transcendental equation governing it. An interval of critical time averaged flux Q is obtained for the existence of a unique solution for the interphase. The physical quantities of importance in peristaltic transport namely, pumping, trapping and reflux are discussed for various parameters of interest governing the flow like Darcy number Da, porosity 6, shear-stress jump constant /3, viscosity ratio /i. It is observed that the peristalsis works as a pump against greater pressure rise with a porous medium in the peripheral layer than a viscous fluid. The limits on the time averaged flux Q for trapping in the core layer are obtained. The existence of reflux near the axis is observed for small values of Darcy number and large values of /?. Chapter five deals with the peristaltic transport in a tube with a poroflexible wall and having a porous material layer in the peripheral region and a Newtonian fluid in the core region. Flow in tube may be more realistic to model a flow in gastrointestinal system. At the poroflexible wall, a slip boundary condition of Saffman.type is used. The fluid flow is studied in a wave frame of reference under lubrication approach. Brinkman extended Darcy equation in cylindrical polar coordinates is considered for the porous medium with a shear-stress jump boundary condition of Ochoa-Tapia and Whitaker at the interface of porous and fluid regions together with the continuity of velocity and normal stress. The interface is found as a part of the solutions using the conservation of mass in both the regions of deformable porous medium and fluid medium independently. The interface equation turns out to be a transcendental equation involving modified Bessel functions and it is solved by using Matlab packages. The uniqueness criterion of the solutions for the interface equation in the flow region is determined for certain values of time averaged flux Q. Pumping characteristics, trapping and reflux phenomena are discussed for various parameters of interest governing the flow like, wall slip constant fc, Darcy number Da, viscosity ratio /x. shear stress jump constant f) and peripheral layer thickness 7. The slip condition at the boundary, arising due to the poroflexible nature of the wall, enhances pumping. The trapped bolus volume in the core layer is observed to decrease with a decrease in Da, /i and k and an increase in /?. The reflux phenomena is discussed in detail. The trapping limits on the flux rate Q in the core region are obtained. As the behaviour of most of the physiological fluids is known to be non-Newtonian, the peristaltic flows of power-law and micro polar fluids are investigated in the next two chapters. In chapter six, the peristaltic transport of a power-law fluid in an axisymmetric tube having poroflexible wall is studied. The power-law model of Ostwald-de Waele type is considered, which accommodates the study of both shear thinning and shear thickening fluids. The flow characteristics are studied in wave frame analysis under lubrication approach. The slip boundary conditions of Beavers-Joseph and Saffman type are considered at the wall in obtaining solutions for the flow and resulting pumping characteristics are investigated with a straight section dominated (SSD) wave form other than the sinusoidal one. It is observed that the time mean flow becomes negative in free pumping for a shear thickening fluid with a SSD expansion wave and the same is observed for a SSD contraction wave in the case of shear thinning fluid. The pressure rise increases with increasing of Darcy number Da against which the peristalsis works as a pump and decreases for an increase in Beaver-Joseph constant a. Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid compared with Newtonian fluid. Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da, a and the fluid behaviour index n. The trapping limits on Q are derived. The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behaviour index decreases, i.e as the fluid behaviour changes from shear thickening to shear thinning, where as it increases with an increase in Darcy number. The rheological properties of fluid, wave shape and porous nature of the wall play an important role in the peristaltic transport and may be useful in understanding the transport of chyme in small intestine. The chapter seven contains the study of peristaltic transport of a micropolar fluid in an axisymmetric tube. Micropolar fluids exhibit some microscopic effects arising from the local structure and micro motion of the fluid elements. Further, they can sustain couple stresses. It is speculated that, in microcirculation, peristalsis may be involved as well in the vasomotion of small blood vessels which change their diameters periodically. Therefore, modelling blood by a micropolar fluid may be more appropriate. The closed form solutions are obtained for velocity, microrotation components, as well as the stream function under the assumption of long wavelength and low Reynolds number. The solution contains new additional parameters namely, N the coupling number and m the microploar parameter. In the case of free pumping (pressure difference Ap = 0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Ap > 0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena aie presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Ap are discussed. The nomenclature of symbols in each chapter is independent of the other. Each of the chapter has its own appendix and they are numbered with the corresponding roman number of the chapters. The purpose of the study here is not to represent exactly the functioning of various physiological applications, but rather to understand the fluid-mechanical aspects inherent in the problems of peristaltic transport.

