Complex Fluids

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. [Phys. Rev. Lett 103, 036001 (2009)] for soft matter, and adapted for granular matter by Kamrin et al. [Phys. Rev. Lett. 108, 178301 (2012)], and the gradient expansion of the local rheology µ(I) that we have proposed [Phys. Rev. Lett. 111, 238301 (2013)]. We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

A binary mixture of granular materials in a horizontal, rotating tube segregates under certain circumstances into an alternating pattern of bands of two types along the tube axis, each type being rich in one of the components. The pattern coarsens with time through band shrinking and merging, until a steady state characterized by some average bandwidth is reached. We have studied experimentally the long-term evolution of segregation patterns in sand-glass bead mixtures. We observe that during coarsening, the two types of band evolve differently, indicating that another transport mechanism is at work besides diffusion. We propose that glass beads are transported axially due to ''avalanche waves,'' a hallmark of the discontinuous flow characterizing sand-rich bands. ͓S1063-651X͑97͒01612-7͔

Using collision driven discrete molecular dynamics (DMD), we investigate the thermodynamics and dynamics of systems of 500 dumbbell molecules interacting by a purely repulsive ramp-like discretized potential, consisting of n steps of equal size. We compare the behavior of the two systems, with n = 18 and n = 144 steps. Each system exhibits both thermodynamic and dynamic anomalies, a density maximum and the translational and rotational mobilities show anomalous behavior. Starting with very dense systems and decreasing the density, both mobilities first increase, reache a maximum, then decrease, reache a minimum, and finally increase; this behavior is similar to the behavior of SPC/E water. The regions in the pressure-temperature plane of translational and rotational mobility anomalies depend strongly on n. The product of the translational diffusion coefficient and the orientational correlation time increases with temperature, in contrast with the behavior of most liquids.

Flow induced mechanical properties are often coupled with instabilities, spurt effects, or induced phase transitions. Recent studies have revealed that side-chain liquid crystal polymers exhibit typically shear-induced phases inside the isotropic ͑nonmesomorphic͒ liquid state. We present an experimental approach which brings a new understanding for nonlinear flow behaviors. The strategy consists in comparing the critical times issued from the flow behavior of a liquid-crystal polymer to the equilibrium orientational-order relaxation time was characterized. We demonstrate that shear-induced phases do not originate from a flow coupling to conventional orientational order parameter fluctuations. It does not also correspond to a direct coupling with the viscoelastic terminal time, leading to the conclusion that an additional relaxation process takes place with time scales longer than the terminal time. The identification of a low-frequency elastic plateau by viscoelastic measurements corroborates this conclusion.

This Complete Formalism (CF11) specifies a falsifiable, derived-limit route by which the VDM metriplectic split (reversible J limb ⊕ irreversible M limb) can be interpreted as an effective two-component "dark sector" at cosmological scales without postulating new fundamental particles. The central technical move is to avoid an ad hoc field split Φ = Φ J +Φ M : instead, a state-level decomposition is defined by spectral (Riesz) projectors of the linearized generator about a coarse-grained background, producing oscillatory (reversible) and relaxational (irreversible) bands with a measurable spectral-gap gate. Sector stress-energy and a tracked interaction remainder are then defined in a quadratic approximation using the energy Hessian inner product, yielding explicit cross-term control metrics. Within clearly stated regime diagnostics, CF11 derives correct bounded equation-of-state limits: a coherent, slowly varying, nearly homogeneous sector satisfies w J ≈-1, while a defect/oscillation-dominated, nonrelativistic sector admits w M ≈ 0 via either particle-kinematics or rapid oscillations in a quadratic minimum. The deliverable is a publishable contract plus binary gates for (i) T2 lattice validation of degeneracy, entropy monotonicity, the spectral split, and causality bounds, and (ii) T3+ observational regression using model selection (AIC/BIC) and a hierarchy-lensing bias statistic. Keywords dark sector • interacting fluids • equation of state • metriplectic dynamics • GENERIC • Riesz projection • spectral gap • scalar field cosmology • telegraph equation • causality • hierarchical interfaces • Void Dynamics Model

An ultrasonic generator was used in the Soxhlet extractor. To evaluate the process, the solvent flow was examined. The influence of the flow time in the Soxhlet on the process was analyzed. The formula for the residence time of streaming particles in the apparatus is given. A standardized volume curve V was formed. The time required for the solvent to remain in the apparatus is important during the extraction process. The description of the structure of flows of mass metabolic processes also means that it allows you to determine the movement and distribution of substances in these flows. Therefore, we wrote a hydrodynamic model of flows in the Soxhlet in the form of equations that represent the change in time in the apparatus. Ways to accelerate the extraction process are considered. The advantages of each method have been explored. Ultrasonic acceleration was selected from the investigated method. The parameters of the generator for generating ultrasound are considered. A compatibl...

The microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under conditions of finite inertia are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, φ. The inertia is characterized by the particle-scale shear flow Reynolds number Re = ρ γa 2 µ , where a is the particle radius, γ is the shear rate and ρ and µ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are studied for 0.005 Re 5 and 0.1 φ 0.35. The flowinduced microstructure is studied using the pair distribution function g(r). Different stress mechanisms, including those due to surface tractions (stresslet), acceleration, and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions of particle force and torque are also presented.

The microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $\phi $. The inertia is characterized by the particle-scale shear flow Reynolds number $\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$, where $a$ is the particle radius, $\dot{\gamma }$ is the shear rate and $\rho $ and $\mu $ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for $0.005\leqslant \mathit{Re}\leqslant 5$ and$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied using the pair distribution function $g(\boldsymbol {r})$. Differen...

Nous étudions l'influence de l'ajout de particules non-colloïdales sur le comportement des fluides à seuil. Les matériaux que nous formulons permettent d'isoler la contribution purement mécanique des changements de propriétés rhéologiques de la pâte lorsque la fraction volumique en particules augmente. Nous trouvons les lois liant les propriétés mécaniques (élasticité, seuil d'écoulement) de la pâte granulaire à celles de la pâte suspendante (indépendamment de leur origine physique) et à la fraction volumique en particules (indépendamment de leur taille et de leur nature). Nous montrons, en accord avec des résultats d'homogénéisation, que les évolutions avec la fraction volumique en particules du module élastique et du seuil d'écoulement sont reliées par une loi simple.

Slip is an important phenomenon that occurs during the flow of yield stress fluids like soft materials and pastes. Densely packed suspensions of hydrogel microparticles are used to show that slip is governed by the tribological interactions occurring between the samples and shearing surfaces. Both attractive/repulsive interactions between the dispersed particles and surface, as well as the viscoelasticity of the suspension, are found to play key roles in slip occurring within rheometric flows. We specifically discover that for two completely different sets of microgels, the sliding stress at which slip occurs scales with both the modulus of the particles and the bulk suspension modulus. This suggests that hysteresis losses within the viscoelastic particles contributes to friction forces and thus slip at the particle-surface tribo-contact. It is also found that slip during large amplitude oscillatory shear and steady shear flows share the same generic features.

We consider the Bogolubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in the case when the magnetic field is present. We (a) discuss their general features, (b) isolate key physical classes of solutions (normal, vortex and vortex lattice states) and (c) prove existence of the normal, vortex and vortex lattice states and stability/instability of the normal states for large/small temperature or/and magnetic fields.

This paper presents an experimental study of a yield stress fluid flow in a rectangular channel containing an abrupt contraction with an aspect ratio of 4:1. Analysis of the flow dynamics is based on the use of Laser Doppler Velocimetry (LDV), enabling local characterization of velocities. The longitudinal and transversal velocity components are measured upstream, at, and downstream of the contraction to assess the effect of this geometric change and inertia on the flow. Profiles of the longitudinal velocity component, u, highlight the existence of a dead zone at the corners of the contraction, where a slip line is identified and located at the same position as the contraction. The downstream flow establishment length is also determined, where a linear correlation is proposed. A plug zone, characterized by a constant velocity at the center of the channel, is observed for different flow rates and position conditions. The transversal velocity component, v, remains nearly zero throughout the domain, except in the contraction region, where elongation effects become significant. Analysis of velocity distribution along the central axis reveals velocity peaks immediately downstream of the contraction, particularly at low flow rates. The elongation rate reaches a maximum at the contraction, and a linear correlation is established between this maximum value and the flow rate. Finally, the study is completed by establishing correlations between the friction factor, f, the Euler number and Reynolds number, which are evaluated at the upstream and downstream regions of the contraction.