This study seeks to understand the interplay of vorticity and elasto-dynamics that forms the basis for a fluttering flag and flapping wing propulsion, and factors that distinguish one from the other. The fluid dynamics is assumed two dimensional and incompressible, and comprises potential and viscous flow simulations. The elastic solid is one dimensional and governed by the Bernoulli-Euler flexure model. The fluid and elastic solid models are coupled using a predictor-corrector algorithm. Flutter of a flag or foil is associated with drag and we show that the pressure on the foil is predominantly circulatory in origin. The circulatory pressure generated on the foil depends primarily on the slope and curvature. The wake vorticity exhibits a wide range of behavior starting from a Kelvin-Helmholtz type instability to a von Kármán wake. Potential flow simulations do not capture the wake accurately both at high and low mass ratios. This is reflected in the flutter boundary and pressure over the foil when compared with viscous flow simulations. Thrust due to heaving of a flexible foil shows maxima at a set of discrete frequencies that coincide with the frequencies at which the flapping velocity of the foil tip is a maximum. The propulsive efficiency shows maxima at a set of discrete frequencies that are close but distinct from the thrust maxima set of frequencies. These discrete frequencies are close to the natural frequencies of vibration of a cantilevered foil vibrating in vacuum. At low frequencies thrust is a consequence of a strong leading edge vortex developed over the foil and it remains attached to the foil as it is convected due to the favorable pressure gradient presented by the time and spatially varying shape of the foil. At moderate and high frequencies of oscillation the pressure, and consequently the thrust, generated by the foil is non-circulatory in origin and they are high where the accelerations of the foil are high. At high frequencies the leading edge vortex is weak. Except in the low frequency range, potential flow simulations qualitatively compares well with viscous flow predictions. We show that thrust and drag on a flexible foil oscillating in a flow is caused by the phase difference between the slope of the foil and the fluid pressure on it. Propulsive efficiency though is governed by the phase difference between foil velocity and fluid pressure and inertia forces. Thus, the interplay of vorticity and elasto-dynamics determine the behavior of a flutter and propulsion of a flexible foil in a fluid flow.

La investigación realizada se enfoca en la evaluación del pabellón B del Hospital Luis Negreiros Vega con planos modificados aplicando disipadores de fluido viscoso en la disposición chevron diagonal y horizontal. En el modelo numérico se aplicaron disipadores lineales y no lineales de acuerdo con las expresiones del FEMA, 356, con el fin de realizar una comparación de la disposición y valor de exponente de velocidad óptimo para una deriva objetivo y amortiguamiento efectivo planteado para cada dirección. Los resultados con los cuales se evaluó esta efectividad, son mejores reducciones de distorsiones, menores fuerzas de disipación, y reducción de la irregularidad torsional que presentaba la estructura inicialmente en la dirección Y. Finalmente, entre los resultados que presenta esta investigación, son que los disipadores chevron horizontales no lineales son los más recomendables, debido a que requieren menores valores de coeficiente de amortiguamiento, reducen distorsiones en mayor medida que los otros modelos, presentan menores valores de fuerzas de disipación y reducen la irregularidad torsional en los pisos inferiores. / The research carried out focuses on the evaluation of pavilion B of the Luis Negreiros Vega Hospital with modified planes applying viscous fluid dissipators in the diagonal and horizontal chevron arrangement. In the numerical model, linear and non-linear dissipators were applied according to the FEMA expressions, 356, in order to make a comparison of the arrangement and value of the optimum speed exponent for a target drift and effective damping proposed for each direction. The results with which this effectiveness was evaluated are better reductions of distortions, lower dissipation forces, and reduction of torsional irregularity that the structure initially presented in the Y direction. Finally, among the results presented by this research, are that the Non-linear horizontal chevron heatsinks are the most recommended, because they require lower values of damping coefficient, reduce distortions to a greater extent than other models, present lower values of dissipation forces and reduce torsional irregularity in the lower floors. / Trabajo de investigación

The laminar-turbulent transition in viscous fluid flows is one of the most intriguing problems in fluid dynamics today. In view of the enormous applications it has in a variety of fields such as aircraft design, turbomachinery, etc., scientists have now realized the importance of tackling this problem effectively. Three-dimensional flows are usually associated with pressure gradient, streamline curvature, streamline convergence / divergence etc., all acting simultaneously. Towards a better understanding of the transition process and modeling the transition zone, it is important to study the effect of each of these parameters on the transitional flow. The present work aims at studying experimentally the effect of lateral streamline convergence alone on the laminar-turbulent transition zone under constant stream-wise pressure. The experimental setup consists of a low turbulence wind tunnel with its test section modified to cause lateral streamline convergence under constant pressure. This is achieved by converging the side-walls and appropriately diverging the roof, thus maintaining a constant stream-wise pressure. The half angle of convergence is chosen as 100 , which is approximately the same as the half of the turbulent spot envelope in constant pressure two-dimensional flows. Experiments are carried out to analyze the development of the laminar and transitional boundary layers, intermittency distribution in the transition zone and the overall characteristics of an artificially induced turbulent spot. The laminar velocity profiles are found to be of the Blasius type for two-dimensional constant pressure flows. However, the converging streamlines are found to contribute to an increased thickness of the boundary layer as compared to the corresponding two-dimensional flow. The intermittency distribution in the transition zone is found to follow the universal intermittency distribution for two-dimensional constant pressure flow. A simple linear-combination model for two-dimensional flows is found to perform very well in predicting the measured velocity profiles in the transition zone. An artificially introduced turbulent spot is found to propagate along a conical envelope with an apex cone angle of 220 which is very nearly the value for a corresponding constant pressure two-dimensional flow. The spot shapes and celerities are also comparable to those in two-dimensional flow. In summary, the present study brings out many similarities between a constant pressure laterally converging flow and a constant pressure two-dimensional flow.