Particle tracking microrheology (PT-µr) exploits the thermal motion of embedded particles to probe the local mechanical properties of soft materials. Despite its appealing conceptual simplicity, PT-µr requires calibration procedures and operating assumptions that constitute a practical barrier to a wider adoption. Here we demonstrate Differential Dynamic Microscopy microrheology (DDMµr), a tracking-free approach based on the multi-scale, temporal correlation study of the image intensity fluctuations that are observed in microscopy experiments as a consequence of the motion of the tracers. We show that the mechanical moduli of an arbitrary sample are determined correctly in a wide frequency range, provided that the standard DDM analysis is reinforced with a novel, iterative, self-consistent procedure that fully exploits the multi-scale information made available by DDM. Our approach to DDM-µr does not require any prior calibration, is in agreement with both traditional rheology and Diffusing Wave Spectroscopy microrheology, and works in conditions where PT-µr fails, providing thus an operationally simple, calibration-free probe of soft materials.

This article analyzes the problem of filtering spam messages and addressing spam messages, Bayesian theorems based on artificial intelligence, LVQ algorithms (LVQ learning vector quantization) and a filtering scheme for systems based on neural networks. The direct construction of an effective neural network model of spam filtering using database recognition technology is considered. The parameters of access to the neural network how to include predefined statistical and non-statistical attributes of messages are given. The structure of neural network technology for classifying emails is also considered. The procedure for analyzing incoming data using the tool included in the analytical platform Deductor Studio 5.3 is described. as a result, a training kit is obtained that is suitable for use.

We introduce a diffusing-wave spectroscopic probe which utilizes light pulses and exploits the phase fluctuations of optically gated photons to eliminate the usual average over photon pathways. The principles are discussed and experimentally demonstrated. In addition to testing several critical elements of the original multiple-light-scattering theories, we have studied diffusion of polystyrene spheres in the high-volume-fraction limit where hydrodynamic interactions are important.

The dynamics of fibre suspension flow, especially breakup and reformation of fibre flocs in a closed channel flow past a forward facing step was studied experimentally using fast CCD camera imaging and image analysis techniques that allow for simultaneous measurement of floc size and turbulent flow field of fibres. The recirculation eddy downstream of the expansion step was found to exists only if the step height exceeds mean fibre length. When existing, the behavior of the eddy is similar to that of Newtonian fluid flows. Experimental correlations between floc size and turbulent flow quantities were found indicating that the ratio of the minimum floc size found at the end of the recirculation region and the floc size upstream of the step is strongly correlated with the size of the largest scales of the turbulent field and less directly with the total turbulent intensity of the flow immediately after the step. In addition, an approximate power law scaling behavior of the floc size with the turbulent intensity was found within the decaying turbulence region downstream of the recirculation eddy.

Bridging the Rheology of Dense Granular Flows in Three Regimes SEBASTIAN CHIALVO, JIN SUN 1 , SANKARAN SUNDARESAN, Princeton University -Using the discrete element method, simulations of simple shear flow of dense assemblies of soft, frictional particles have been carried out over a range of shear rates and volume fractions in order to characterize the rheology of granular flows in three regimes. In agreement with previous results for frictionless spheres [1], the pressure in each regime is found to obey an asymptotic power law relation with shear rate. These relations are then used to construct a blended pressure model. Additionally, we constitute the shear stress ratio in terms of two dimensionless groups: the inertia number [2], which governs the rheology of hard particles, and the ratio of shear time to the particle binary collision time, which characterizes the departure from hard-sphere behavior. The pressure and shear stress ratio relations form a rheological model that, in the hard-sphere limit, can be written as a modified kinetic theory for dense granular flows .

Percolation velocity dependence on local concentration in bidisperse granular flows 1 RYAN P. JONES, HONGYI XIAO, ZHEKAI DENG, PAUL B. UMBANHOWAR, RICHARD M. LUEPTOW, Northwestern University -The percolation velocity, u p , of granular material in size or density bidisperse mixtures depends on the local concentration, particle size ratio, particle density ratio, and shear rate, γ. Discrete element method computational results were obtained for bounded heap flows with size ratios between 1 and 3 and for density ratios between 1 and 4. The results indicate that small particles percolate downward faster when surrounded by large particles than large particles percolate upward when surrounded by small particles, as was recently observed in shear-box experiments. Likewise, heavy particles percolate downward faster when surrounded by light particles than light particles percolate upward when surrounded by heavy particles. The dependence of u p / γ on local concentration results in larger percolation flux magnitudes at high concentrations of large (or light) particles compared to high concentrations of small (or heavy) particles, while local volumetric flux is conserved. The dependence of u p / γ on local concentration can be incorporated into a continuum model, but the impact on global segregation patterns is usually minimal.