Image registration is a fundamental problem that can be found in a diverse range of fields within the research community. It is used in areas such as engineering, science, medicine, robotics, computer vision and image processing, which often require the process of developing a spatial mapping between sets of data. Registration plays a crucial role in the medical imaging field where continual advances in imaging modalities, including MRI, CT and PET, allow the generation of 3D images that explicitly outline detailed in vivo information of not only human anatomy, but also human function. Mutual Information (MI) is a popular entropy-based similarity measure which has found use in a large number of image registration applications. Stemming from information theory, this measure generally outperforms most other intensity-based measures in multimodal applications as it does not assume the existence of any specific relationship between image intensities. It only assumes a statistical dependence. The basic concept behind any approach using MI is to find a transformation, which when applied to an image, will maximise the MI between two images. This thesis presents research using MI in three major topics encompassed by the computer vision and medical imaging field: rigid image registration, stereo vision, and non-rigid image registration. In the rigid domain, a novel gradient-based registration algorithm (MIGH) is proposed that uses Parzen windows to estimate image density functions and Gauss-Hermite quadrature to estimate the image entropies. The use of this quadrature technique provides an effective and efficient way of estimating entropy while bypassing the need to draw a second sample of image intensities (a procedure required in previous Parzen-based MI registration approaches). It is possible to achieve identical results with the MIGH algorithm when compared to current state of the art MI-based techniques. These results are achieved using half the previously required sample sizes, thus doubling the statistical power of the registration algorithm. Furthermore, the MIGH technique improves algorithm complexity by up to an order of N, where N represents the number of samples extracted from the images. In stereo vision, a popular passive method of depth perception, new extensions have been pro- posed in order to increase the robustness of MI-based stereo matching algorithms. Firstly, prior probabilities are incorporated into the MI measure to considerably increase the statistical power of the matching windows. The statistical power, directly related to the number of samples, can become too low when small matching windows are utilised. These priors, which are calculated from the global joint histogram, are tuned to a two level hierarchical approach. A 2D match surface, in which the match score is computed for every possible combination of template and matching windows, is also utilised to enforce left-right consistency and uniqueness constraints. These additions to MI-based stereo matching significantly enhance the algorithms ability to detect correct matches while decreasing computation time and improving the accuracy, particularly when matching across multi-spectra stereo pairs. MI has also recently found use in the non-rigid domain due to a need to compute multimodal non-rigid transformations. The viscous fluid algorithm is perhaps the best method for re- covering large local mis-registrations between two images. However, this model can only be used on images from the same modality as it assumes similar intensity values between images. Consequently, a hybrid MI-Fluid algorithm is proposed to compute a multimodal non-rigid registration technique. MI is incorporated via the use of a block matching procedure to generate a sparse deformation field which drives the viscous fluid algorithm, This algorithm is also compared to two other popular local registration techniques, namely Gaussian convolution and the thin-plate spline warp, and is shown to produce comparable results. An improved block matching procedure is also proposed whereby a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler is used to optimally locate grid points of interest. These grid points have a larger concentration in regions of high information and a lower concentration in regions of small information. Previous methods utilise only a uniform distribution of grid points throughout the image.