Stratification of size-bidisperse granular mixtures in a quasi-2D bounded heap with periodic flow modulation 1 HONGYI XIAO, ZHEKAI DENG, PAUL UMBANHOWAR, JULIO OTTINO, RICHARD LUEPTOW, Northwestern University -Segregation of disperse granular materials in unsteady flows is ubiquitous in nature and industry, yet remains largely unexplored. In this study, unsteady flows are generated by feeding size-bidisperse granular mixtures onto a quasi-2D bounded heap using alternating feed rates, which results in stratified layers of large and small particles. The mechanism of stratification is investigated in detail using Discrete Element Method (DEM) simulations of the flow. During the transition from the slow to the fast feed rate, a segregating wedge propagates downstream and forms a large particle layer extending upstream. During the opposite transition, upstream segregated small particles relax downstream and form a small particle layer extending downstream. The transient kinematics from DEM simulations are quantified and used to inform a time-dependent continuum model that captures the interplay of advection, diffusion, and segregation in the flowing layer. The continuum model reproduces the principle characteristics of the stratification patterns observed in experiments and simulations.

The American Physical Society Continuum modeling of segregation for tridisperse granular materials in developing chute flow ZHEKAI DENG, PAUL UMBANHOWAR, RICHARD LUEPTOW, Northwestern University -Predicting segregation and mixing of size polydisperse granular material is a challenging problem and is relevant to many industrial applications. We develop and implement a continuum-based theoretical model that captures the effects of segregation, diffusion and advection on size tridisperse granular flow in developing quasi-two-dimensional chute flow. Unlike segregation models that rely on arbitrary fitting parameters, our model uses parameters based on kinematics measured using discrete element method (DEM) simulations. The model depends on both the Péclet number, Pe, which we defined as the ratio of the segregation rate to the diffusion rate, and the relative segregation strength between particle species. At large Pe, segregation dominates and chute flow consists of distinct stratified regions of small(bottom), medium(center) and large (top) particles, whereas at small Pe, diffusion dominates, which results in a well mixed flow. As relative segregation strength between any two particle species is increased, the segregation between them becomes quicker. However, as relative segregation strength between them is decreased, they remain mixed with each other. Preliminary results from DEM simulations support our theoretical model.

Percolation velocity dependence on local concentration in bidisperse granular flows 1 RYAN P. JONES, HONGYI XIAO, ZHEKAI DENG, PAUL B. UMBANHOWAR, RICHARD M. LUEPTOW, Northwestern University -The percolation velocity, u p , of granular material in size or density bidisperse mixtures depends on the local concentration, particle size ratio, particle density ratio, and shear rate, γ. Discrete element method computational results were obtained for bounded heap flows with size ratios between 1 and 3 and for density ratios between 1 and 4. The results indicate that small particles percolate downward faster when surrounded by large particles than large particles percolate upward when surrounded by small particles, as was recently observed in shear-box experiments. Likewise, heavy particles percolate downward faster when surrounded by light particles than light particles percolate upward when surrounded by heavy particles. The dependence of u p / γ on local concentration results in larger percolation flux magnitudes at high concentrations of large (or light) particles compared to high concentrations of small (or heavy) particles, while local volumetric flux is conserved. The dependence of u p / γ on local concentration can be incorporated into a continuum model, but the impact on global segregation patterns is usually minimal.

Submitted for the DFD16 Meeting of The American Physical Society Stratification of size-bidisperse granular mixtures in a quasi-2D bounded heap with periodic flow modulation1 HONGYI XIAO, ZHEKAI DENG, PAUL UMBANHOWAR, JULIO OTTINO, RICHARD LUEPTOW, Northwestern University — Segregation of disperse granular materials in unsteady flows is ubiquitous in nature and industry, yet remains largely unexplored. In this study, unsteady flows are generated by feeding size-bidisperse granular mixtures onto a quasi-2D bounded heap using alternating feed rates, which results in stratified layers of large and small particles. The mechanism of stratification is investigated in detail using Discrete Element Method (DEM) simulations of the flow. During the transition from the slow to the fast feed rate, a segregating wedge propagates downstream and forms a large particle layer extending upstream. During the opposite transition, upstream segregated small particles relax downstream and form a small par...

Stratification of size-bidisperse granular mixtures in a quasi-2D bounded heap with periodic flow modulation 1 HONGYI XIAO, ZHEKAI DENG, PAUL UMBANHOWAR, JULIO OTTINO, RICHARD LUEPTOW, Northwestern University -Segregation of disperse granular materials in unsteady flows is ubiquitous in nature and industry, yet remains largely unexplored. In this study, unsteady flows are generated by feeding size-bidisperse granular mixtures onto a quasi-2D bounded heap using alternating feed rates, which results in stratified layers of large and small particles. The mechanism of stratification is investigated in detail using Discrete Element Method (DEM) simulations of the flow. During the transition from the slow to the fast feed rate, a segregating wedge propagates downstream and forms a large particle layer extending upstream. During the opposite transition, upstream segregated small particles relax downstream and form a small particle layer extending downstream. The transient kinematics from DEM simulations are quantified and used to inform a time-dependent continuum model that captures the interplay of advection, diffusion, and segregation in the flowing layer. The continuum model reproduces the principle characteristics of the stratification patterns observed in experiments and simulations.

A diffuse-interface finite-element method has been applied to simulate the flow of twocomponent rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystalswhich features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

A diffuse-interface finite-element method has been applied to simulate the flow of twocomponent rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B mode...

This paper is mainly about the areas of non-Newtonian fluid mechanics which are not investigated or not appropriately and sufficiently investigated. In fact, this should also include emerging areas of research in the field of non-Newtonian fluid mechanics due to new scientific and technological developments and advancements. The purpose of the paper is to highlight and draw the attention to these areas so that researchers (especially the young researchers and newcomers to research such as PhD students) invest their resources and efforts in these areas instead of investing in other areas which are previously investigated and hence they are of less priority from this aspect. Apart from the obvious benefit of "leveling up" in research, the attention to these rather neglected and nonexplored areas of research can be beneficial at the scientific and individual levels since it can lead to breakthroughs and new discoveries in these areas of research by inspecting and assessing their potentials and impacts at the theoretical and practical levels and probing their beneficial applications. We will also provide a brief discussion about the possibility of introducing novel tools and methods in these areas of research (and in non-Newtonian fluid mechanics research in general) as well as highlighting some of the existing limitations of the past and current research in the field of non-Newtonian fluid mechanics (noting that this discussion should help in achieving the ultimate objective of this investigation).

The flow of viscoplastic fluids is often encountered in several industrial sectors, such as food
pumping,  polymer  formatting  processes,  and  others.  Understanding  their  behavior  and  flow  in
different  geometries  is  of  major  importance.  The  rheological  characterization  of  these  fluids is
complex due to their intrinsic characteristics, notably the slip effect, as well as the inert unyielded
zones that form at the corners of the contraction when flowing through a rectangular pipe with an
abrupt contraction. The main objective of this study is to analyze, firstly, the rheological behavior
of Carbopol solutions using laser Doppler velocimetry (LDV) as a non-intrusive, in-situ method.
By  measuring  velocity  profiles  and  associated  pressure  drops,  the  analysis  of  flow  curves  will
enable us to characterize the rheology of the fluids studied. Two approaches are used. The first
involves  fitting  the  analytical  profile  to  the  experimental  profile  obtained  by  laser  Doppler
velocimetry (LDV), while the second involves converting local velocity profiles into local shear
rate profiles, and pressure drops into local shear stress profiles.
The flow of this fluid in the rectangular channel was analyzed using LDV, taking into account
the associated head losses. Velocity profiles revealed the presence of a moving zone at constant
velocity, called 'plug', in the center of the channel, as well as the formation of inert dead zones at
the  corners  of  the  contraction.  The  impact  of  contraction  and  inertia  on  flow  structure  was
examined first, highlighting the influence of both factors. The interface between the static dead
zone and the fluid zone was identified and characterized for various flow rates. Velocity profiles
revealed the  existence of a line known as the 'slip line', where all profiles intersect  at a single
point. The position of this line is found to be independent of flow  rate, while its velocity varies
with flow rate, for which a correlation has been proposed. This  slip  line  coincides  with  the
contraction height. Local shear rate profiles are provided for each flow rate. These profiles show
a non-monotonic evolution: they increase from zero at the solid-liquid interface to reach a peak,
then decrease again to zero in the 'plug' region at the center of the pipe. This variation suggests
the presence of different layers between the solid-liquid interface and the slip line. The position
of  the  maximum  shear  rate  line  remains  constant  irrespective  of  flow  rate,  suggesting  that  the
The width of the zone between the slip line and this line remains constant for all flow rates. In
addition,  the  study  includes  an  analysis  of  head  losses  upstream, downstream, and  at  the
contraction, for which correlations have been proposed concerning the friction factor  f  and the
Euler number Eu as a function of the generalized Reynolds number Regen.

RIO DE JANEIRO,RJ-BRASIL JANEIRO DE 1977 ,"'v'1 "Nas planfcies da hesitação branqueiam os ossos de incontestáveis milh~es, os quais, na alvorad• da vitória, sentaram-se para descansare descansando morreram " i i "Dedico este trabalho a ORLINDA e LUIZ , meus pais, como prova de amor, respeito e admiração li que tenho por eles. i i i AGRADECIMENTOS -Ao Prof. Luis Bevilacqua, orientador e amigo de todas as horas que, com segurança e sabedoria, pode mostrar-me o caminho a seguir. -A Escola de Engenharia Mauá, pelos seus incentivos a pesquisa e ao aprimoramento do ensino a mim demonstrados. (*) -Aos Profs. Liu Hsu, Raúl Feijóo e Cesar Camacho, e aos colegas Ablmael Dourado e Augusto Galeão, pelas discussões que me proporcionaram, fazendo com que eu pudesse melhorar este trabalho. -Aos meus irmãos: Luiz, Maria lzabel, Margarida Maria e Maria Emília, pela compreensão e apoio. -Aos funcionários da Biblioteca Central e do Núcleo de Computação Eletrônica, pelo despreendimento e solicitude. -Ao Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), pelo apoio financeiro. -A todos aqueles que direta ou indiretamente, associados à boa vontade e espírito de cooperaçao, fizeram com que eu, assim sendo, pudesse vencer mais uma etapa proposta em minha vida. (*) IMPA -Instituto de Matemática Pura e Aplicada. V i RtSUMt La stabil ité lateral e de poutres soumises a une "protension" externe est étudiée par l'application du "Critêre Dynamique de Stabilité", à l'aide de la Méthode de Rayleigh -Ritz. Uneétude de bifurcation est entreprise, en tenant compte des termes non-linéaires pour un des cas considérés. En outre, on fait une discussion de la stabilité basée sur les paramêtres de 1 'equation caracteristique obtenue du problême des valeurs propses . i V SINOPSE I:' . investigada a estabilidade lateral de hastes submetidas a uma pretensão externa aplicando-se o "Critério Di nâmico de Estabilidade", via Método de Rayleigh-Ritz. Faz-se um estudo de bifurcação tendo-se em conta os termos não-! ineares para um dos casos considerados, bem como a discussão da estabilidade por meio dos parâmetros da equ~ ção caracterTstica obtida do problema de autovalores.

E investigada a estabilidade lateral de hastes submetidas a uma protensao externa aplicando-se o "Criterio Dinâmico de Estabilidade", via Metodo de Rayleigh-Ritz. Faz-se um estudo de bifurcacao tendo-se em conta os termos nao lineares para um dos casos considerados, bem como a discussao da estabilidade por meio dos parâmetros da equacao caracteristica obtida do problema de autovalores.

Flow properties of complex fluids such as colloidal suspensions, polymer solutions, fiber suspensions and blood have a vital function in many technological applications and biological systems. Yet, the basic knowledge on their properties is inadequate for many practical purposes. One important reason for this has been the lack of effective experimental methods that would allow detailed study of the flow behavior of especially opaque multi-phase fluids. Optical Coherence Tomography (OCT) is an emerging technique capable of simultaneous measurement of the internal structure and motion of most opaque materials, with resolution in the micrometer scale and measurement frequency up to 100 kHz. This mini-review will examine the recent results on the use of Doppler-OCT in the context of flows and rheological properties of complex fluids outside biomedical field.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.